diff --git a/research/fixed-caller-query-and-host-limits/LICENSE b/research/fixed-caller-query-and-host-limits/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/research/fixed-caller-query-and-host-limits/PROVENANCE.json b/research/fixed-caller-query-and-host-limits/PROVENANCE.json
new file mode 100644
index 0000000000..f04268077a
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/PROVENANCE.json
@@ -0,0 +1,81 @@
+{
+  "upstream_files": [
+    {
+      "pr": 7000,
+      "head": "93effe2a135bf57b9e484cb630d8dd057159aec9",
+      "path": "research/shared-wire-split-composition/data/caller.json",
+      "vendored": "PR7000-CALLER.json",
+      "sha256": "3828d53e80ea97e8b866320f081af20b6b93bfebd58b95b56b85a7afe151af5e"
+    },
+    {
+      "pr": 7001,
+      "head": "d777f3a0aa2878bea0478918923dabcf86b9878b",
+      "path": "research/paired-query-only-bit/EFREE-RESULT.json",
+      "vendored": "PR7001-RESULT.json",
+      "sha256": "a46b6c6040f75184cab5467656811ad988c216e3bc8e44d595a5015b6e49620b"
+    },
+    {
+      "pr": 7002,
+      "head": "ed1a0a83dfe5d28db9a971bcfc1403bcdc03a49b",
+      "path": "research/connected-l18-root-caller/COALESCING-WINDOW.json",
+      "vendored": "connected7002/COALESCING-WINDOW.json",
+      "sha256": "86eb8ec70f899637089a741548659f433854fa3a8b2532937eb0679d89e8114f"
+    },
+    {
+      "pr": 7002,
+      "head": "ed1a0a83dfe5d28db9a971bcfc1403bcdc03a49b",
+      "path": "research/connected-l18-root-caller/COST.json",
+      "vendored": "connected7002/COST.json",
+      "sha256": "4ccdea7cdbc7d5553a21ddd3b10a1973ce9ae8e5e7724513faee81fa4922322a"
+    },
+    {
+      "pr": 7002,
+      "head": "ed1a0a83dfe5d28db9a971bcfc1403bcdc03a49b",
+      "path": "research/connected-l18-root-caller/inputs/base_invoice.json",
+      "vendored": "connected7002/inputs/base_invoice.json",
+      "sha256": "87a41b13bdd9248d538805f76a970f51335567845dfc0070698b6979a08b70d6"
+    },
+    {
+      "pr": 7002,
+      "head": "ed1a0a83dfe5d28db9a971bcfc1403bcdc03a49b",
+      "path": "research/connected-l18-root-caller/root_L18.json",
+      "vendored": "connected7002/root_L18.json",
+      "sha256": "be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34"
+    },
+    {
+      "pr": 7002,
+      "head": "ed1a0a83dfe5d28db9a971bcfc1403bcdc03a49b",
+      "path": "research/connected-l18-root-caller/idle_coalescing.py",
+      "vendored": "connected7002/idle_coalescing.py",
+      "sha256": "7f4b45b1d197b45284d73141b21af518fe39fd58fecfaeec29dd1feda13d2fd0"
+    },
+    {
+      "pr": 7004,
+      "head": "2ee11a4460f23abf06d16b12f18c8ef9aca889f1",
+      "path": "research/peer-move-retiming/RESULT.json",
+      "vendored": "PR7004-RESULT.json",
+      "sha256": "555310519298a04dc00dc72b34073e4ad868620e7abb7a009d520ced27a2c4ba"
+    },
+    {
+      "pr": 6824,
+      "head": "2a7ca44fbda3abaa4df355b183ed7d7478eef7c1",
+      "path": "research/p104-shared-carrier-input-lift/native.py",
+      "vendored": "supplier6824/native.py",
+      "sha256": "9994a38b2ddf3d6208be92728e1cc6b80aac5b3773aa79fac147ccf60c1db556"
+    },
+    {
+      "pr": 6980,
+      "head": "617903497387a98f7ca929ad0b6928dd32abffec",
+      "path": "research/p104-query-only-interval/reference/jclib_6936.py",
+      "vendored": "jclib_6936.py",
+      "sha256": "bdbd89da0125a41514ea10330bccd25de5dd626ac8b2d671c88dc2e4b8fb93c4"
+    }
+  ],
+  "generated_word": {
+    "vendored": "supplier6824/F6824.json.gz",
+    "pr": 6824,
+    "head": "2a7ca44fbda3abaa4df355b183ed7d7478eef7c1",
+    "sha256": "8016ff736f25dc6d1a14f47da271c9e0ebd70a5e158e44d3ac51c00bb949816d",
+    "scope": "Normalized generated word. Replay checks all endpoints and the paid and helper histograms against the retained #7002 invoice. The hook uses the generated word as its input."
+  }
+}
diff --git a/research/fixed-caller-query-and-host-limits/README.md b/research/fixed-caller-query-and-host-limits/README.md
new file mode 100644
index 0000000000..6b9a821891
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/README.md
@@ -0,0 +1,29 @@
+# Fixed caller query and native HOST repair limits
+
+This follow-up to [PR #7098](https://github.com/CrocSwap/integer-mult-bounds/pull/7098) records three bounded results from the search for κ = .005 and ultimately .01. The results are about the specified normalized operators and tariffs. There is no new exponent claim.
+
+## Results
+
+- **Fixed central interval of #7000.** Between the first and last central QUERY in each branch there is no native J. The required operator difference at q and −q has rank four in each branch under the exact finite-field specialization. Any sign-even step contributes zero to the telescoping product difference, and each permitted QUERY contributes rank at most one. Four QUERYs per branch are therefore necessary to preserve those interval operators over the dyadic formal ring. All eight literal omissions change the operator. A separate prefix-transport screen found zero proportional source or range directions among 300 tested query/query and query/native pairs. That screen addresses the directions at their original prefixes.
+- **Whole #7000 caller and the #7004/#7001 tariffs.** At unit stage weights the sign-relative map is −I on 38 roles in each branch. It requires at least 39 rank-one transvections. Eighteen native J calls contribute at most 36, leaving a global floor of three QUERYs per branch under the retained factorization. Even a hypothetical saving of one QUERY in each branch leaves the complex signed moment at approximately −462.571 at .005. The unchanged BIT moment is approximately −444.063. At .004 those values are −48.708 and −57.182. The two deletions are granted for pricing only.
+- **Fixed-chronology #6824 HOST repair.** For the specified same-port rank-one repair, no insertion of up to two distinct-register coframed ADDs achieves the normalized endpoint on any of the 104 ports. Replay first checks the original endpoint and the paid and helper histograms. The first-order census excludes all direct X←Y sensitivity. The two-add expansion then forces the mixed term to supply this entry. If both intervening factors survive, the change has rank two. Exact cancellation and scratch reachability checks cover the remaining degenerate cases. This uses the fixed scalar chronology and endpoint.
+- **Connected #7002 idle schedule.** The revised projector allocation reduces 181 idle jobs to 75 per port in the normalized 18-stage schedule, versus 76 in #7098. Exact commutation and both signed role-level controls are replayed. The additional saving across 104 ports is about 5.697 at .005. The composed F+H1 raw complex moment still encloses −814.90413 at .005 and −502.85167 at .004. A strictly positive raw .005 moment would require at least 815 further rank-one cost equivalents at fixed targets. Physical packing and ordinary work, BIT, precision and the outer reduction remain separate obligations.
+
+## Reproduction
+
+```sh
+python3 -B scripts/research_package.py --package research/fixed-caller-query-and-host-limits
+```
+
+The three registered checks hash the inputs and replay the operator bounds, projector allocation and rational price checks, and the fixed-chronology census. They compare regenerated JSON with the archived receipts. The normalized #6824 word is a pinned generated input. The replay checks its endpoint and inventory directly. It does not regenerate that word from the upstream construction chain. These checks do not reproduce the complete physical suppliers or the conditional multiplication theorem.
+
+For the 39-factor bound, rank of −I minus I first forces at least 38 factors. With exactly 38, their update directions must form a basis. In this basis only the first-applied transvection updates the first coordinate, and its square-zero condition keeps that diagonal entry at +1. All subsequent transvections leave that coordinate unchanged, contradicting −I.
+
+## Open next questions
+
+- Can a changed native macro supply more independent sign-sensitive directions? Start by certifying the full arbitrary-input operator of one replacement macro in both signs and inventory every paid step. Retaining the current two-shear macro leaves the global query floor.
+- Can a changed entrance implement the HOST boundary within budget? Start with a new chronological frame path and recheck the full normalized word before lowering it. Two added coframed ADDs on the current word are excluded, and the concrete idle savings leave a substantial deficit.
+
+## Credit
+
+Rohan Arun with substantial OpenAI Codex assistance. [#7000](https://github.com/CrocSwap/integer-mult-bounds/pull/7000), [#7001](https://github.com/CrocSwap/integer-mult-bounds/pull/7001), [#7002](https://github.com/CrocSwap/integer-mult-bounds/pull/7002) and [#6980](https://github.com/CrocSwap/integer-mult-bounds/pull/6980) are by Jerry Chen / CubeJerry. [#6824](https://github.com/CrocSwap/integer-mult-bounds/pull/6824) is by DreamingOfClouds and retains the native verifier and constructive lineage credited upstream. [#7004](https://github.com/CrocSwap/integer-mult-bounds/pull/7004) is by ToikY. See the vendored notices and exact inputs in `PROVENANCE.json`. Apache-2.0.
diff --git a/research/fixed-caller-query-and-host-limits/SHA256.json b/research/fixed-caller-query-and-host-limits/SHA256.json
new file mode 100644
index 0000000000..2676f8b5e9
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/SHA256.json
@@ -0,0 +1,42 @@
+{
+  "PROVENANCE.json": "0d8acbb6a6f558931e2aa234aa10eab1f7e9913479502034668cb93b5f2cd186",
+  "expected/PR6824-MIXED-FIRST-ORDER-HOST-CONTACTS.json": "c164c1f833be0b4cffab3fb93f7d0dd6becb5912f584f7891a5ee0313eda8ded",
+  "expected/PR6824-TWO-ADD-HOST-OBSTRUCTION.json": "811e827474ea20caa0c1d024e8b5aadf23b9401abcdffd459a28adf41add1092",
+  "expected/PR6824-TWO-CONTACT-DARK-REACHABILITY.json": "e7d7c508e07e8031cdb5198f6e67250b97350944d793c1ef0acd066a149d53b7",
+  "expected/PR6824-TWO-EDIT-MIXED-CANCELLATION.json": "f135748ff2c2ee325bf7503df1f200426f73eb2752efde6cb90cd66f0c494a72",
+  "expected/PR7000-CENTRAL-QUERY-SIGN-RANK.json": "77021d6d9aa3e0a5ff27735b8ed809ab752b4796f2f1fb71dc869d76205b4a61",
+  "expected/PR7000-QUERY-COUNT-SIGN-LOWER-BOUND.json": "6e3639e7510ceda5eafa75da30b5ea18f0a8f77b4b44694e1ea80036b44126cf",
+  "expected/PR7000-QUERY-HOST-TRANSPORT-CONTACTS.json": "637906ede30ae82082282fec9d5358c72ecdc102c2a4991efdd0c954c40b28e1",
+  "expected/PR7002-75-JOB-COMPOSITION-PRICE.json": "439a6d1cf685cd7f0f56724f9f9aeddf59f83791b94d9e4efc21b913eda91598",
+  "expected/PR7002-CHRONOLOGICAL-IDLE-GROUPS.json": "7b20506428a97139c0d5e5cb0e79c8e0d764f4d5033c487e9bd0394c12b371be",
+  "expected/PR7002-IDLE-PROJECTOR-ORDER-SEARCH.json": "e0a40d80c7e9a52b3d3156b6128c8b44d0d8326967a10f0ae00527d0f121e268",
+  "expected/PR7002-NONCOORDINATE-IDLE-WORD.json": "d136d12485d348112b7c7d690b4df7e8f6e50596b6f35c4662ab666ce5fedf8f",
+  "expected/PR7004-QUERY-FAMILY-TARGET-PRICE.json": "3e405ce18bb219f81f77077087fd200fb06961e3e99d1a2b91219b6be2efb994",
+  "replay/PR7000-CALLER.json": "3828d53e80ea97e8b866320f081af20b6b93bfebd58b95b56b85a7afe151af5e",
+  "replay/PR7001-RESULT.json": "a46b6c6040f75184cab5467656811ad988c216e3bc8e44d595a5015b6e49620b",
+  "replay/PR7004-RESULT.json": "555310519298a04dc00dc72b34073e4ad868620e7abb7a009d520ced27a2c4ba",
+  "replay/certify_6824_two_add_obstruction.py": "0810f9c1f7f014772b227f54ee997073e49b3e5e1e012a2f574ed3ac367ab4eb",
+  "replay/certify_7000_sign_query_floor.py": "865ffb698489df50ba377b0f6f3302c7ccffb6f27dd454ace857e84fb89c917e",
+  "replay/connected7002/COALESCING-WINDOW.json": "86eb8ec70f899637089a741548659f433854fa3a8b2532937eb0679d89e8114f",
+  "replay/connected7002/COST.json": "4ccdea7cdbc7d5553a21ddd3b10a1973ce9ae8e5e7724513faee81fa4922322a",
+  "replay/connected7002/idle_coalescing.py": "7f4b45b1d197b45284d73141b21af518fe39fd58fecfaeec29dd1feda13d2fd0",
+  "replay/connected7002/inputs/base_invoice.json": "87a41b13bdd9248d538805f76a970f51335567845dfc0070698b6979a08b70d6",
+  "replay/connected7002/root_L18.json": "be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34",
+  "replay/construct_7002_chronological_idle_groups.py": "08748b3e3df9aa1d1cf30a33e3b185b5af3ce5b4fda17c2cc425194e165b7eec",
+  "replay/construct_7002_noncoordinate_idle.py": "54c29d107f8784591727b203d7072884d576d57c30a1ed179f7c84af13fc4372",
+  "replay/jclib_6936.py": "bdbd89da0125a41514ea10330bccd25de5dd626ac8b2d671c88dc2e4b8fb93c4",
+  "replay/package/verify.py": "5cd51c2489ab862162a6f649715fef6567c25f17735c018bc4b5e59fd2e601f5",
+  "replay/price_7002_75_job_composition.py": "ac58b6f8db3335db07879fc28585b509e2945c09dc170e99a306c4de5de24cd6",
+  "replay/price_7004_query_families.py": "1adcbe429f9be2cbf7ea0c006cc1973ade10ebcb9d030ac8da0f942bf2e74686",
+  "replay/reprice_7002_host.py": "68fff36e060ca22d0e6d90aa3284fcaf37d203a25b190cf20429150e43bcfbf1",
+  "replay/screen_6824_dark_two_contact.py": "c56a775ac7c916fa36632e9a1174eb079ef529d00d0f0f9ea8fa72435e032556",
+  "replay/screen_6824_mixed_first_order.py": "faaafe302c03a16286a9176676babe26f95651ef9665d32cf95d0bbd0e7d5f98",
+  "replay/screen_6824_two_edit_mixed.py": "f8e358d1dbc96e111904cfab15a3004ec0cd094ee8317b2657dcacba591b3cb5",
+  "replay/screen_7000_central_query_rank.py": "2c15bdd2e209343908ce739a0abc0b3298ab355cd7d408f19c14c3fd480aae1d",
+  "replay/screen_7000_query_host_contacts.py": "471f41db34c38506a7636d5d9ca77559e4e79e214f64fbc0ca297e2908b2f195",
+  "replay/screen_7000_transported_idle_projectors.py": "9e18ed5d8e0d4b52f3c4b23b5406cf9e897095f1d88900838ac30a963b3054dc",
+  "replay/search_6824_host_entrance_contacts.py": "d36725c17610a8b939de58b947b4da882731eff4a64cf1f4ac2feef1548c555a",
+  "replay/search_7002_idle_projector_order.py": "4240199b9b42765e116eaff6b65c804c886ee5c87501eff3f1c8d5827489ca2e",
+  "replay/supplier6824/F6824.json.gz": "8016ff736f25dc6d1a14f47da271c9e0ebd70a5e158e44d3ac51c00bb949816d",
+  "replay/supplier6824/native.py": "9994a38b2ddf3d6208be92728e1cc6b80aac5b3773aa79fac147ccf60c1db556"
+}
diff --git a/research/fixed-caller-query-and-host-limits/SOURCES.json b/research/fixed-caller-query-and-host-limits/SOURCES.json
new file mode 100644
index 0000000000..68fe2b9c1b
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/SOURCES.json
@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
+  "base_commit": "f16923d466a6aba912299882e0545564d2ba7bb2",
+  "files": [
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
+      "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa"
+    }
+  ]
+}
diff --git a/research/fixed-caller-query-and-host-limits/TASK.json b/research/fixed-caller-query-and-host-limits/TASK.json
new file mode 100644
index 0000000000..495b63fcfb
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/TASK.json
@@ -0,0 +1,89 @@
+{
+  "schema_version": 1,
+  "task_id": "joint-query-controller",
+  "priority_revision": 8,
+  "base_commit": "f16923d466a6aba912299882e0545564d2ba7bb2",
+  "original_card": {
+    "id": "joint-query-controller",
+    "question": "Can a changed query demand or caller remove real work while satisfying native chronology and restoration?",
+    "starting_points": [
+      "docs/research/current-priorities.md",
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md"
+    ],
+    "methods": [
+      "Construct and independently check one source-bound instance of the stated first experiment.",
+      "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change."
+    ],
+    "acceptance_gate": "A source-bound arbitrary-input identity and legal producer/consumer boundary with the complete paid and productive target invoice, including restoration, ownership, native alignment and extra charges. Price under the actual current model; historical ceiling.py assumptions must be established before use. A favorable optimistic relaxation keeps a route open but is not a completed supplier. A scoped local result remains useful; expansion requires the family-level budget gate.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_selected_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.",
+      "scope": "Source-bound orientation only, not a supplier replay or theorem proof."
+    },
+    "first_experiment": "Choose an exact caller and a new demand/interface hypothesis. Read the scoped #5617/#5631/#5649/#5747 and #5720/#5745 objections before rebuilding an excluded schedule. Compare the complete matched source/consumer protocols including all retained helper outputs. For an active-mode injection, first check #5745: its canonical delivery claim repays the eight removed centre jobs. Audit that exact claim or change its channel/feedback hypothesis; do not repeat the same free-injection search. Stop if the full favorable budget fails or the required restored output is unobservable.",
+    "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.",
+    "allowed_variations": [
+      "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes."
+    ],
+    "scope_change_triggers": [
+      "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.",
+      "Treating an archived proposal or local numerical pass as complete supplier admission."
+    ],
+    "overlap_terms": [
+      "query demand",
+      "active mode",
+      "5720",
+      "5745",
+      "5747",
+      "caller"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.",
+        "evidence": "research/qq16-caller-install/README.md",
+        "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.",
+        "status": "author-checked",
+        "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.",
+        "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md",
+        "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.",
+        "status": "reviewed",
+        "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137",
+        "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5"
+      }
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Exact query bounds on the fixed #7000 caller, a two-ADD #6824 entrance obstruction, and the normalized #7002 idle schedule and tariff.",
+  "scope_change_reason": "Use matched source operators and tariffs to identify which small fixed-interface changes cannot close the target budget.",
+  "bottleneck_link": "The replacement needs new sign-sensitive capacity and enough productive rank surplus to pay its complete bill.",
+  "stop_rule": "Close only the explicitly stated operator families and budgets.",
+  "outcome": "negative-result",
+  "evidence": "README.md, verify.py, expected/, PROVENANCE.json",
+  "author": "Rohan Arun",
+  "ai_assistance": "Substantial OpenAI Codex assistance.",
+  "open_questions": [
+    {
+      "question": "Can a changed native macro supply more independent sign-sensitive directions?",
+      "why_it_matters": "The fixed two-shear macro leaves a query floor.",
+      "first_step": "Replay one replacement macro on every input in both signs and recount paid jobs.",
+      "blocked_by": "The tested central interval already requires four queries."
+    },
+    {
+      "question": "Can a changed entrance implement HOST within budget?",
+      "why_it_matters": "Actual idle grouping still leaves an 815-equivalent raw complex deficit at .005.",
+      "first_step": "Synthesize a new chronological frame path and replay the full normalized endpoint.",
+      "blocked_by": "The existing word admits no two-ADD coframe repair."
+    }
+  ]
+}
diff --git a/research/fixed-caller-query-and-host-limits/VERIFY.json b/research/fixed-caller-query-and-host-limits/VERIFY.json
new file mode 100644
index 0000000000..2115d11ff9
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/VERIFY.json
@@ -0,0 +1,39 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py",
+        "caller"
+      ],
+      "timeout_seconds": 240,
+      "checks": "Exact query sign ranks, transport contacts, and signed tariff bounds."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py",
+        "idle"
+      ],
+      "timeout_seconds": 240,
+      "checks": "Normalized projector allocation and exact raw moment enclosure."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py",
+        "host"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Exact first-order and two-edit scans on the pinned normalized word."
+    }
+  ]
+}
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR6824-MIXED-FIRST-ORDER-HOST-CONTACTS.json b/research/fixed-caller-query-and-host-limits/expected/PR6824-MIXED-FIRST-ORDER-HOST-CONTACTS.json
new file mode 100644
index 0000000000..c939660aab
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR6824-MIXED-FIRST-ORDER-HOST-CONTACTS.json
@@ -0,0 +1 @@
+{"ports": {"0": {"contacts_by_support": [], "compact_directions": []}, "1": {"contacts_by_support": [], "compact_directions": []}, "2": {"contacts_by_support": [], "compact_directions": []}, "4": {"contacts_by_support": [], "compact_directions": []}, "5": {"contacts_by_support": [], "compact_directions": []}, "6": {"contacts_by_support": [], "compact_directions": []}, "7": {"contacts_by_support": [], "compact_directions": []}, "8": {"contacts_by_support": [], "compact_directions": []}, "9": {"contacts_by_support": [], "compact_directions": []}, "10": {"contacts_by_support": [], "compact_directions": []}, "11": {"contacts_by_support": [], "compact_directions": []}, "12": {"contacts_by_support": [], "compact_directions": []}, "13": {"contacts_by_support": [], "compact_directions": []}, "15": {"contacts_by_support": [], "compact_directions": []}, "16": {"contacts_by_support": [], "compact_directions": []}, "17": {"contacts_by_support": [], "compact_directions": []}, "18": {"contacts_by_support": [], "compact_directions": []}, "19": {"contacts_by_support": [], "compact_directions": []}, "20": {"contacts_by_support": [], "compact_directions": []}, "22": {"contacts_by_support": [], "compact_directions": []}, "23": {"contacts_by_support": [], "compact_directions": []}, "24": {"contacts_by_support": [], "compact_directions": []}, "25": {"contacts_by_support": [], "compact_directions": []}, "26": {"contacts_by_support": [], "compact_directions": []}, "27": {"contacts_by_support": [], "compact_directions": []}, "28": {"contacts_by_support": [], "compact_directions": []}, "29": {"contacts_by_support": [], "compact_directions": []}, "30": {"contacts_by_support": [], "compact_directions": []}, "31": {"contacts_by_support": [], "compact_directions": []}, "32": {"contacts_by_support": [], "compact_directions": []}, "33": {"contacts_by_support": [], "compact_directions": []}, "35": {"contacts_by_support": [], "compact_directions": []}, "36": {"contacts_by_support": [], "compact_directions": []}, "37": {"contacts_by_support": [], "compact_directions": []}, "38": {"contacts_by_support": [], "compact_directions": []}, "40": {"contacts_by_support": [], "compact_directions": []}, "41": {"contacts_by_support": [], "compact_directions": []}, "42": {"contacts_by_support": [], "compact_directions": []}, "43": {"contacts_by_support": [], "compact_directions": []}, "44": {"contacts_by_support": [], "compact_directions": []}, "45": {"contacts_by_support": [], "compact_directions": []}, "46": {"contacts_by_support": [], "compact_directions": []}, "47": {"contacts_by_support": [], "compact_directions": []}, "48": {"contacts_by_support": [], "compact_directions": []}, "49": {"contacts_by_support": [], "compact_directions": []}, "50": {"contacts_by_support": [], "compact_directions": []}, "51": {"contacts_by_support": [], "compact_directions": []}, "52": {"contacts_by_support": [], "compact_directions": []}, "53": {"contacts_by_support": [], "compact_directions": []}, "54": {"contacts_by_support": [], "compact_directions": []}, "55": {"contacts_by_support": [], "compact_directions": []}, "56": {"contacts_by_support": [], "compact_directions": []}, "57": {"contacts_by_support": [], "compact_directions": []}, "58": {"contacts_by_support": [], "compact_directions": []}, "59": {"contacts_by_support": [], "compact_directions": []}, "60": {"contacts_by_support": [], "compact_directions": []}, "62": {"contacts_by_support": [], "compact_directions": []}, "63": {"contacts_by_support": [], "compact_directions": []}, "64": {"contacts_by_support": [], "compact_directions": []}, "65": {"contacts_by_support": [], "compact_directions": []}, "66": {"contacts_by_support": [], "compact_directions": []}, "67": {"contacts_by_support": [], "compact_directions": []}, "68": {"contacts_by_support": [], "compact_directions": []}, "69": {"contacts_by_support": [], "compact_directions": []}, "70": {"contacts_by_support": [], "compact_directions": []}, "71": {"contacts_by_support": [], "compact_directions": []}, "72": {"contacts_by_support": [], "compact_directions": []}, "73": {"contacts_by_support": [], "compact_directions": []}, "74": {"contacts_by_support": [], "compact_directions": []}, "75": {"contacts_by_support": [], "compact_directions": []}, "77": {"contacts_by_support": [], "compact_directions": []}, "78": {"contacts_by_support": [], "compact_directions": []}, "79": {"contacts_by_support": [], "compact_directions": []}, "80": {"contacts_by_support": [], "compact_directions": []}, "81": {"contacts_by_support": [], "compact_directions": []}, "82": {"contacts_by_support": [], "compact_directions": []}, "83": {"contacts_by_support": [], "compact_directions": []}, "84": {"contacts_by_support": [], "compact_directions": []}, "85": {"contacts_by_support": [], "compact_directions": []}, "86": {"contacts_by_support": [], "compact_directions": []}, "87": {"contacts_by_support": [], "compact_directions": []}, "88": {"contacts_by_support": [], "compact_directions": []}, "89": {"contacts_by_support": [], "compact_directions": []}, "90": {"contacts_by_support": [], "compact_directions": []}, "91": {"contacts_by_support": [], "compact_directions": []}, "92": {"contacts_by_support": [], "compact_directions": []}, "94": {"contacts_by_support": [], "compact_directions": []}, "95": {"contacts_by_support": [], "compact_directions": []}, "96": {"contacts_by_support": [], "compact_directions": []}, "97": {"contacts_by_support": [], "compact_directions": []}, "98": {"contacts_by_support": [], "compact_directions": []}, "99": {"contacts_by_support": [], "compact_directions": []}, "100": {"contacts_by_support": [], "compact_directions": []}, "101": {"contacts_by_support": [], "compact_directions": []}, "102": {"contacts_by_support": [], "compact_directions": []}, "103": {"contacts_by_support": [], "compact_directions": []}, "104": {"contacts_by_support": [], "compact_directions": []}, "105": {"contacts_by_support": [], "compact_directions": []}, "106": {"contacts_by_support": [], "compact_directions": []}, "107": {"contacts_by_support": [], "compact_directions": []}, "108": {"contacts_by_support": [], "compact_directions": []}, "109": {"contacts_by_support": [], "compact_directions": []}, "110": {"contacts_by_support": [], "compact_directions": []}, "111": {"contacts_by_support": [], "compact_directions": []}}, "scope": "Exact first-order contacts on fixed normalized chronology. Large support contacts counted only. Extra tensor entries and higher-order interactions still have to cancel."}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR6824-TWO-ADD-HOST-OBSTRUCTION.json b/research/fixed-caller-query-and-host-limits/expected/PR6824-TWO-ADD-HOST-OBSTRUCTION.json
new file mode 100644
index 0000000000..72959a1407
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR6824-TWO-ADD-HOST-OBSTRUCTION.json
@@ -0,0 +1,18 @@
+{
+  "status": "PASS_FIXED_CHRONOLOGY_TWO_ADD_HOST_OBSTRUCTION",
+  "ports": 104,
+  "evidence": {
+    "first_order": "PR6824-MIXED-FIRST-ORDER-HOST-CONTACTS.json",
+    "one_zero": "PR6824-TWO-EDIT-MIXED-CANCELLATION.json",
+    "both_zero": "PR6824-TWO-CONTACT-DARK-REACHABILITY.json"
+  },
+  "proof": [
+    "Two additions at ordered cuts give endpoint delta c1 B1 A1 + c2 B2 A2 + c1 c2 h B2 A1, where A are baseline donor rows, B are baseline suffix columns and h is the interposed scalar transfer.",
+    "To have nonzero x,y coefficient, the mixed term must supply it because no baseline single ADD has nonzero x,y derivative. Hence B2[x] and A1[y] are nonzero, B1[x] and A2[y] are zero, and the interposed coefficient is nonzero.",
+    "If B1 and A2 are both nonzero, the two suffix columns are independent (their x coordinates differ by zero/nonzero), and the rows A1 and A2 + c1 h A1 are independent (A2 has no y). The endpoint delta has rank two, contradicting the rank-one repair.",
+    "If only B1 is zero, B2 must be an isolated X+Y suffix and the non-Y part of A1 must cancel the nonzero A2. The chronological mixed-cancellation census excludes every such signature.",
+    "If only A2 is zero, A1 must be pure Y and the nonzero B1 must match the residual after normalizing B2 at X. The chronological mixed-cancellation census excludes every such signature.",
+    "If B1 and A2 are both zero, the pure-Y first donor and isolated X+Y second sink must be connected via the dark scratch path. The generous support transfer scan excludes it."
+  ],
+  "scope": "Exact normalized scalar circuit with the fixed chronological MOVE/COPY/INIT/CLEAR schedule. The required repair is one specified same-port rank-one F-to-HOST entrance transvection. At most two newly inserted distinct-register coframe ADDs. Changing MOVE timing or chart shape, scalings, cross-port block outputs, or adding three or more contacts is outside scope."
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR6824-TWO-CONTACT-DARK-REACHABILITY.json b/research/fixed-caller-query-and-host-limits/expected/PR6824-TWO-CONTACT-DARK-REACHABILITY.json
new file mode 100644
index 0000000000..4fac77ddea
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR6824-TWO-CONTACT-DARK-REACHABILITY.json
@@ -0,0 +1,7 @@
+{
+  "reachable_ports": {},
+  "dark_entry_registers": 1,
+  "potential_dark_exit_ports": 0,
+  "cuts": 18623,
+  "scope": "Necessary path condition. First edit reads pure Y into a baseline suffix-zero register; second edit reads a baseline-zero source into an isolated X+Y suffix. Existing linear dependencies are granted even if their coefficients cancel. Baseline COPY is modeled as transfer with zero destination."
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR6824-TWO-EDIT-MIXED-CANCELLATION.json b/research/fixed-caller-query-and-host-limits/expected/PR6824-TWO-EDIT-MIXED-CANCELLATION.json
new file mode 100644
index 0000000000..e903d50b67
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR6824-TWO-EDIT-MIXED-CANCELLATION.json
@@ -0,0 +1,113 @@
+{
+  "prefix_signature_counts": {
+    "82": 72,
+    "0": 501,
+    "1": 136,
+    "2": 154,
+    "4": 130,
+    "5": 112,
+    "6": 131,
+    "7": 302,
+    "8": 98,
+    "9": 174,
+    "10": 207,
+    "11": 69,
+    "12": 242,
+    "13": 391,
+    "15": 141,
+    "16": 326,
+    "17": 65,
+    "18": 123,
+    "19": 66,
+    "20": 183,
+    "22": 111,
+    "23": 68,
+    "24": 236,
+    "25": 151,
+    "26": 95,
+    "27": 487,
+    "28": 202,
+    "29": 110,
+    "30": 126,
+    "31": 239,
+    "32": 70,
+    "33": 241,
+    "35": 17,
+    "36": 355,
+    "37": 116,
+    "38": 68,
+    "40": 67,
+    "41": 12,
+    "42": 723,
+    "43": 71,
+    "44": 332,
+    "45": 17,
+    "46": 179,
+    "47": 149,
+    "48": 72,
+    "49": 241,
+    "50": 71,
+    "51": 374,
+    "52": 25,
+    "53": 136,
+    "54": 57,
+    "55": 276,
+    "56": 117,
+    "57": 296,
+    "58": 204,
+    "59": 112,
+    "60": 125,
+    "62": 185,
+    "63": 65,
+    "64": 63,
+    "65": 110,
+    "66": 104,
+    "67": 95,
+    "68": 132,
+    "69": 114,
+    "70": 277,
+    "71": 65,
+    "72": 125,
+    "73": 61,
+    "74": 202,
+    "75": 69,
+    "77": 68,
+    "78": 69,
+    "79": 313,
+    "80": 164,
+    "81": 103,
+    "83": 204,
+    "84": 63,
+    "85": 119,
+    "86": 95,
+    "87": 42,
+    "88": 163,
+    "89": 123,
+    "90": 63,
+    "91": 277,
+    "92": 102,
+    "94": 311,
+    "95": 103,
+    "96": 108,
+    "97": 65,
+    "98": 117,
+    "99": 69,
+    "100": 117,
+    "101": 277,
+    "102": 60,
+    "103": 70,
+    "104": 65,
+    "105": 718,
+    "106": 12,
+    "107": 232,
+    "108": 69,
+    "109": 108,
+    "110": 113,
+    "111": 404
+  },
+  "tested_later_isolated_sink_ports": 104,
+  "tested_later_zero_source_ports": 104,
+  "first_suffix_zero_candidates": {},
+  "second_donor_zero_candidates": {},
+  "scope": "Necessary temporal cancellation matches for the one-zero-factor cases of two coframe ADDs. Transfer amplitude, COPY legality and full endpoint replay still required for survivors. Both-zero dark path tested separately."
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR7000-CENTRAL-QUERY-SIGN-RANK.json b/research/fixed-caller-query-and-host-limits/expected/PR7000-CENTRAL-QUERY-SIGN-RANK.json
new file mode 100644
index 0000000000..123b30d792
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR7000-CENTRAL-QUERY-SIGN-RANK.json
@@ -0,0 +1,282 @@
+{
+  "source_sha256": "3828d53e80ea97e8b866320f081af20b6b93bfebd58b95b56b85a7afe151af5e",
+  "prime": 2147483629,
+  "branches": {
+    "A": {
+      "query_indices": [
+        532,
+        538,
+        549,
+        717
+      ],
+      "tested_differences": [
+        {
+          "q": 1,
+          "stage_values": {
+            "1": 1,
+            "2": 1,
+            "3": 1,
+            "4": 1,
+            "5": 1,
+            "6": 1,
+            "7": 1,
+            "8": 1,
+            "9": 1,
+            "10": 1,
+            "11": 1,
+            "12": 1,
+            "13": 1,
+            "14": 1,
+            "15": 1,
+            "16": 1,
+            "17": 1,
+            "18": 1
+          },
+          "rank": 4,
+          "pivot_columns": [
+            0,
+            2,
+            19,
+            20
+          ]
+        },
+        {
+          "q": 1,
+          "stage_values": {
+            "1": 42628720,
+            "2": 658182651,
+            "3": 542191716,
+            "4": 251413995,
+            "5": 956912165,
+            "6": 953225032,
+            "7": 2044045994,
+            "8": 1088794337,
+            "9": 1730610827,
+            "10": 534202141,
+            "11": 1632347269,
+            "12": 2051884149,
+            "13": 74566505,
+            "14": 1703735303,
+            "15": 1204015065,
+            "16": 1625319335,
+            "17": 599967768,
+            "18": 1133836870
+          },
+          "rank": 4,
+          "pivot_columns": [
+            0,
+            2,
+            19,
+            20
+          ]
+        },
+        {
+          "q": 1518275076,
+          "stage_values": {
+            "1": 1,
+            "2": 1,
+            "3": 1,
+            "4": 1,
+            "5": 1,
+            "6": 1,
+            "7": 1,
+            "8": 1,
+            "9": 1,
+            "10": 1,
+            "11": 1,
+            "12": 1,
+            "13": 1,
+            "14": 1,
+            "15": 1,
+            "16": 1,
+            "17": 1,
+            "18": 1
+          },
+          "rank": 4,
+          "pivot_columns": [
+            0,
+            2,
+            19,
+            20
+          ]
+        },
+        {
+          "q": 1518275076,
+          "stage_values": {
+            "1": 341910843,
+            "2": 2104325677,
+            "3": 159767649,
+            "4": 902561379,
+            "5": 59484417,
+            "6": 1335370517,
+            "7": 1577311538,
+            "8": 302664532,
+            "9": 286485654,
+            "10": 2027263919,
+            "11": 1698402509,
+            "12": 206362991,
+            "13": 875902737,
+            "14": 569277415,
+            "15": 119860073,
+            "16": 2022938178,
+            "17": 1004872545,
+            "18": 1808673014
+          },
+          "rank": 4,
+          "pivot_columns": [
+            0,
+            2,
+            19,
+            20
+          ]
+        }
+      ],
+      "fixed_interval_query_lower_bound": 4,
+      "literal_omission_negative_controls": [
+        0,
+        6,
+        17,
+        185
+      ]
+    },
+    "B": {
+      "query_indices": [
+        1079,
+        1157,
+        1190,
+        2091
+      ],
+      "tested_differences": [
+        {
+          "q": 1,
+          "stage_values": {
+            "1": 1,
+            "2": 1,
+            "3": 1,
+            "4": 1,
+            "5": 1,
+            "6": 1,
+            "7": 1,
+            "8": 1,
+            "9": 1,
+            "10": 1,
+            "11": 1,
+            "12": 1,
+            "13": 1,
+            "14": 1,
+            "15": 1,
+            "16": 1,
+            "17": 1,
+            "18": 1
+          },
+          "rank": 4,
+          "pivot_columns": [
+            38,
+            39,
+            40,
+            41
+          ]
+        },
+        {
+          "q": 1,
+          "stage_values": {
+            "1": 917768279,
+            "2": 1843444028,
+            "3": 1145820542,
+            "4": 1110064911,
+            "5": 1911322794,
+            "6": 292004977,
+            "7": 1378978860,
+            "8": 22862112,
+            "9": 422592694,
+            "10": 262678509,
+            "11": 1470061717,
+            "12": 539376086,
+            "13": 1115773558,
+            "14": 1341551033,
+            "15": 1720863636,
+            "16": 978732232,
+            "17": 102128237,
+            "18": 754790939
+          },
+          "rank": 4,
+          "pivot_columns": [
+            38,
+            39,
+            40,
+            41
+          ]
+        },
+        {
+          "q": 1518275076,
+          "stage_values": {
+            "1": 1,
+            "2": 1,
+            "3": 1,
+            "4": 1,
+            "5": 1,
+            "6": 1,
+            "7": 1,
+            "8": 1,
+            "9": 1,
+            "10": 1,
+            "11": 1,
+            "12": 1,
+            "13": 1,
+            "14": 1,
+            "15": 1,
+            "16": 1,
+            "17": 1,
+            "18": 1
+          },
+          "rank": 4,
+          "pivot_columns": [
+            38,
+            39,
+            40,
+            41
+          ]
+        },
+        {
+          "q": 1518275076,
+          "stage_values": {
+            "1": 1058886400,
+            "2": 303974971,
+            "3": 1884634545,
+            "4": 1866939806,
+            "5": 1523890482,
+            "6": 1150608862,
+            "7": 639463024,
+            "8": 1328381080,
+            "9": 530589251,
+            "10": 909610971,
+            "11": 2015779255,
+            "12": 1370693450,
+            "13": 1812631943,
+            "14": 345220238,
+            "15": 2027617720,
+            "16": 1048154315,
+            "17": 289255931,
+            "18": 1842365285
+          },
+          "rank": 4,
+          "pivot_columns": [
+            38,
+            39,
+            40,
+            41
+          ]
+        }
+      ],
+      "fixed_interval_query_lower_bound": 4,
+      "literal_omission_negative_controls": [
+        0,
+        78,
+        111,
+        1012
+      ]
+    }
+  },
+  "proof": "Each even ordinary map is equal at q and -q. Each odd query changes its sign, so its two maps differ by a rank-one matrix. A telescoping product difference has rank at most the sum of those ranks. A finite-field specialization where the required difference has rank r proves at least r queries for this fixed interval over the dyadic operator ring.",
+  "scope": "Preserves the full input/output operator of the central interval. Moving a QUERY across a J call, changing the boundary operator or making new sign-sensitive native calls is outside the bound."
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR7000-QUERY-COUNT-SIGN-LOWER-BOUND.json b/research/fixed-caller-query-and-host-limits/expected/PR7000-QUERY-COUNT-SIGN-LOWER-BOUND.json
new file mode 100644
index 0000000000..357b7b7c2c
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR7000-QUERY-COUNT-SIGN-LOWER-BOUND.json
@@ -0,0 +1,29 @@
+{
+  "source_sha256": "3828d53e80ea97e8b866320f081af20b6b93bfebd58b95b56b85a7afe151af5e",
+  "types": {
+    "A": {
+      "roles": 38,
+      "ports": 96,
+      "native_calls": 18,
+      "current_queries": 4,
+      "minimum_queries_with_current_HOST_factorization": 3,
+      "maximum_removed_queries": 1
+    },
+    "B": {
+      "roles": 38,
+      "ports": 8,
+      "native_calls": 18,
+      "current_queries": 4,
+      "minimum_queries_with_current_HOST_factorization": 3,
+      "maximum_removed_queries": 1
+    }
+  },
+  "proof": [
+    "Specialize D_j=1 and compare the complete q=-1 map to the q=1 map. Both targets are scalar signs on all 38 roles, so their relative map is -I.",
+    "Ordinary ADD, SWAP, SCALE and LAMBDA events agree between the two signs. Each QUERY shear changes its coefficient sign; its relative factor is a rank-one transvection.",
+    "At a J event each branch consists of two elementary sign-sensitive shears and sign-independent D_j factors. Factoring the two signed full products by telescoping yields a product of conjugates of these elementary relative factors.",
+    "A product of rank-one transvections giving -I in dimension n needs at least n+1 factors: rank(M-I) forces at least n independent directions, and with exactly n the first updated row in that basis keeps diagonal coefficient +1 to the end.",
+    "Therefore each branch needs at least 39 sign-sensitive transvections. With 18 native events contributing at most two each, at least three QUERY events remain per branch."
+  ],
+  "scope": "Fixed 38-role targets and native factorization, with even ordinary operators. New native macros, extra degrees of freedom, changed targets or further physical relations may fall outside the bound."
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR7000-QUERY-HOST-TRANSPORT-CONTACTS.json b/research/fixed-caller-query-and-host-limits/expected/PR7000-QUERY-HOST-TRANSPORT-CONTACTS.json
new file mode 100644
index 0000000000..5a662466c9
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR7000-QUERY-HOST-TRANSPORT-CONTACTS.json
@@ -0,0 +1,6 @@
+{
+  "tested_pairs": 300,
+  "matches": [],
+  "sample_count": 8,
+  "scope": "Conjugated shear image and source directions at the original prefixes in the fixed operator word. Exact finite-field evaluations exclude proportionality over the dyadic formal ring if any evaluation differs. General resynthesis is outside this screen."
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR7002-75-JOB-COMPOSITION-PRICE.json b/research/fixed-caller-query-and-host-limits/expected/PR7002-75-JOB-COMPOSITION-PRICE.json
new file mode 100644
index 0000000000..e521e59ae6
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR7002-75-JOB-COMPOSITION-PRICE.json
@@ -0,0 +1,28 @@
+{
+  "jobs_per_port": 75,
+  "tests": {
+    "1/250": {
+      "exact_104_port_saving": [
+        "571129386331237500496356243721/125000000000000000000000000000",
+        "7139117329140468756204453047/1562500000000000000000000000"
+      ],
+      "new_margin": [
+        "-50285167377779360563856010566997/100000000000000000000000000000",
+        "-251425836888896802819280052795509/500000000000000000000000000000"
+      ],
+      "remaining_rank_one_equivalents": 503
+    },
+    "1/200": {
+      "exact_104_port_saving": [
+        "142436399948865247532126790477/25000000000000000000000000000",
+        "89022749968040779707579244053/15625000000000000000000000000"
+      ],
+      "new_margin": [
+        "-81490413070956168953734354253433/100000000000000000000000000000",
+        "-407452065354780844768671771227689/500000000000000000000000000000"
+      ],
+      "remaining_rank_one_equivalents": 815
+    }
+  },
+  "scope": "Exact normalized schedule with the retained F+H1 tariff. Physical packed IDLE and basis costs, BIT and outer admission remain open."
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR7002-CHRONOLOGICAL-IDLE-GROUPS.json b/research/fixed-caller-query-and-host-limits/expected/PR7002-CHRONOLOGICAL-IDLE-GROUPS.json
new file mode 100644
index 0000000000..bb15ab9691
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR7002-CHRONOLOGICAL-IDLE-GROUPS.json
@@ -0,0 +1,221 @@
+{
+  "stage_count": 18,
+  "old_jobs": 181,
+  "new_jobs": 121,
+  "paid_idle_rank_profile": {
+    "8": 105,
+    "56": 4,
+    "40": 2,
+    "32": 4,
+    "16": 2,
+    "24": 2,
+    "48": 2
+  },
+  "commuting_groups": [
+    {
+      "role": 2,
+      "cut": 3,
+      "stages": [
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7
+      ]
+    },
+    {
+      "role": 3,
+      "cut": 3,
+      "stages": [
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7
+      ]
+    },
+    {
+      "role": 5,
+      "cut": 6,
+      "stages": [
+        3,
+        4,
+        5,
+        6,
+        7
+      ]
+    },
+    {
+      "role": 6,
+      "cut": 6,
+      "stages": [
+        3,
+        4,
+        5,
+        6,
+        7
+      ]
+    },
+    {
+      "role": 8,
+      "cut": 9,
+      "stages": [
+        4,
+        5,
+        6,
+        7
+      ]
+    },
+    {
+      "role": 9,
+      "cut": 9,
+      "stages": [
+        4,
+        5,
+        6,
+        7
+      ]
+    },
+    {
+      "role": 11,
+      "cut": 12,
+      "stages": [
+        6,
+        7
+      ]
+    },
+    {
+      "role": 12,
+      "cut": 12,
+      "stages": [
+        6,
+        7
+      ]
+    },
+    {
+      "role": 14,
+      "cut": 15,
+      "stages": [
+        7
+      ]
+    },
+    {
+      "role": 15,
+      "cut": 15,
+      "stages": [
+        7
+      ]
+    },
+    {
+      "role": 23,
+      "cut": 0,
+      "stages": [
+        9
+      ]
+    },
+    {
+      "role": 24,
+      "cut": 0,
+      "stages": [
+        9
+      ]
+    },
+    {
+      "role": 26,
+      "cut": 0,
+      "stages": [
+        9,
+        10,
+        11
+      ]
+    },
+    {
+      "role": 27,
+      "cut": 0,
+      "stages": [
+        9,
+        10,
+        11
+      ]
+    },
+    {
+      "role": 29,
+      "cut": 0,
+      "stages": [
+        9,
+        10,
+        11,
+        12
+      ]
+    },
+    {
+      "role": 30,
+      "cut": 0,
+      "stages": [
+        9,
+        10,
+        11,
+        12
+      ]
+    },
+    {
+      "role": 32,
+      "cut": 0,
+      "stages": [
+        9,
+        10,
+        11,
+        12,
+        13,
+        14
+      ]
+    },
+    {
+      "role": 33,
+      "cut": 0,
+      "stages": [
+        9,
+        10,
+        11,
+        12,
+        13,
+        14
+      ]
+    },
+    {
+      "role": 35,
+      "cut": 0,
+      "stages": [
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15
+      ]
+    },
+    {
+      "role": 36,
+      "cut": 0,
+      "stages": [
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15
+      ]
+    }
+  ],
+  "per_port_saving_at_005": [
+    "4.87313163684216460139832230867568012633778428",
+    "4.87313163684216460139832230867568012634082200"
+  ],
+  "scope": "Constructed commuting normalized root schedule, universal over stage variables. Grouped jobs require the retained whole-mask IDLE tariff and physical adapters. No native price reduction, outer admission or kappa claim."
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR7002-IDLE-PROJECTOR-ORDER-SEARCH.json b/research/fixed-caller-query-and-host-limits/expected/PR7002-IDLE-PROJECTOR-ORDER-SEARCH.json
new file mode 100644
index 0000000000..c057d28a02
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR7002-IDLE-PROJECTOR-ORDER-SEARCH.json
@@ -0,0 +1,2503 @@
+{
+  "trials": [
+    {
+      "seed": 0,
+      "strength": 0,
+      "paid_moment_diagnostic": "1424.3326278371382677657970999979",
+      "jobs": 76
+    },
+    {
+      "seed": 1,
+      "strength": 0,
+      "paid_moment_diagnostic": "1424.2778446063887042090539743092",
+      "jobs": 75
+    },
+    {
+      "seed": 2,
+      "strength": 0.3333333333333333,
+      "paid_moment_diagnostic": "1424.2778446063887042090539743092",
+      "jobs": 75
+    },
+    {
+      "seed": 3,
+      "strength": 0.6666666666666666,
+      "paid_moment_diagnostic": "1424.2778446063887042090539743092",
+      "jobs": 75
+    },
+    {
+      "seed": 4,
+      "strength": 1.0,
+      "paid_moment_diagnostic": "1424.3326278371382677657970999979",
+      "jobs": 76
+    },
+    {
+      "seed": 5,
+      "strength": 1.3333333333333333,
+      "paid_moment_diagnostic": "1424.3326278371382677657970999979",
+      "jobs": 76
+    },
+    {
+      "seed": 6,
+      "strength": 1.6666666666666667,
+      "paid_moment_diagnostic": "1424.5696727125188955991531091148",
+      "jobs": 78
+    },
+    {
+      "seed": 7,
+      "strength": 2.0,
+      "paid_moment_diagnostic": "1425.1234754750954333743249680503",
+      "jobs": 84
+    },
+    {
+      "seed": 8,
+      "strength": 2.3333333333333335,
+      "paid_moment_diagnostic": "1424.7356878892300101814349850343",
+      "jobs": 79
+    },
+    {
+      "seed": 9,
+      "strength": 2.6666666666666665,
+      "paid_moment_diagnostic": "1425.3159373456904123118929893015",
+      "jobs": 83
+    },
+    {
+      "seed": 10,
+      "strength": 3.0,
+      "paid_moment_diagnostic": "1424.5674453337279460394138443143",
+      "jobs": 77
+    },
+    {
+      "seed": 11,
+      "strength": 3.3333333333333335,
+      "paid_moment_diagnostic": "1425.1663265873943686311593550680",
+      "jobs": 83
+    },
+    {
+      "seed": 12,
+      "strength": 3.6666666666666665,
+      "paid_moment_diagnostic": "1425.0553248064076500515991914749",
+      "jobs": 83
+    },
+    {
+      "seed": 13,
+      "strength": 4.0,
+      "paid_moment_diagnostic": "1425.8747792702803357195777569233",
+      "jobs": 86
+    },
+    {
+      "seed": 14,
+      "strength": 4.333333333333333,
+      "paid_moment_diagnostic": "1425.3271671923186978317518072258",
+      "jobs": 86
+    },
+    {
+      "seed": 15,
+      "strength": 4.666666666666667,
+      "paid_moment_diagnostic": "1425.1872146820361837342598469202",
+      "jobs": 84
+    },
+    {
+      "seed": 16,
+      "strength": 5.0,
+      "paid_moment_diagnostic": "1425.6990909385444227772793478704",
+      "jobs": 89
+    },
+    {
+      "seed": 17,
+      "strength": 5.333333333333333,
+      "paid_moment_diagnostic": "1425.3169798193119051035905599955",
+      "jobs": 85
+    },
+    {
+      "seed": 18,
+      "strength": 5.666666666666667,
+      "paid_moment_diagnostic": "1426.0055693387950063984450672787",
+      "jobs": 92
+    },
+    {
+      "seed": 19,
+      "strength": 6.0,
+      "paid_moment_diagnostic": "1426.0006901507121282244372554190",
+      "jobs": 89
+    },
+    {
+      "seed": 20,
+      "strength": 6.333333333333333,
+      "paid_moment_diagnostic": "1426.0542396552427553778738986295",
+      "jobs": 92
+    },
+    {
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+      "strength": 6.666666666666667,
+      "paid_moment_diagnostic": "1425.8822437781919429672140754006",
+      "jobs": 89
+    }
+  ],
+  "best_seed": 1,
+  "rank_histogram": {
+    "64": 3,
+    "56": 4,
+    "48": 4,
+    "40": 4,
+    "32": 4,
+    "24": 4,
+    "16": 5,
+    "8": 47
+  },
+  "104_port_advantage_at_005_diagnostic": "5.6974559979546099012850716248",
+  "best_projectors": [
+    [
+      9,
+      16,
+      [
+        "0",
+        "0",
+        "0",
+        "0",
+        "0",
+        "0",
+        "0",
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+        "0",
+        "0",
+        "0",
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+        "0",
+        "0",
+        "0",
+        "0",
+        "-1",
+        "1",
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+        "0"
+      ],
+      [
+        "0",
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+  ],
+  "scope": "Bounded deterministic seed/order search on exact projector construction. Exact role-level relocation controls on the best profile; cost comparison diagnostic only."
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR7002-NONCOORDINATE-IDLE-WORD.json b/research/fixed-caller-query-and-host-limits/expected/PR7002-NONCOORDINATE-IDLE-WORD.json
new file mode 100644
index 0000000000..8b539d9bb6
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR7002-NONCOORDINATE-IDLE-WORD.json
@@ -0,0 +1,2289 @@
+{
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+  "104_port_saving_over_coordinate_lower": "396.976217584871796346219095780246739493152900",
+  "scope": "Exact normalized role-level relocation by orthogonal projectors, with all-column rational controls. Requires physical whole-idle composition, ordinary map costs, and the native HOST construction."
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/expected/PR7004-QUERY-FAMILY-TARGET-PRICE.json b/research/fixed-caller-query-and-host-limits/expected/PR7004-QUERY-FAMILY-TARGET-PRICE.json
new file mode 100644
index 0000000000..fd266f33eb
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/expected/PR7004-QUERY-FAMILY-TARGET-PRICE.json
@@ -0,0 +1,61 @@
+{
+  "queries_by_family": {
+    "A": 4,
+    "B": 4
+  },
+  "ports": {
+    "A": 96,
+    "B": 8
+  },
+  "target_prices": {
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+          "-7635395162402395149172963628807/50000000000000000000000000000"
+        ],
+        "minimum_rank_one_equivalent": 153,
+        "after_one_A_query_removed": [
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+          "-2835395162402395149172963628807/50000000000000000000000000000"
+        ],
+        "after_one_A_and_one_B_query_removed": [
+          "-1217697581201197574586481817537/25000000000000000000000000000",
+          "-2435395162402395149172963628807/50000000000000000000000000000"
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+          "-1786923912456594692793584683623/31250000000000000000000000000"
+        ],
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+          "-141642726926408456182450136197021/250000000000000000000000000000"
+        ],
+        "minimum_rank_one_equivalent": 567,
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+          "-117642726926408456182450136197021/250000000000000000000000000000"
+        ],
+        "after_one_A_and_one_B_query_removed": [
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+          "-115642726926408456182450136197021/250000000000000000000000000000"
+        ]
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+          "-222031608216169820492373385806903/500000000000000000000000000000"
+        ],
+        "minimum_rank_one_equivalent": 445
+      }
+    }
+  },
+  "scope": "Exact raw-moment bounds with fixed targets, using source-bound complex and BIT invoices. Query removal is a hypothetical change and not an operator identity, physical or outer admission."
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/notices/PR6824-NOTICE b/research/fixed-caller-query-and-host-limits/notices/PR6824-NOTICE
new file mode 100644
index 0000000000..4f06037678
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/notices/PR6824-NOTICE
@@ -0,0 +1,5 @@
+Native main-retiming/helper retirement extension by Jerry Chen / @CubeJerry, with substantial OpenAI Codex assistance and separate source-bound review. Apache-2.0.
+
+Original retained headers, licenses and notices remain unchanged. See retained/caller/NOTICE for the full native/caller/compiler/interval lineage; Ali Romman supplies the helper-basis mechanism, DreamingOfClouds the #6702 native source, and zxv the #6726 caller.
+
+Shared-carrier input-lift step (lift.py, LIFT.json, PROOF.md) by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Apache-2.0. The input-lift move class follows Ali Romman's #6349 line of work.
diff --git a/research/fixed-caller-query-and-host-limits/notices/PR7000-NOTICE b/research/fixed-caller-query-and-host-limits/notices/PR7000-NOTICE
new file mode 100644
index 0000000000..a3687d65a0
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/notices/PR7000-NOTICE
@@ -0,0 +1,9 @@
+New shared-wire composition, seventeenth wire, and two enabling splits: developed with substantial OpenAI assistance, 2026. Apache-2.0.
+
+Frozen predecessor native words and odd verifier: DreamingOfClouds, with Claude Opus 5.5 (Anthropic), from #6936 and #6937.
+
+Retained Clifford compiler and exact native interpreter retain their original headers and lineage from #6833: native source by DreamingOfClouds; independent-helper mechanism by Ali Romman; inventory, retiming and helper-retirement extensions by Jerry Chen / @CubeJerry with OpenAI assistance.
+
+Helper-split lemma: Ali Romman (#5599). Shared native applications: CubeJerry (#6916). Caller blocks: CubeJerry (#6912). Owned-rise argument: CubeJerry (#6914). Width-2 phase convention: unpaidmoon (#6930). Odd-grid precedent: icekylinx (#104).
+
+The higher-level caller and BIT integration require their own source attribution and pins.
diff --git a/research/fixed-caller-query-and-host-limits/notices/PR7001-NOTICE b/research/fixed-caller-query-and-host-limits/notices/PR7001-NOTICE
new file mode 100644
index 0000000000..32c2936ea0
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/notices/PR7001-NOTICE
@@ -0,0 +1,26 @@
+Paired E-free BIT specialization and complete accounting, with substantial
+OpenAI Codex assistance, for the integer-multiplication research project.
+Apache-2.0; LICENSE is retained from the source project.
+
+DreamingOfClouds (Claude Opus assistance) receives credit for #6834's chain-root
+BIT caller, #6937's E-free roots and the underlying two-chain construction.
+@CubeJerry (OpenAI assistance) receives credit for #6980's four-input three-query
+identity, separated interval replacement and QUERY-only caller. The complete
+#6980 proof is retained byte-for-byte in data/6980_PROOF.md.
+
+The new contribution specializes that existing caller to the actual #6726 BIT
+native, supplies the parity-driven pairing of two real 111-port invocations,
+and checks the complete E-free finite/compiler/ordinary budget from the selected
+ordinary backend. No general QUERY-only mechanism, chain root or new raw kappa
+is claimed as new here.
+
+independent/bit_review.py and independent/interval_gate.py were written by a
+separate OpenAI Codex research worker for an implementation-independent scalar
+and arithmetic audit. This is model-run checking, not external human review.
+
+zxv and retained predecessor authors receive credit for #6726's source-native
+export, integer-before-mod2 transfer, complete source checking and admission
+framework. Ali Romman and Cinna Davis retain the root/native lineage credit.
+The copied arithmetic and native checker retain their original headers; see
+retained/NOTICE. The selected .0034 backend retains the source and contributor
+credits in data/selected_record.json and data/selected_review.md.
diff --git a/research/fixed-caller-query-and-host-limits/notices/PR7002-NOTICE b/research/fixed-caller-query-and-host-limits/notices/PR7002-NOTICE
new file mode 100644
index 0000000000..f5d981b979
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/notices/PR7002-NOTICE
@@ -0,0 +1,15 @@
+Connected L18 root geometry and emitted caller: substantial OpenAI Codex-assisted research.
+Apache-2.0; no human or maintainer review.
+
+Prior complete-sign/single-chain mechanism and sector normalization: DreamingOfClouds,
+including PR6842, PR6936 and PR6937, prepared with Claude Opus 5.5 via Claude Code.
+Retained type A root: @CubeJerry (Jerry Chen), PR6912. Caller and native lineage
+includes Ali Romman, unpaidmoon and icekylinx, as credited by PR6936.
+Independent root, tariff and reverse replay implementations were prepared separately
+with OpenAI Codex assistance and import no primary construction/replay code.
+Input JSON exports are copied without modification and pinned in INPUT-PINS.json.
+
+The vendored companion native word retains its complete attribution in inputs/NATIVE-NOTICE.
+Its new shared-wire composition, seventeenth wire and enabling splits were developed with
+substantial OpenAI assistance in2026, Apache-2.0; predecessor native/compiler lineage
+remains DreamingOfClouds, Ali Romman and Jerry Chen / @CubeJerry as recorded there.
diff --git a/research/fixed-caller-query-and-host-limits/notices/PR7004-NOTICE b/research/fixed-caller-query-and-host-limits/notices/PR7004-NOTICE
new file mode 100644
index 0000000000..a773fca904
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/notices/PR7004-NOTICE
@@ -0,0 +1,5 @@
+The peer retiming builds on the #7003 stop-fusion contribution prepared for
+ToikY, DreamingOfClouds' #6932 retiming and #6936/#6937 words, and CubeJerry's
+#7000 shared-wire composition and #7001 paired BIT construction. Original
+source licenses and notices remain attached to the predecessor packages.
+Prepared for ToikY with substantial OpenAI Codex assistance. Apache-2.0.
diff --git a/research/fixed-caller-query-and-host-limits/replay/PR7000-CALLER.json b/research/fixed-caller-query-and-host-limits/replay/PR7000-CALLER.json
new file mode 100644
index 0000000000..cf55f42710
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/PR7000-CALLER.json
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diff --git a/research/fixed-caller-query-and-host-limits/replay/PR7001-RESULT.json b/research/fixed-caller-query-and-host-limits/replay/PR7001-RESULT.json
new file mode 100644
index 0000000000..575f76487f
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/PR7001-RESULT.json
@@ -0,0 +1,19787 @@
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diff --git a/research/fixed-caller-query-and-host-limits/replay/PR7004-RESULT.json b/research/fixed-caller-query-and-host-limits/replay/PR7004-RESULT.json
new file mode 100644
index 0000000000..9310cd05b5
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/PR7004-RESULT.json
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+            "entrance_defect": "126563650963042505306559371472874199746674734468806236693462980865328400127210079753664342564751885790032979244207967695979116795226632889247301/2448074784719624078780006400000000000000000"
+          },
+          {
+            "event": 2958,
+            "stage": 18,
+            "entrance_mass": "363421601940370671219209686545270656",
+            "entrance_defect": "107778012552827346405847104423459712043992723422974845622861307836188983347714236386920204945834586535869101223279216908028946278696468822744901/90669436471097188102963200000000000000000"
+          }
+        ],
+        "independent_adjoint": {
+          "M_caller": {
+            "entrance_mass": "1683307283016999532839217702665847040",
+            "residual_mass": "2695731259664671076054039120630302290804707477143926198908206538844775877602956477228348077432250517175435896637972296457629495898943097624737901/489614956943924815756001280000000000000000",
+            "joint_coefficient": "274838256141142176415070287809505/2",
+            "primitive_coefficient": "104781665096099932454228246133920343"
+          },
+          "Sigma_caller": {
+            "entrance_mass": "1683307283016999532839217702665847040",
+            "residual_mass": "2695731259664671076054039120630302290804707477143926198908206538844775877602956477228348077432250517175435896637972296457629495898943097624737901/489614956943924815756001280000000000000000",
+            "joint_coefficient": "274838256141142176415070287809505/2",
+            "primitive_coefficient": "104781665096099932454228246133920343"
+          },
+          "M_joint_entrance": {
+            "entrance_mass": "363421601940370671219209686545270656",
+            "residual_mass": "107778012552827346405847104423459712043992723422974845622861307836188983347714236386920204945834586535869101223279216908028946278696468822744901/90669436471097188102963200000000000000000",
+            "joint_coefficient": "59336854494143543914675236360327/2",
+            "primitive_coefficient": "22622085086540611235550148326673690"
+          },
+          "E_joint_entrance": {
+            "entrance_mass": "363421601940370671219209686545270656",
+            "residual_mass": "107778012552827346405847104423459712043992723422974845622861307836188983347714236386920204945834586535869101223279216908028946278696468822744901/90669436471097188102963200000000000000000",
+            "joint_coefficient": "59336854494143543914675236360327/2",
+            "primitive_coefficient": "22622085086540611235550148326673690"
+          },
+          "Gamma_context": {
+            "entrance_mass": "59038824075417799032780136585499589",
+            "residual_mass": "5042543099912900584634479237866816375710352420271633339290359319183724747139660012073844315372616663103054927249151863454851308445018630759374251/26112797703675990173653401600000000000000000",
+            "joint_coefficient": "308461849925427171118076353794753/64",
+            "primitive_coefficient": "117600608836679351835159084859338679/32"
+          }
+        },
+        "physical_main_inputs": 3952,
+        "fresh_arbitrary_helpers": 19440,
+        "helper_allocation_premise": "distinct (stage, helper) public inputs as in frozen caller proof"
+      }
+    },
+    "threshold": {
+      "H": 14181100000000000000,
+      "LP": 2229,
+      "Kstar_bits": 14073,
+      "scaled4096_Kstar_bits": 14085
+    },
+    "negative_grid_controls": {
+      "S375_f24": "integer grid rejection at event 36836: denominator 48",
+      "S225_f24": "integer grid rejection at event 1118: denominator 250",
+      "S1125_f23": "integer grid rejection at event 61560: denominator 64"
+    },
+    "scope": "Exact children for common grid. Total RDiv plus complete-fibre unitary contracts for rounded envelopes. Neither is a physical provider admission."
+  },
+  "controls": {
+    "changed_scalar_rejected": true,
+    "old_invoice_rejects_claim": true,
+    "changed_phase_rejected": true,
+    "insufficient_grid_rejected": true
+  }
+}
diff --git a/research/fixed-caller-query-and-host-limits/replay/certify_6824_two_add_obstruction.py b/research/fixed-caller-query-and-host-limits/replay/certify_6824_two_add_obstruction.py
new file mode 100644
index 0000000000..1ae223fbc9
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/certify_6824_two_add_obstruction.py
@@ -0,0 +1,29 @@
+"""Verify the case split excluding two added coframe ADDs on pinned F6824."""
+import json
+from pathlib import Path
+
+root=Path(__file__).resolve().parent
+files={
+ "first_order":"PR6824-MIXED-FIRST-ORDER-HOST-CONTACTS.json",
+ "one_zero":"PR6824-TWO-EDIT-MIXED-CANCELLATION.json",
+ "both_zero":"PR6824-TWO-CONTACT-DARK-REACHABILITY.json",
+}
+data={name:json.loads((root/path).read_text()) for name,path in files.items()}
+assert len(data["first_order"]["ports"])==104
+assert all(not r["contacts_by_support"] for r in data["first_order"]["ports"].values())
+assert not data["one_zero"]["first_suffix_zero_candidates"]
+assert not data["one_zero"]["second_donor_zero_candidates"]
+assert not data["both_zero"]["reachable_ports"]
+proof=[
+    "Two additions at ordered cuts give endpoint delta c1 B1 A1 + c2 B2 A2 + c1 c2 h B2 A1, where A are baseline donor rows, B are baseline suffix columns and h is the interposed scalar transfer.",
+    "To have nonzero x,y coefficient, the mixed term must supply it because no baseline single ADD has nonzero x,y derivative. Hence B2[x] and A1[y] are nonzero, B1[x] and A2[y] are zero, and the interposed coefficient is nonzero.",
+    "If B1 and A2 are both nonzero, the two suffix columns are independent (their x coordinates differ by zero/nonzero), and the rows A1 and A2 + c1 h A1 are independent (A2 has no y). The endpoint delta has rank two, contradicting the rank-one repair.",
+    "If only B1 is zero, B2 must be an isolated X+Y suffix and the non-Y part of A1 must cancel the nonzero A2. The chronological mixed-cancellation census excludes every such signature.",
+    "If only A2 is zero, A1 must be pure Y and the nonzero B1 must match the residual after normalizing B2 at X. The chronological mixed-cancellation census excludes every such signature.",
+    "If B1 and A2 are both zero, the pure-Y first donor and isolated X+Y second sink must be connected via the dark scratch path. The generous support transfer scan excludes it."
+]
+with (root/"PR6824-TWO-ADD-HOST-OBSTRUCTION.json").open("x") as out:
+    json.dump({"status":"PASS_FIXED_CHRONOLOGY_TWO_ADD_HOST_OBSTRUCTION",
+               "ports":104,"evidence":files,"proof":proof,
+               "scope":"Exact normalized scalar circuit with the fixed chronological MOVE/COPY/INIT/CLEAR schedule. The required repair is one specified same-port rank-one F-to-HOST entrance transvection. At most two newly inserted distinct-register coframe ADDs. Changing MOVE timing or chart shape, scalings, cross-port block outputs, or adding three or more contacts is outside scope."},out,indent=2)
+print("PASS_FIXED_CHRONOLOGY_TWO_ADD_HOST_OBSTRUCTION 104")
diff --git a/research/fixed-caller-query-and-host-limits/replay/certify_7000_sign_query_floor.py b/research/fixed-caller-query-and-host-limits/replay/certify_7000_sign_query_floor.py
new file mode 100644
index 0000000000..443fd72b65
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/certify_7000_sign_query_floor.py
@@ -0,0 +1,47 @@
+"""A rank-one length certificate for the #7000/#7004 caller's two sign branches."""
+from pathlib import Path
+from fractions import Fraction as F
+from hashlib import sha256
+import json
+
+root=Path(__file__).resolve().parent
+p=root/"PR7000-CALLER.json"
+caller=json.loads(p.read_bytes())
+code=(root/"jclib_6936.py").read_text()
+ns={"__file__":str(root/"jclib_6936.py")}
+exec(code[:code.index("CONST =")]+code[code.index("PM ="):code.index("# ---------------------------------------------------------------- own resynthesis")],ns)
+prime=ns["PM"]
+stages=caller["stages"]
+variables={j:1 for j in range(1,stages+1)}
+for sign in (1,prime-1):
+    matrix=ns["replay_matrix"](caller,sign,variables)
+    assert all(value==(sign if i==j else 0) for i,row in enumerate(matrix) for j,value in enumerate(row))
+
+result={}
+for tag,typ in caller["types"].items():
+    n=typ["roles"]
+    assert all(row[0]%2==1 for row in typ["diagonal"])
+    native=sum(e[0]=="J" for e in caller["events"])
+    query=sum(e[0]==tag and e[1]=="QUERY" for e in caller["events"])
+    minimum=n+1-2*native
+    assert minimum==3 and query==4
+    result[tag]={"roles":n,"ports":len(typ["ports"]),"native_calls":native,"current_queries":query,
+                 "minimum_queries_with_current_HOST_factorization":minimum,
+                 "maximum_removed_queries":query-minimum}
+price=json.loads((root/"PR7004-QUERY-FAMILY-TARGET-PRICE.json").read_text())
+for k,rows in price["target_prices"].items():
+    m=F(rows["complex"]["signed_moment"][1])
+    maximum=sum(r["ports"]*r["maximum_removed_queries"] for r in result.values())
+    assert m+maximum<0
+    print(k,"optimistic margin after both removable query slots",float(m+maximum))
+with (root/"PR7000-QUERY-COUNT-SIGN-LOWER-BOUND.json").open("x") as out:
+    json.dump({"source_sha256":sha256(p.read_bytes()).hexdigest(),"types":result,
+               "proof":[
+                   "Specialize D_j=1 and compare the complete q=-1 map to the q=1 map. Both targets are scalar signs on all 38 roles, so their relative map is -I.",
+                   "Ordinary ADD, SWAP, SCALE and LAMBDA events agree between the two signs. Each QUERY shear changes its coefficient sign; its relative factor is a rank-one transvection.",
+                   "At a J event each branch consists of two elementary sign-sensitive shears and sign-independent D_j factors. Factoring the two signed full products by telescoping yields a product of conjugates of these elementary relative factors.",
+                   "A product of rank-one transvections giving -I in dimension n needs at least n+1 factors: rank(M-I) forces at least n independent directions, and with exactly n the first updated row in that basis keeps diagonal coefficient +1 to the end.",
+                   "Therefore each branch needs at least 39 sign-sensitive transvections. With 18 native events contributing at most two each, at least three QUERY events remain per branch."
+               ],
+               "scope":"Fixed 38-role targets and native factorization, with even ordinary operators. New native macros, extra degrees of freedom, changed targets or further physical relations may fall outside the bound."},out,indent=2)
+print("PASS_7000_SIGN_QUERY_FLOOR",result)
diff --git a/research/fixed-caller-query-and-host-limits/replay/connected7002/COALESCING-WINDOW.json b/research/fixed-caller-query-and-host-limits/replay/connected7002/COALESCING-WINDOW.json
new file mode 100644
index 0000000000..975d44be4c
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/connected7002/COALESCING-WINDOW.json
@@ -0,0 +1,109 @@
+{
+  "status": "PASS_UNIFORM_NEGATIVITY",
+  "root_sha256": "be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34",
+  "native_invoice_sha256": "87a41b13bdd9248d538805f76a970f51335567845dfc0070698b6979a08b70d6",
+  "engine_sha256": "60a743d13f668ef86db4b8215b4d5d04430a671ba6f1fe06d9c1c4c3dfe86da5",
+  "interval": [
+    "181350941/50000000000",
+    "1/100"
+  ],
+  "T": {
+    "1": 252,
+    "2": 144,
+    "3": 72,
+    "4": 1962,
+    "5": 306,
+    "6": 54,
+    "7": 180,
+    "8": 720,
+    "9": 6774,
+    "17": 312,
+    "25": 520,
+    "33": 416,
+    "41": 312,
+    "49": 520,
+    "57": 416,
+    "65": 520,
+    "73": 416,
+    "81": 104,
+    "145": 104
+  },
+  "P": {
+    "1": 42396,
+    "2": 8172,
+    "3": 8802,
+    "4": 1980,
+    "5": 2736,
+    "6": 126,
+    "7": 162,
+    "8": 330,
+    "16": 208,
+    "24": 520,
+    "32": 416,
+    "40": 312,
+    "48": 520,
+    "56": 416,
+    "64": 312,
+    "72": 208,
+    "80": 104,
+    "144": 104
+  },
+  "rank_surplus": 760,
+  "optimal_degrees": [
+    18,
+    9,
+    7,
+    7,
+    8,
+    6,
+    6,
+    7,
+    4,
+    4,
+    5,
+    3,
+    3,
+    4,
+    1,
+    1,
+    1,
+    0,
+    0,
+    3,
+    0,
+    0,
+    4,
+    2,
+    2,
+    6,
+    3,
+    3,
+    7,
+    5,
+    5,
+    9,
+    6,
+    6,
+    10,
+    8,
+    8,
+    0
+  ],
+  "left_endpoint_margin": [
+    "-1947598170433159634755026544042426492172302230996912227162842431465986628465463463/50000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "-243449771304144954344378318005303311521537778874614028395355303933248328556043649/6250000000000000000000000000000000000000000000000000000000000000000000000000000"
+  ],
+  "left_endpoint_margin_float": [
+    -38.95196340866319,
+    -38.95196340866319
+  ],
+  "uniform_derivative_upper_interval": [
+    "-4959594734641481397754468477409242373438945362069616735797101018360054020832519343721/25000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "-9919189469282962795508936954818484746877890724139233471594202036720108041664860049897/50000000000000000000000000000000000000000000000000000000000000000000000000000000"
+  ],
+  "uniform_derivative_upper_float": [
+    -198383.78938565924,
+    -198383.78938565924
+  ],
+  "scope": "Fixed104-port F+H1 supplier,18 full paid/helper invoices,3thinH1 perport,and181 idle incidences optimally coalesced in the fixed38 coordinate-role relaxation. Ordinary implementation work is optimistically free. Not a general root/native obstruction."
+}
diff --git a/research/fixed-caller-query-and-host-limits/replay/connected7002/COST.json b/research/fixed-caller-query-and-host-limits/replay/connected7002/COST.json
new file mode 100644
index 0000000000..71ffcc064f
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/connected7002/COST.json
@@ -0,0 +1,163 @@
+{
+  "3": {
+    "roles": 8,
+    "stages": 3,
+    "events": 191,
+    "event_counts": {
+      "ADD": 87,
+      "SCALE": 28,
+      "SWAP": 44,
+      "LAMBDA": 20,
+      "QUERY": 3,
+      "HOST": 3,
+      "IDLE_ONE": 6
+    },
+    "ordinary_events": 179,
+    "target_histogram": {
+      "9": 5,
+      "17": 2,
+      "25": 1
+    },
+    "target_rank_mass": 104,
+    "paid_outside_native": {
+      "8": 6,
+      "1": 3
+    },
+    "paid_outside_native_mass": 51,
+    "ordinary_scalar_denominator_lcm": "6",
+    "max_abs_ordinary_scalar": "3",
+    "native_gates": {
+      "selected_complex": {
+        "comparison_kappa": "0.003125804",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.4843080869728003788800832613933994107627318594142812410079",
+        "allowance_above_two_H8": "1.5879696527372231758936282716102426015761391318128899249442",
+        "direct_baseline_signed_moment": "-1.236091041788330472319115185169272195271582604561330225167"
+      },
+      "pending_complex_6936": {
+        "comparison_kappa": "0.00362701882",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.4552303348641031828548299485292027354066579477326847872936",
+        "allowance_above_two_H8": "1.5754511794416558860023781546789599010436945883769335958376",
+        "direct_baseline_signed_moment": "-1.273646461675032341992865535963120296868916234869199212487"
+      },
+      "ordinary_BIT_6726": {
+        "comparison_kappa": "0.00376669",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.4471353689880173282352372261088732550512243452946422105081",
+        "allowance_above_two_H8": "1.5719676360206178990526638106345372230747882511325091855385",
+        "direct_baseline_signed_moment": "-1.284097091938146302842008568096388330775635246602472443385"
+      }
+    }
+  },
+  "9": {
+    "roles": 20,
+    "stages": 9,
+    "events": 776,
+    "event_counts": {
+      "ADD": 339,
+      "SCALE": 84,
+      "SWAP": 245,
+      "LAMBDA": 44,
+      "QUERY": 3,
+      "HOST": 9,
+      "IDLE_ONE": 52
+    },
+    "ordinary_events": 712,
+    "target_histogram": {
+      "9": 1,
+      "17": 4,
+      "25": 6,
+      "33": 6,
+      "41": 2,
+      "73": 1
+    },
+    "target_rank_mass": 580,
+    "paid_outside_native": {
+      "8": 52,
+      "1": 3
+    },
+    "paid_outside_native_mass": 419,
+    "ordinary_scalar_denominator_lcm": "6",
+    "max_abs_ordinary_scalar": "3",
+    "native_gates": {
+      "selected_complex": {
+        "comparison_kappa": "0.003125804",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.495701886657033145636409723610846431616109791663676616169",
+        "allowance_above_two_H8": "1.5993634524214559426499547338276896224295170640622853001053",
+        "direct_baseline_signed_moment": "-3.605728928206896516150407395550793398134346423439432299053"
+      },
+      "pending_complex_6936": {
+        "comparison_kappa": "0.00362701882",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.4331797209823169335965523056515178829992190357283974839384",
+        "allowance_above_two_H8": "1.5534005655598696367441005118012750486362556763726462924824",
+        "direct_baseline_signed_moment": "-4.019394909961173269303095393788524562273698912646183367658"
+      },
+      "ordinary_BIT_6726": {
+        "comparison_kappa": "0.00376669",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.4157826512019132391499231525983617384070475822265108385921",
+        "allowance_above_two_H8": "1.5406149182345138099673497371240257064306114880643778136225",
+        "direct_baseline_signed_moment": "-4.134465735889375710293852365883768642124496607420599677397"
+      }
+    }
+  },
+  "18": {
+    "roles": 38,
+    "stages": 18,
+    "events": 2370,
+    "event_counts": {
+      "ADD": 1041,
+      "SCALE": 189,
+      "SWAP": 858,
+      "LAMBDA": 80,
+      "QUERY": 3,
+      "HOST": 18,
+      "IDLE_ONE": 181
+    },
+    "ordinary_events": 2168,
+    "target_histogram": {
+      "9": 3,
+      "17": 3,
+      "25": 5,
+      "33": 4,
+      "41": 3,
+      "49": 5,
+      "57": 4,
+      "65": 5,
+      "73": 4,
+      "81": 1,
+      "145": 1
+    },
+    "target_rank_mass": 1774,
+    "paid_outside_native": {
+      "8": 181,
+      "1": 3
+    },
+    "paid_outside_native_mass": 1451,
+    "ordinary_scalar_denominator_lcm": "2",
+    "max_abs_ordinary_scalar": "5/2",
+    "native_gates": {
+      "selected_complex": {
+        "comparison_kappa": "0.003125804",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.24273344786332293410495368703241064490922674815243677043",
+        "allowance_above_two_H8": "1.3463950136277457311184986972492538357226340205510454543663",
+        "direct_baseline_signed_moment": "-11.76488975470057683986702344951343095699258763008118182141",
+        "retained_F_plus_H1_cost_per_port": "17.6703991996227234141399345320028861136206598559402746515482",
+        "retained_F_plus_H1_excess": "0.4276657517594004800349808449704754687114331077878378811182"
+      },
+      "pending_complex_6936": {
+        "comparison_kappa": "0.00362701882",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.1313409028543326190363539979855487854614834640682540794906",
+        "allowance_above_two_H8": "1.2515617474318853221839022041353059510985201047125028880346",
+        "direct_baseline_signed_moment": "-13.47188854622606420068976032556449288022663811517494801538",
+        "retained_F_plus_H1_cost_per_port": "17.6914424603474237437422676600591888259630220558867211828222",
+        "retained_F_plus_H1_excess": "0.5601015574930911247059136620736400405015385918184671033316"
+      },
+      "ordinary_BIT_6726": {
+        "comparison_kappa": "0.00376669",
+        "max_native_signed_cost_per_port_per_call_before_ordinary_outer": "17.1003547369028679713425656375523992710112972290322356119039",
+        "allowance_above_two_H8": "1.2251870039354685421599922220780632390348611348701025869343",
+        "direct_baseline_signed_moment": "-13.94663392916156624112014000259486169737249957233815343518",
+        "retained_F_plus_H1_cost_per_port": "17.6973009591869876138450219486899064090893373235044463699870",
+        "retained_F_plus_H1_excess": "0.5969462222841196425024563111375071380780400944722107580831"
+      }
+    }
+  }
+}
diff --git a/research/fixed-caller-query-and-host-limits/replay/connected7002/idle_coalescing.py b/research/fixed-caller-query-and-host-limits/replay/connected7002/idle_coalescing.py
new file mode 100644
index 0000000000..66091e8538
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/connected7002/idle_coalescing.py
@@ -0,0 +1,192 @@
+#!/usr/bin/env python3
+"""Exact eligibility-compression certificate for the optimistic L18 idle bill.
+Standard library; rational transcendental bounds; checks stay active under -O.
+"""
+from fractions import Fraction as Q
+from functools import lru_cache
+from itertools import combinations
+from pathlib import Path
+from hashlib import sha256
+from decimal import Decimal, localcontext, ROUND_FLOOR, ROUND_CEILING
+from collections import Counter
+import json
+import argparse
+
+HERE=Path(__file__).resolve().parent
+PIN_DIGESTS={
+ 'root_L18.json':'be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34',
+ 'caller_L18.json':'f4090329f219edd493b4ca592128521e867a355fb528556b15201e759783568b',
+ 'inputs/base_invoice.json':'87a41b13bdd9248d538805f76a970f51335567845dfc0070698b6979a08b70d6',
+}
+K=Q('0.00362701882')
+REQUIRED=Q('10.081828') # Checked below against the source-bound rational full bill.
+
+
+def need(ok,label):
+    if not ok:raise ValueError(label)
+
+
+def log_series(z,terms=40):
+    """2atanh(z), z in[0,1/3], exact positive-series lower/tail upper."""
+    need(0<=z<=Q(1,3),'log range reduction')
+    lo=sum((2*z**(2*j+1)/Q(2*j+1) for j in range(terms)),Q(0))
+    tail=2*z**(2*terms+1)/(Q(2*terms+1)*(1-z*z))
+    return lo,lo+tail
+
+
+@lru_cache(None)
+def log_bounds(n):
+    e=n.bit_length()-1;p=2**e
+    a,b=log_series(Q(1,3));c,d=log_series(Q(n-p,n+p))
+    return e*a+c,e*b+d
+
+
+def exp_neg_bounds(x):
+    """Alternating Taylor series bounds for exp(-x), 0<=x<1."""
+    need(0<=x<1,'exponential alternating-series range')
+    term=Q(1);s=term
+    for j in range(1,31):term*=(-x)/j;s+=term
+    hi=s # even partial sum is an upper bound
+    term*=(-x)/31
+    return s+term,hi
+
+
+@lru_cache(None)
+def power_bounds(n):
+    if not n:return Q(0),Q(0)
+    need(isinstance(n,int) and n>0,'positive integral child rank')
+    ll,lu=log_bounds(n)
+    low=exp_neg_bounds(K*lu)[0];high=exp_neg_bounds(K*ll)[1]
+    return n*low,n*high
+
+
+def cost_bounds(degree):
+    return power_bounds(8*degree)
+
+
+def histogram_bounds(histogram):
+    need(all(int(r)>0 and isinstance(c,int) and c>=0 for r,c in histogram.items()),'nonnegative invoice counts')
+    return (sum((c*power_bounds(int(r))[0] for r,c in histogram.items()),Q(0)),
+            sum((c*power_bounds(int(r))[1] for r,c in histogram.items()),Q(0)))
+
+
+def required_savings_bounds(caller,invoice):
+    counts=Counter(e[0] for e in caller['events'])
+    need(counts['HOST']==18 and counts['IDLE_ONE']==181 and counts['QUERY']==3,'source-bound recursive census')
+    target=Counter(1+8*m.bit_count() for m in caller['masks'])
+    tl,tu=histogram_bounds(target)
+    pl,pu=histogram_bounds(invoice['local_paid'])
+    hl,hu=histogram_bounds(invoice['helpers'])
+    fl,fu=(pl-hu)/104+1,(pu-hl)/104+1
+    el,eu=power_bounds(8)
+    return 18*fl-tu+181*el+3,18*fu-tl+181*eu+3
+
+
+def savings_bounds(degrees):
+    l1,u1=cost_bounds(1);D=sum(degrees)
+    return D*l1-sum(cost_bounds(d)[1] for d in degrees),D*u1-sum(cost_bounds(d)[0] for d in degrees)
+
+
+def decimal(q,rounding=ROUND_FLOOR):
+    with localcontext() as c:
+        c.prec=45;c.rounding=rounding
+        return str(Decimal(q.numerator)/Decimal(q.denominator))
+
+
+def allowed_host_pairs(mask,eligibility):
+    # Compression-stable idle sets imply that a host set is downward closed
+    # under STRICT eligibility inclusion. Equal-eligibility roles need no tie.
+    return [list(h) for h in combinations(mask,2)
+            if all(not (eligibility[j]<eligibility[i] and i in h and j not in h)
+                   for i in mask for j in mask)]
+
+
+def degrees_from_hosts(masks,hosts):
+    need(len(hosts)==len(masks),'stage count')
+    for m,h in zip(masks,hosts):need(len(h)==2 and len(set(h))==2 and set(h)<=set(m),'two eligible host roles')
+    idle=[[role for role in m if role not in h] for m,h in zip(masks,hosts)]
+    return validate_idle_assignment(masks,idle)
+
+
+def validate_idle_assignment(masks,idle):
+    need(len(idle)==len(masks),'idle-stage count')
+    for m,fields in zip(masks,idle):
+        need(len(fields)==len(set(fields)),'independent idle incidences are distinct')
+        need(set(fields)<=set(m),'every idle role is eligible at that stage')
+        need(len(fields)==len(m)-2,'exact stage idle count must be retained')
+    degrees=[sum(role in fields for fields in idle) for role in range(38)]
+    need(sum(degrees)==181,'all181 idle actions are retained')
+    return degrees
+
+
+def validate_compressed_hosts(hosts,allowed):
+    need(len(hosts)==len(allowed),'compressed stage count')
+    for pair,possibilities in zip(hosts,allowed):
+        need(set(pair) in [set(p) for p in possibilities],'hostset must be downward-closed under eligibility inclusion')
+
+
+def main():
+    parser=argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--package-root',type=Path,default=HERE)
+    parser.add_argument('--receipt',type=Path,help='Optional retained JSON receipt to compare; never written')
+    args=parser.parse_args();base=args.package_root.resolve()
+    for name,digest in PIN_DIGESTS.items():
+        need(sha256((base/name).read_bytes()).hexdigest()==digest,'source hash '+name)
+    root=json.loads((base/'root_L18.json').read_text())
+    caller=json.loads((base/'caller_L18.json').read_text())
+    invoice=json.loads((base/'inputs/base_invoice.json').read_text())
+    required_lo,required_hi=required_savings_bounds(caller,invoice)
+    need(required_lo>REQUIRED,'source-bound invoice certifies conservative required saving')
+    masks=[s['mask'] for s in root['stages']]
+    need(root['n']==38 and len(masks)==18,'L18 source dimensions')
+    need(all(len(set(m))==len(m) for m in masks),'mask roles are independent and distinct')
+    eligibility=[{s for s,m in enumerate(masks) if r in m} for r in range(38)]
+    need([sum(1<<s for s in e) for e in eligibility]==caller['masks'],'caller/root mask binding')
+    caps=list(map(len,eligibility));need(sum(caps)==217 and sum(len(m)-2 for m in masks)==181,'exact idle mass')
+    allowed=[allowed_host_pairs(m,eligibility) for m in masks]
+    need([len(x) for x in allowed]==[1]*8+[2]+[1]*9,'compression forces17 stages and2 bridge cases')
+    need({tuple(sorted(x)) for x in allowed[8]}=={(16,37),(19,37)},'two bridge host pairs')
+    host0=[x[0] for x in allowed];host1=[x[0] for x in allowed]
+    host0[8]=[16,37];host1[8]=[19,37]
+    validate_compressed_hosts(host0,allowed);validate_compressed_hosts(host1,allowed)
+    d0=degrees_from_hosts(masks,host0);d1=degrees_from_hosts(masks,host1)
+    need(all(d0[r]==d1[r] for r in range(38) if r not in(16,19)),'only two bridge degrees differ')
+    need((d0[16],d0[19],d1[16],d1[19])==(1,3,2,2),'concavity comparison is(1,3)vs(2,2)')
+    # Since0<1-K<1, concavity gives f(1)+f(3)<=2f(2), selecting d0.
+    need(0<K<1,'strict concavity parameter')
+    lo,hi=savings_bounds(d0)
+    need(hi<REQUIRED,'even optimum coalescing is below required full-bill saving')
+    need(hi-lo<Q(1,10**30),'rational interval precision')
+    # Controls: illegal host role, omitted idle action, and an optimistic
+    # degree-only allocation that cannot satisfy the stage incidence rules.
+    bad=[h[:] for h in host0];bad[0]=[2,37]
+    try:degrees_from_hosts(masks,bad)
+    except ValueError:pass
+    else:raise ValueError('ineligible host mutation accepted')
+    bad_idle=[[role for role in m if role not in h] for m,h in zip(masks,host0)]
+    bad_idle[0].pop() # Delete one real idle incidence from the certified optimum.
+    try:validate_idle_assignment(masks,bad_idle)
+    except ValueError:pass
+    else:raise ValueError('omitted idle incidence mutation accepted')
+    bad_closed=[h[:] for h in host0];bad_closed[0]=[0,1]
+    degrees_from_hosts(masks,bad_closed) # Valid ordinary assignment; compression alone excludes it.
+    try:validate_compressed_hosts(bad_closed,allowed)
+    except ValueError:pass
+    else:raise ValueError('non-downward-closed hostset mutation accepted')
+    left=181;relaxed=[]
+    for cap in sorted(caps,reverse=True):v=min(cap,left);relaxed.append(v);left-=v
+    rlo,rhi=savings_bounds(relaxed)
+    need(rlo>REQUIRED,'degree-only relaxation must remain visibly insufficient')
+    report={'status':'OPTIMISTIC_COALESCING_ONLY_ROUTE_CLOSED','kappa_probe':str(K),'independent_roles':38,'stages':18,'idle_actions':181,
+            'host_roles_by_stage':host0,'optimal_degrees':d0,'optimal_degree_histogram':dict(sorted(Counter(d0).items())),
+            'optimal_savings_interval':[decimal(lo),decimal(hi,ROUND_CEILING)],
+            'required_saving_interval':[decimal(required_lo),decimal(required_hi,ROUND_CEILING)],
+            'required_saving_lower':decimal(REQUIRED),'shortfall_lower':decimal(required_lo-hi),
+            'degree_only_upper_interval':[decimal(rlo),decimal(rhi,ROUND_CEILING)],'candidate_native_per_stage':'17.69144246035','uncoalesced_gate_per_stage':'17.13134090285',
+            'proof':'eligibility union/intersection compression plus two exact bridge cases; rational ln/exp enclosures','scope':'fixed38 coordinate roles;181 idles;two coordinate hosts perstage;free all-occurrence same-role merging;no noncoordinate or general native obstruction;no supplier or kappa claim'}
+    if args.receipt:
+        need(json.loads(json.dumps(report))==json.loads(args.receipt.read_text()),'retained receipt matches recomputation')
+    print(json.dumps(report,sort_keys=True))
+    print('PASS_L18_IDLE_COALESCING_BOUND optimum_savings_lt_9.707290 required_gt_10.081828 independent_roles=38 controls=3_REJECT degree_only_relaxation=DISTINGUISHED')
+
+if __name__=='__main__':main()
diff --git a/research/fixed-caller-query-and-host-limits/replay/connected7002/inputs/base_invoice.json b/research/fixed-caller-query-and-host-limits/replay/connected7002/inputs/base_invoice.json
new file mode 100644
index 0000000000..f2a6958ee2
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/connected7002/inputs/base_invoice.json
@@ -0,0 +1,61 @@
+{
+ "helpers": {
+  "1": 14,
+  "2": 8,
+  "3": 4,
+  "4": 109,
+  "5": 17,
+  "6": 3,
+  "7": 10,
+  "8": 40,
+  "9": 359
+ },
+ "kappa_literal": "0.00337180047549672",
+ "local_paid": {
+  "1": 2234,
+  "2": 454,
+  "3": 489,
+  "4": 110,
+  "5": 152,
+  "6": 7,
+  "7": 9,
+  "8": 1
+ },
+ "paid": {
+  "1": 40524,
+  "16": 208,
+  "2": 8172,
+  "24": 208,
+  "3": 8802,
+  "32": 208,
+  "4": 1980,
+  "40": 208,
+  "48": 208,
+  "5": 2736,
+  "56": 208,
+  "6": 126,
+  "64": 208,
+  "7": 162,
+  "8": 226
+ },
+ "targets": {
+  "1": 356,
+  "145": 104,
+  "17": 208,
+  "2": 144,
+  "25": 208,
+  "3": 72,
+  "33": 208,
+  "4": 1962,
+  "41": 208,
+  "49": 208,
+  "5": 306,
+  "57": 208,
+  "6": 54,
+  "65": 208,
+  "7": 180,
+  "73": 208,
+  "8": 720,
+  "9": 6670
+ }
+}
\ No newline at end of file
diff --git a/research/fixed-caller-query-and-host-limits/replay/connected7002/root_L18.json b/research/fixed-caller-query-and-host-limits/replay/connected7002/root_L18.json
new file mode 100644
index 0000000000..e2d43655b2
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/connected7002/root_L18.json
@@ -0,0 +1 @@
+{"n": 38, "N": 39, "X": [["1", "1", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "1", "1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "2", "0", "0", "1", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "2", "0", "0", "1", "1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], ["1", "2", 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26], "mask": [0, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]}, {"units": [27, 28], "mask": [0, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]}, {"units": [29, 30], "mask": [0, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]}, {"units": [31, 32], "mask": [0, 28, 29, 30, 31, 32, 33, 34, 35, 36]}, {"units": [33, 34], "mask": [0, 31, 32, 33, 34, 35, 36]}, {"units": [35, 36], "mask": [0, 31, 32, 33, 34, 35, 36]}, {"units": [37, 38], "mask": [0, 34, 35, 36]}]}
diff --git a/research/fixed-caller-query-and-host-limits/replay/construct_7002_chronological_idle_groups.py b/research/fixed-caller-query-and-host-limits/replay/construct_7002_chronological_idle_groups.py
new file mode 100644
index 0000000000..897ef04720
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/construct_7002_chronological_idle_groups.py
@@ -0,0 +1,92 @@
+"""Compile actual commuting coordinate idle groups of the connected L18 root."""
+from collections import Counter,defaultdict
+from fractions import Fraction as F
+from hashlib import sha256
+from pathlib import Path
+import importlib.util
+import json
+
+root=Path(__file__).resolve().parent
+package=root/"connected7002"
+source=package/"root_L18.json"
+assert sha256(source.read_bytes()).hexdigest()=="be4a2beed3a40de6d2c5dcc6e4f25f3c2a4375551b70e63fb0e9a03041db6a34"
+spec=json.loads(source.read_bytes())
+n=spec["n"]
+X,Y=([list(map(F,row)) for row in spec[label]] for label in ("X","Y"))
+stages=spec["stages"]
+boundaries={max(stage["units"])+1:j for j,stage in enumerate(stages)}
+masks=[set(stage["mask"]) for stage in stages]
+
+def clean_role(role,unit):
+    return not X[unit][role] and not Y[unit][role]
+
+# At a stage boundary r is an actual idle summand when its coordinate
+# projector kills the two HOST directions on both sides.
+eligible={(role,j) for j,stage in enumerate(stages) for role in masks[j]
+          if all(clean_role(role,u) for u in stage["units"])}
+assert len(eligible)<=sum(len(mask)-2 for mask in masks)
+groups=defaultdict(list)
+for role,j in sorted(eligible):
+    cut=max(stages[j]["units"])+1
+    # Pull the idle to the earliest cut in the current untouched run.
+    previous=max((u+1 for u in range(cut) if not clean_role(role,u)),default=0)
+    assert all(clean_role(role,u) for u in range(previous,cut))
+    groups[role,previous].append(j)
+
+paid=Counter({8:sum(len(mask)-2 for mask in masks)-len(eligible)})
+for labels in groups.values():
+    paid[8*len(labels)]+=1
+assert sum(r*c for r,c in paid.items())==8*sum(len(mask)-2 for mask in masks)
+
+# Independent value replay. At each gap, compare the original stream and the
+# relocated stream on every column, in both sign sectors and two unrelated
+# positive variable settings. Universal equality follows from the per-crossing
+# zero row/column checks, not from these finite evaluations.
+def replay(sign,variables,grouped):
+    A=[[F(i==j) for j in range(n)] for i in range(n)]
+    def scale(role,c):
+        A[role]=[c*v for v in A[role]]
+    moved=defaultdict(list)
+    if grouped:
+        for (role,cut),labels in groups.items():
+            factor=1
+            for j in labels:
+                factor*=variables[j]
+            moved[cut].append((role,factor))
+    for cut in range(len(X)+1):
+        if cut in boundaries:
+            j=boundaries[cut]
+            for role in masks[j]:
+                if not grouped or (role,j) not in eligible:
+                    scale(role,variables[j])
+        for role,amount in moved[cut]:
+            scale(role,amount)
+        if cut<len(X) and sign!=1:
+            x,y=X[cut],Y[cut]
+            row=[sum(y[i]*A[i][j] for i in range(n) if y[i]) for j in range(n)]
+            for i,scalar in enumerate(x):
+                if scalar:
+                    A[i]=[v+(sign-1)*scalar*z for v,z in zip(A[i],row)]
+    return A
+
+for sign in (-1,1):
+    for shift in (2,13):
+        variables=[(j+shift)**2+1 for j in range(len(stages))]
+        assert replay(sign,variables,False)==replay(sign,variables,True)
+
+ps=importlib.util.spec_from_file_location("power",package/"idle_coalescing.py")
+power=importlib.util.module_from_spec(ps)
+ps.loader.exec_module(power)
+power.K=F(1,200)
+mass=sum(paid.values())
+base_jobs=sum(len(mask)-2 for mask in masks)
+saving_lo=base_jobs*power.power_bounds(8)[0]-sum(c*power.power_bounds(r)[1] for r,c in paid.items())
+saving_hi=base_jobs*power.power_bounds(8)[1]-sum(c*power.power_bounds(r)[0] for r,c in paid.items())
+assert saving_lo>0
+with (root/"PR7002-CHRONOLOGICAL-IDLE-GROUPS.json").open("x") as f:
+    json.dump({"stage_count":len(stages),"old_jobs":base_jobs,"new_jobs":mass,"paid_idle_rank_profile":paid,
+               "commuting_groups":[{"role":role,"cut":cut,"stages":labels} for (role,cut),labels in sorted(groups.items())],
+               "per_port_saving_at_005":[power.decimal(saving_lo),power.decimal(saving_hi,"ROUND_CEILING")],
+               "scope":"Constructed commuting normalized root schedule, universal over stage variables. Grouped jobs require the retained whole-mask IDLE tariff and physical adapters. No native price reduction, outer admission or kappa claim."},f,indent=2)
+print("old jobs",base_jobs,"grouped jobs",mass,"histogram",dict(sorted(paid.items())),
+      "per-port savings",float(saving_lo),"104-port savings",float(104*saving_lo),flush=True)
diff --git a/research/fixed-caller-query-and-host-limits/replay/construct_7002_noncoordinate_idle.py b/research/fixed-caller-query-and-host-limits/replay/construct_7002_noncoordinate_idle.py
new file mode 100644
index 0000000000..0c067006c8
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/construct_7002_noncoordinate_idle.py
@@ -0,0 +1,124 @@
+"""Construct persistent noncoordinate idle projectors and replay their relocation."""
+from collections import Counter, defaultdict
+from fractions import Fraction as F
+from pathlib import Path
+import json
+
+root=Path(__file__).resolve().parent
+base=root/"construct_7002_chronological_idle_groups.py"
+ns={"__file__":str(base)}
+exec(base.read_text().split("def clean_role")[0],ns)
+n,X,Y,stages,masks,boundaries=(ns[k] for k in ("n","X","Y","stages","masks","boundaries"))
+def dot(a,b):
+    return sum(x*y for x,y in zip(a,b) if x and y)
+
+def nullspace(constraints,indices):
+    width=len(indices)
+    pivots={}
+    for row in constraints:
+        v=[row[i] for i in indices]
+        for j in range(width):
+            c=v[j]
+            if not c:
+                continue
+            if j not in pivots:
+                pivots[j]=[x/c for x in v]
+                break
+            v=[x-c*y for x,y in zip(v,pivots[j])]
+    result=[]
+    for free in range(width):
+        if free in pivots:
+            continue
+        u=[F(i==free) for i in range(width)]
+        for pivot,row in sorted(pivots.items(),reverse=True):
+            u[pivot]=-dot(row,u)
+        v=[F(0)]*n
+        for i,x in zip(indices,u):
+            v[i]=x
+        result.append(v)
+    return result
+
+def paired(a,b):
+    while a and b:
+        pivot=next(((i,j,dot(v,u)) for i,v in enumerate(a) for j,u in enumerate(b) if dot(v,u)),None)
+        if pivot is None:
+            break
+        i,j,c=pivot
+        v=a.pop(i)
+        u=[z/c for z in b.pop(j)]
+        a=[[x-dot(u,w)*y for x,y in zip(w,v)] for w in a]
+        b=[[x-dot(v,w)*y for x,y in zip(w,u)] for w in b]
+        yield v,u
+
+intervals=sorted(((i,j) for i in range(len(stages)) for j in range(i+1,len(stages))),
+                 key=lambda t:(t[0]-t[1],t[0]))
+chosen=[]
+for i,j in intervals:
+    support=sorted(set.intersection(*masks[i:j+1]))
+    if not support:
+        continue
+    units=range(min(stages[i]["units"]),max(stages[j]["units"])+1)
+    overlaps=[(v,u) for a,b,v,u in chosen if max(i,a)<=min(j,b)]
+    vectors=nullspace([Y[k] for k in units]+[u for _,u in overlaps],support)
+    duals=nullspace([X[k] for k in units]+[v for v,_ in overlaps],support)
+    for v,u in paired(vectors,duals):
+        assert dot(v,u)==1
+        assert all(dot(v,Y[k])==dot(u,X[k])==0 for k in units)
+        assert all(dot(v,old_u)==dot(u,old_v)==0 for old_v,old_u in overlaps)
+        overlaps.append((v,u))
+        chosen.append((i,j,v,u))
+# Replay explicit projection products. At stage j remove grouped projectors
+# from the diagonal dilation and issue their product at the first stage.
+def replay(sign,weights,grouped):
+    A=[[F(i==j) for j in range(n)] for i in range(n)]
+    def correction(v,u,scale,input_rows):
+        coeff=[dot(u,column) for column in zip(*input_rows)]
+        for r,rv in enumerate(v):
+            if rv:
+                A[r]=[a+scale*rv*c for a,c in zip(A[r],coeff)]
+    for cut in range(len(X)+1):
+        if cut in boundaries:
+            stage=boundaries[cut]
+            before=[row[:] for row in A]
+            d=weights[stage]
+            for i in masks[stage]:
+                A[i]=[d*x for x in before[i]]
+            if grouped:
+                for start,end,v,u in chosen:
+                    if start<=stage<=end:
+                        correction(v,u,1-d,before)
+                for start,end,v,u in chosen:
+                    if start==stage:
+                        value=1
+                        for j in range(start,end+1):
+                            value*=weights[j]
+                        correction(v,u,value-1,A)
+        if cut<len(X) and sign!=1:
+            correction(X[cut],Y[cut],sign-1,A)
+    return A
+
+for sign in (-1,1):
+    for shift in (3,17):
+        weights=[(j+shift)**2+1 for j in range(len(stages))]
+        assert replay(sign,weights,False)==replay(sign,weights,True)
+profile=Counter(8*(j-i+1) for i,j,_,_ in chosen)
+base_jobs=sum(len(mask)-2 for mask in masks)
+profile[8]=base_jobs-sum(r*c//8 for r,c in profile.items())
+assert profile[8]>=0
+assert sum(r*c for r,c in profile.items())==base_jobs*8
+import importlib.util
+ps=importlib.util.spec_from_file_location("power",root/"connected7002"/"idle_coalescing.py")
+power=importlib.util.module_from_spec(ps)
+ps.loader.exec_module(power)
+power.K=F(1,200)
+low=base_jobs*power.power_bounds(8)[0]-sum(c*power.power_bounds(r)[1] for r,c in profile.items())
+high=base_jobs*power.power_bounds(8)[1]-sum(c*power.power_bounds(r)[0] for r,c in profile.items())
+coordinate=json.loads((root/"PR7002-CHRONOLOGICAL-IDLE-GROUPS.json").read_text())
+advantage=104*(low-F(coordinate["per_port_saving_at_005"][1]))
+with (root/"PR7002-NONCOORDINATE-IDLE-WORD.json").open("x") as f:
+    json.dump({"idle_rank_profile":profile,"base_jobs":base_jobs,"projectors":[[i,j,list(map(str,v)),list(map(str,u))] for i,j,v,u in chosen],
+               "per_port_saved_interval":[power.decimal(low),power.decimal(high,"ROUND_CEILING")],
+               "104_port_saving_over_coordinate_lower":power.decimal(advantage),
+               "scope":"Exact normalized role-level relocation by orthogonal projectors, with all-column rational controls. Requires physical whole-idle composition, ordinary map costs, and the native HOST construction."},f,indent=2)
+print("projectors",len(chosen),"profile",dict(profile),"old",base_jobs,"new",sum(profile.values()),
+      "104 port extra savings over coordinate",float(advantage),flush=True)
diff --git a/research/fixed-caller-query-and-host-limits/replay/jclib_6936.py b/research/fixed-caller-query-and-host-limits/replay/jclib_6936.py
new file mode 100644
index 0000000000..48a55ab03a
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/jclib_6936.py
@@ -0,0 +1,331 @@
+"""Library of check_caller_blocks.py: constant-block rewrite of the joint caller (idea and method: CubeJerry #6912; the code is this package's).
+
+Mathematics.  A constant block is a maximal run of ADD / SCALE(-1) / SWAP events of one port type between two
+nonconstant events of that type (LAMBDA, IDLE_ONE, QUERY) or a joint contact J.  Applied to the role vector it is
+left-multiplication by one integer matrix M in GL_n(Z) (n = 40 for type A, 38 for type B).  Replace the block by any other
+constant block with the same matrix M: then, by induction over the anchors, the whole caller is the same operator for every
+substitution of the anchor operators (the anchors are not touched and each block is a left factor between them).
+Type A rows (0..39) and type B rows (40..77) are disjoint, so an A block commutes with every B event: its position inside the
+window between the same two A-anchors is immaterial.  Nothing but the constant-gate count changes."""
+import json, random
+from fractions import Fraction as Q
+
+CONST = ('ADD', 'SCALE', 'SWAP')
+OFF = {'A': 0, 'B': 40}
+NR = {'A': 40, 'B': 38}
+
+
+def need(ok, msg):
+    if not ok:
+        raise ValueError(msg)
+
+
+def ev_roles(e):
+    """role indices an event reads or writes (joint indexing); J returns both types' roles"""
+    if e[0] == 'J':
+        return list(e[2]) + list(e[3][:2])
+    op = e[1]
+    if op in ('ADD', 'SWAP', 'QUERY'):
+        return [e[2], e[3]]
+    return [e[2]]
+
+
+def check_disjoint(C):
+    """every A event touches only roles 0..39, every B event only 40..77 (J is the only coupling)"""
+    for e in C['events']:
+        if e[0] == 'A':
+            need(all(0 <= r < 40 for r in ev_roles(e)), 'A event leaves its roles: %r' % (e,))
+        elif e[0] == 'B':
+            need(all(40 <= r < 78 for r in ev_roles(e)), 'B event leaves its roles: %r' % (e,))
+        else:
+            need(e[0] == 'J', 'unknown tag')
+    return True
+
+
+def is_const(e, ty):
+    return e[0] == ty and e[1] in CONST
+
+
+def is_anchor(e, ty):
+    """nonconstant event of the type's own stream: its nonconstant events and every joint contact"""
+    return (e[0] == ty and e[1] not in CONST) or e[0] == 'J'
+
+
+def slots(events, ty):
+    """list of (indices of the constant events of slot k); slot k lies between anchors k-1 and k.  Also returns the
+    global index of the anchor that closes each slot (len(events) for the last)."""
+    out, closes, cur = [], [], []
+    for i, e in enumerate(events):
+        if is_const(e, ty):
+            cur.append(i)
+        elif is_anchor(e, ty):
+            out.append(cur); closes.append(i); cur = []
+    out.append(cur); closes.append(len(events))
+    return out, closes
+
+
+def apply_const(rows, e):
+    """act on the matrix of accumulated rows exactly as the caller replay does: rows[i] += c*rows[j] etc (joint indices)"""
+    op = e[1]
+    if op == 'ADD':
+        c = Q(e[4]); need(c.denominator == 1, 'integer ADD'); c = int(c)
+        rows[e[2]] = [a + c * b for a, b in zip(rows[e[2]], rows[e[3]])]
+    elif op == 'SCALE':
+        c = Q(e[3]); need(c == -1, 'SCALE -1'); rows[e[2]] = [-a for a in rows[e[2]]]
+    elif op == 'SWAP':
+        rows[e[2]], rows[e[3]] = rows[e[3]], rows[e[2]]
+    else:
+        raise ValueError('nonconstant')
+
+
+def block_matrix(block, ty):
+    """exact integer matrix of a constant block (list of full joint events), n x n in type-local indices"""
+    n, off = NR[ty], OFF[ty]
+    rows = {off + i: [int(i == j) for j in range(n)] for i in range(n)}
+    for e in block:
+        need(e[0] == ty and e[1] in CONST, 'block holds a nonconstant or foreign event')
+        for r in ([e[2], e[3]] if e[1] != 'SCALE' else [e[2]]):
+            need(off <= r < off + n, 'role outside type')
+        apply_const(rows, e)
+    return [rows[off + i] for i in range(n)]
+
+
+def alphabet_ok(block, limit=2):
+    for e in block:
+        if e[1] == 'ADD':
+            c = Q(e[4]); need(c.denominator == 1 and 0 < abs(c) <= limit, 'ADD coefficient outside alphabet %r' % (e,))
+            need(e[2] != e[3], 'self ADD')
+        elif e[1] == 'SCALE':
+            need(Q(e[3]) == -1, 'SCALE not -1')
+        elif e[1] == 'SWAP':
+            need(e[2] != e[3], 'self SWAP')
+    return True
+
+
+def splice(C, ty, new_blocks):
+    """new_blocks[k] = list of full joint events for slot k of type ty.  New block is written at the position of the first
+    old event of its slot (or just before the closing anchor if the old slot was empty).  Everything else keeps its order."""
+    sl, closes = slots(C['events'], ty)
+    need(len(new_blocks) == len(sl), 'slot count %d != %d' % (len(new_blocks), len(sl)))
+    first, drop, ins = {}, set(), {}
+    for k, idxs in enumerate(sl):
+        if idxs:
+            first[idxs[0]] = k; drop.update(idxs[1:])
+        elif new_blocks[k]:
+            ins.setdefault(closes[k], []).append(k)
+    ev = []
+    for i, e in enumerate(C['events']):
+        for k in ins.get(i, []):
+            ev.extend(json.loads(json.dumps(x)) for x in new_blocks[k])
+        if i in drop:
+            continue
+        if i in first:
+            ev.extend(json.loads(json.dumps(x)) for x in new_blocks[first[i]])
+        elif not is_const(e, ty):
+            ev.append(e)
+        # a first-index const event is replaced above; other const events of this type are in drop
+    for k in ins.get(len(C['events']), []):
+        ev.extend(new_blocks[k])
+    out = {k: v for k, v in C.items() if k != 'events'}
+    out['events'] = ev
+    return out
+
+
+def old_blocks(C, ty):
+    sl, _ = slots(C['events'], ty)
+    return [[C['events'][i] for i in idxs] for idxs in sl]
+
+
+def from_6912(after, ty='A'):
+    """read #6912's caller-after.json (plain A-stream events, no tag) as data: list of per-slot blocks, tagged joint events.
+    slots are delimited by its nonconstant events (everything that is not ADD/SCALE/SWAP)."""
+    blocks, cur, anchors = [], [], []
+    for e in after['events']:
+        if e[0] in CONST:
+            cur.append([ty] + list(e))
+        else:
+            blocks.append(cur); cur = []; anchors.append(e)
+    blocks.append(cur)
+    return blocks, anchors
+
+
+# ---------------------------------------------------------------- exact replay of the joint caller mod p
+PM = 2147483629
+IM = next(pow(g, (PM - 1) // 4, PM) for g in range(2, 99) if pow(g, (PM - 1) // 2, PM) == PM - 1)
+HALF = (PM + 1) // 2
+
+
+def fm(x):
+    f = Q(x); return f.numerator % PM * pow(f.denominator, PM - 2, PM) % PM
+
+
+def replay_matrix(C, qv, Dv):
+    """the full 78 x 78 matrix of the joint caller at the point (q, D_1..D_18) over F_PM; semantics as in the package
+    (J = HOST2 on the A roles and HOST on the B roles at one stage)."""
+    n = C['roles']; R = [[int(i == j) for j in range(n)] for i in range(n)]; qi = pow(qv, PM - 2, PM)
+    a2 = fm(C['types']['A']['alpha2'])
+    for e in C['events']:
+        if e[0] == 'J':
+            d = Dv[e[1]]; src, dst, x2, y2 = e[2]
+            R[dst] = [(a + qi * b) % PM for a, b in zip(R[dst], R[src])]
+            R[x2] = [(a + a2 * qv % PM * b) % PM for a, b in zip(R[x2], R[y2])]
+            for r in (src, dst, x2, y2):
+                R[r] = [a * d % PM for a in R[r]]
+            s, t = e[3][0], e[3][1]; al, be = fm(e[3][2]), fm(e[3][3]); tt = al * be % PM
+            ns = [(x + al * qv % PM * y) % PM * d % PM for x, y in zip(R[s], R[t])]
+            nd = [(be * qi % PM * x + (1 + tt) * y) % PM * d % PM for x, y in zip(R[s], R[t])]
+            R[s], R[t] = ns, nd
+            continue
+        op = e[1]
+        if op == 'ADD':
+            R[e[2]] = [(a + fm(e[4]) * b) % PM for a, b in zip(R[e[2]], R[e[3]])]
+        elif op == 'SCALE':
+            c = fm(e[3]); R[e[2]] = [a * c % PM for a in R[e[2]]]
+        elif op == 'SWAP':
+            R[e[2]], R[e[3]] = R[e[3]], R[e[2]]
+        elif op == 'QUERY':
+            c = pow(qv, e[4] % 4, PM); R[e[2]] = [(a + c * b) % PM for a, b in zip(R[e[2]], R[e[3]])]
+        elif op == 'LAMBDA':
+            s = e[3]; c = ((1 + s * IM) * HALF + (1 - s * IM) * HALF * qv * qv) % PM; R[e[2]] = [a * c % PM for a in R[e[2]]]
+        elif op == 'IDLE_ONE':
+            c = 1
+            for k in e[3]:
+                c = c * Dv[k] % PM
+            R[e[2]] = [a * c % PM for a in R[e[2]]]
+        else:
+            raise ValueError('unknown op ' + str(op))
+    return R
+
+
+def target_bad(C, R, qv, Dv):
+    n = C['roles']; bad = 0
+    for role in range(n):
+        t, off = (C['types']['A'], 0) if role < 40 else (C['types']['B'], 40)
+        dg = t['diagonal'][role - off]; c = pow(qv, dg[0] % 4, PM)
+        for k, bit in enumerate(dg[2:]):
+            if bit:
+                c = c * Dv[k + 1] % PM
+        bad += sum(R[role][j] != (c if j == role else 0) for j in range(n))
+    return bad
+
+
+def random_points(seed=5, k=4):
+    r = random.Random(seed); pts = []
+    for qv in (1, IM, PM - 1, PM - IM):
+        pts.append((qv, {s: r.randrange(2, PM) for s in range(1, 19)}))
+    for _ in range(k):
+        pts.append((r.randrange(2, PM), {s: r.randrange(2, PM) for s in range(1, 19)}))
+    return pts
+
+
+# ---------------------------------------------------------------- own resynthesis of a constant block (Euclid elimination)
+def synth(M, ty):
+    """own synthesis: reduce M to I by row operations with a Euclidean algorithm per column, ADD coefficients split into
+    +-1,+-2; the op list that rebuilds M is the reversed list of inverses.  Local indices; returns full joint events."""
+    n, off = NR[ty], OFF[ty]; M = [r[:] for r in M]; ops = []
+
+    def add(i, j, c):          # row_i += c * row_j   (c in {+-1,+-2} after splitting)
+        while c:
+            s = 1 if c > 0 else -1; step = s * min(2, abs(c))
+            M[i] = [a + step * b for a, b in zip(M[i], M[j])]; ops.append(('ADD', i, j, step)); c -= step
+    for col in range(n):
+        while True:
+            nz = [r for r in range(col, n) if M[r][col]]
+            need(nz, 'singular block')
+            if len(nz) == 1 and abs(M[nz[0]][col]) == 1:
+                break
+            p = min(nz, key=lambda r: (abs(M[r][col]), r))
+            for r in nz:
+                if r != p:
+                    qq = round(Q(M[r][col], M[p][col]))
+                    if qq:
+                        add(r, p, -qq)
+        p = nz[0]
+        if p != col:
+            M[p], M[col] = M[col], M[p]; ops.append(('SWAP', p, col))
+        if M[col][col] == -1:
+            M[col] = [-a for a in M[col]]; ops.append(('SCALE', col))
+        for r in range(n):
+            if r != col and M[r][col]:
+                add(r, col, -M[r][col])
+    need(all(M[i][j] == int(i == j) for i in range(n) for j in range(n)), 'did not reach identity')
+    out = []
+    for o in reversed(ops):
+        if o[0] == 'ADD':
+            out.append([ty, 'ADD', o[1] + off, o[2] + off, str(-o[3])])
+        elif o[0] == 'SWAP':
+            out.append([ty, 'SWAP', o[1] + off, o[2] + off])
+        else:
+            out.append([ty, 'SCALE', o[1] + off, '-1'])
+    return out
+
+
+# ---------------------------------------------------------------- raw bound (formulas of the package's check.py / ordinary.py)
+def swaps(sel):
+    wanted = set(range(len(sel))); return len(list(zip(sorted(set(sel) - wanted), sorted(wanted - set(sel)))))
+
+
+def shim(J, ty):
+    t = J['types'][ty]; off = t['offset']; ev = []
+    for e in J['events']:
+        if e[0] == 'J':
+            ev.append(['HOST', e[1]])
+        elif e[0] == ty:
+            e = list(e[1:])
+            if e[0] in ('ADD', 'SWAP', 'QUERY'):
+                e[1] -= off; e[2] -= off
+            else:
+                e[1] -= off
+            ev.append(e)
+    return dict(events=ev, roles=t['roles'], ambient_rank=J['ambient_rank'], diagonal=t['diagonal'])
+
+
+def rest_of(C, ports):
+    ev = C['events']; roles = C['roles']; amb = C['ambient_rank']; mx = mn = mp = 0
+    for role, (qp, zero, *sel) in enumerate(C['diagonal']):
+        axes = ([0] if qp else []) + [a for st, y in enumerate(sel, 1) if y for a in range(9 + 8 * (st - 1), 9 + 8 * st)]
+        k = swaps(axes); mx += 2 * k * ports; mn += 2 * bool(qp) * ports; mp += int(qp == -1) * ports
+    ie = 0; qn = qph = 0
+    for e in ev:
+        if e[0] == 'IDLE_ONE':
+            ie += 2 * swaps([a for st in e[2] for a in range(9 + 8 * (st - 1), 9 + 8 * st)]) * ports
+        elif e[0] == 'QUERY':
+            qn += 2 * ports; qph += int(e[3] == -1) * ports
+    return (32 * roles * ports * len(ev) + sum(e[0] == 'QUERY' for e in ev) * 16 * ports + roles * ports * 26
+            + (mx + mn + mp) * 1000 + ie * 1000 + (qn + qph) * 1000)
+
+
+def word_terms(W):
+    """per-call terms of a word: allowance, reviewed upper, routes, public count, nD"""
+    from collections import Counter
+    H = W['hosted']; nD = len(H['Dports']); n = len(W['initial']); live = set(W['live'])
+    main = live | {r + 112 for r in live} | set(H['X2']) | set(H['Y2'])
+    dim = [len(b) for b in W['frames']]
+    paid = Counter(abs(dim[e[3]] - dim[e[2]]) for e in W['program'] if e[0] == 'MOVE')
+    hel = Counter(dim[W['final'][r]] - dim[W['initial'][r]] for r in range(n) if r not in main)
+    life = sum(e[0] == 'INIT' for e in W['program']); allow = upper = 0
+    for e in W['program']:
+        if e[0] in ('INIT', 'CLEAR'):
+            allow += 2
+        elif e[0] == 'SCALE':
+            q = Q(e[2]); a, d = abs(q.numerator), q.denominator
+            allow += 2 * (abs(a.bit_length() - d.bit_length()) + int(q < 0)); upper += 4 * (a.bit_length() + d.bit_length() + 1)
+        elif e[0] in ('ADD', 'COPY'):
+            q = Q(e[3]); a, d = abs(q.numerator), q.denominator
+            allow += 2 * (3 + a.bit_length() - 1 + bin(a).count('1') + d.bit_length() - 1); upper += 4 * (a.bit_length() + bin(a).count('1') + d.bit_length() + 1)
+    routes = (sum(paid.values()) + 2 * sum(hel.values()) + 208 + 2 * nD + 4 * 104 + 4 * nD + 4 * life) * 1000
+    return dict(allow=allow, upper=upper, routes=routes, n=n, nD=nD, paid=paid, hel=hel)
+
+
+scale_cost = lambda S: 4 * (S.bit_length() + 1 + 1) + 4 * (1 + S.bit_length() + 1)       # one SCALE by S at entry and one by 1/S at exit at the reviewed upper rate: 80 for S = 225, 104 for S = 1125
+
+
+def raw_all(J, W, S):
+    t = word_terms(W); nA, nB = len(J['types']['A']['ports']), len(J['types']['B']['ports'])
+    need((nA, nB) == (t['nD'], 104 - t['nD']), 'port split of the caller differs from the word')
+    rest = rest_of(shim(J, 'A'), nA) + rest_of(shim(J, 'B'), nB)
+    lam = sum(1 for e in J['events'] if e[0] == 'A' and e[1] == 'LAMBDA') * nA + sum(1 for e in J['events'] if e[0] == 'B' and e[1] == 'LAMBDA') * nB
+    debit = 1000 * lam; per_in = 18 * t['n'] * scale_cost(S)
+    lit = 18 * 10 ** 7 + rest; act = 18 * (t['allow'] + t['routes']) + rest; up = 18 * (t['upper'] + t['routes']) + rest
+    return dict(rest=rest, literal=lit, actual=act, upper=up, recharge=up + debit, per_input=up + per_in, per_input_recharge=up + per_in + debit,
+                lambda_jobs=lam, debit=debit, per_in=per_in, public=t['n'])
diff --git a/research/fixed-caller-query-and-host-limits/replay/package/verify.py b/research/fixed-caller-query-and-host-limits/replay/package/verify.py
new file mode 100644
index 0000000000..7047c4b786
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/package/verify.py
@@ -0,0 +1,15 @@
+"""Rational power enclosure retained from PR #7098 by Rohan Arun."""
+
+SCALE = 10**30
+
+def enclosure(rank, saving):
+    exponent = 1 - saving
+    target = rank**exponent.numerator * SCALE**exponent.denominator
+    lower, upper = 0, (rank + 1) * SCALE
+    while upper - lower > 1:
+        mid = (lower + upper) // 2
+        if mid**exponent.denominator <= target:
+            lower = mid
+        else:
+            upper = mid
+    return lower, upper
diff --git a/research/fixed-caller-query-and-host-limits/replay/price_7002_75_job_composition.py b/research/fixed-caller-query-and-host-limits/replay/price_7002_75_job_composition.py
new file mode 100644
index 0000000000..5b7a0b2357
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/price_7002_75_job_composition.py
@@ -0,0 +1,36 @@
+"""Enclose the real 75-job normalized schedule's savings and remaining gaps."""
+from collections import Counter
+from fractions import Fraction as F
+import json
+from pathlib import Path
+
+root=Path(__file__).resolve().parent
+src=root/"reprice_7002_host.py"
+ns={"__file__":str(src)}
+exec(src.read_text().split("report={}")[0],ns)
+price,ports,t,p,C,native,stages=(ns[k] for k in ("price","ports","t","p","C","native","stages"))
+new=json.loads((root/"PR7002-IDLE-PROJECTOR-ORDER-SEARCH.json").read_text())
+old=json.loads((root/"PR7002-NONCOORDINATE-IDLE-WORD.json").read_text())
+new_idle={int(k):ports*v for k,v in new["rank_histogram"].items()}
+old_idle={int(k):ports*v for k,v in old["idle_rank_profile"].items()}
+assert sum(r*n for r,n in new_idle.items())==sum(r*n for r,n in old_idle.items())
+def invoice(idle):
+    paid=Counter({int(k):stages*v for k,v in native["local_paid"].items()})
+    paid.update(idle)
+    paid[1]+=ports*(stages+C["paid_outside_native"]["1"])
+    assert sum(r*n for r,n in paid.items())==sum(r*n for r,n in p.items())
+    return paid
+result={}
+for k in (F(".004"),F(".005")):
+    saving=price(old_idle,new_idle,k)
+    assert saving[0]>0
+    gap=price(t,invoice(new_idle),k)
+    assert gap[1]<0
+    floor=(-gap[1])//1+1
+    assert floor==(-gap[0])//1+1
+    result[str(k)]={"exact_104_port_saving":list(map(str,saving)),
+                   "new_margin":list(map(str,gap)),"remaining_rank_one_equivalents":floor}
+    print(k,"saving",float(saving[0]),"margin",float(gap[1]),"still need",floor,flush=True)
+with (root/"PR7002-75-JOB-COMPOSITION-PRICE.json").open("x") as out:
+    json.dump({"jobs_per_port":sum(new["rank_histogram"].values()),"tests":result,
+               "scope":"Exact normalized schedule with the retained F+H1 tariff. Physical packed IDLE and basis costs, BIT and outer admission remain open."},out,indent=2)
diff --git a/research/fixed-caller-query-and-host-limits/replay/price_7004_query_families.py b/research/fixed-caller-query-and-host-limits/replay/price_7004_query_families.py
new file mode 100644
index 0000000000..d818e4dcfe
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/price_7004_query_families.py
@@ -0,0 +1,34 @@
+"""Measure what an entire caller-level QUERY family would buy on pinned invoices."""
+from collections import Counter
+from fractions import Fraction as F
+from pathlib import Path
+import json
+root=Path(__file__).resolve().parent
+ref=root/"reprice_7002_host.py"
+ns={"__file__":str(ref)}
+exec(ref.read_text().split("report={}")[0],ns)
+price=ns["price"]
+caller=json.loads((root/"PR7000-CALLER.json").read_text())
+c={name:len(typ["ports"]) for name,typ in caller["types"].items()}
+data=json.loads((root/"PR7004-RESULT.json").read_text())
+bit=json.loads((root/"PR7001-RESULT.json").read_text())
+complex_pair=tuple({int(r):v for r,v in data["invoice"][key].items()} for key in ("T","P"))
+bit_pair=tuple({int(r):v for r,v in bit[key].items()} for key in ("targets","paid"))
+result={}
+for k in (F(".004"),F(".005")):
+    cases={}
+    for name,(target,paid) in (("complex",complex_pair),("bit",bit_pair)):
+        lo,hi=price(target,paid,k)
+        case={"signed_moment":list(map(str,(lo,hi))),
+              "minimum_rank_one_equivalent":max(0,(-hi)//1+1)}
+        if name=="complex":
+            case["after_one_A_query_removed"]=list(map(str,(lo+c["A"],hi+c["A"])))
+            case["after_one_A_and_one_B_query_removed"]=list(map(str,(lo+sum(c.values()),hi+sum(c.values()))))
+        cases[name]=case
+        print(k,name,"margin",float(hi),"need",case["minimum_rank_one_equivalent"])
+    print(k,"complex after one A query",float(F(cases["complex"]["after_one_A_query_removed"][1])))
+    result[str(k)]=cases
+with (root/"PR7004-QUERY-FAMILY-TARGET-PRICE.json").open("x") as out:
+    json.dump({"queries_by_family":dict(Counter(e[0] for e in caller["events"] if e[1]=="QUERY")),
+               "ports":c,"target_prices":result,
+               "scope":"Exact raw-moment bounds with fixed targets, using source-bound complex and BIT invoices. Query removal is a hypothetical change and not an operator identity, physical or outer admission."},out,indent=2)
diff --git a/research/fixed-caller-query-and-host-limits/replay/reprice_7002_host.py b/research/fixed-caller-query-and-host-limits/replay/reprice_7002_host.py
new file mode 100644
index 0000000000..ebc6d72633
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/reprice_7002_host.py
@@ -0,0 +1,58 @@
+"""Independent rational target budgets for the connected L18 caller."""
+from fractions import Fraction
+from hashlib import sha256
+import json
+from pathlib import Path
+import sys
+
+root=Path(__file__).resolve().parent
+sys.path.insert(0,str(root/"package"))
+from verify import enclosure,SCALE
+source=root/"connected7002"/"COALESCING-WINDOW.json"
+receipt=json.loads(source.read_bytes())
+native=json.loads((root/"connected7002"/"inputs/base_invoice.json").read_bytes())
+C=json.loads((root/"connected7002"/"COST.json").read_bytes())["18"]
+ports=104
+stages=C["stages"]
+repairs=ports*stages
+def hist(d):
+    return {int(k):v for k,v in d.items()}
+t,p=map(hist,(receipt["T"],receipt["P"]))
+assert p[1]==stages*hist(native["local_paid"])[1]+ports*C["paid_outside_native"]["1"]+repairs
+assert t[1]==stages*hist(native["helpers"])[1]
+assert sum(r*(t.get(r,0)-p.get(r,0)) for r in t.keys()|p.keys())==receipt["rank_surplus"]
+def price(t,p,k):
+    low=high=0
+    for r in t.keys()|p.keys():
+        c=t.get(r,0)-p.get(r,0)
+        if not c:
+            continue
+        lo,hi=enclosure(r,k)
+        low+=c*(lo if c>0 else hi)
+        high+=c*(hi if c>0 else lo)
+    return Fraction(low,SCALE),Fraction(high,SCALE)
+report={}
+for k in (Fraction(1,200),Fraction(1,100)):
+    lo,hi=price(t,p,k)
+    assert hi<0
+    lower_minimum=(-hi)//1+1
+    assert lower_minimum==(-lo)//1+1
+    free=(lo+repairs,hi+repairs)
+    assert free[0]>0
+    eight_batched={**p,1:p[1]-repairs,8:p[8]+repairs//8}
+    assert repairs%8==0
+    eight=price(t,eight_batched,k)
+    assert eight[1]<0
+    allowed=repairs-lower_minimum
+    report[str(k)]={"fixed_F_plus_H1_moment":list(map(str,(lo,hi))),
+                    "minimum_removed_H1_equivalents_for_raw_positivity":lower_minimum,
+                    "maximum_H1_equivalents_remaining":allowed,
+                    "max_fraction_of_original_H1_repair_budget_remaining":str(Fraction(allowed,repairs)),
+                    "free_repairs_moment":list(map(str,free)),
+                    "hypothetical_same_rank_mass_rank8_pack_moment":list(map(str,eight))}
+    print(k,"baseline",float(hi),"min H1 removed",lower_minimum,"allowed",allowed,"free",float(free[0]),"rank8 pack",float(eight[1]))
+with (root/"PR7002-HOST-REPAIR-TARGET-BUDGET.json").open("x") as out:
+    json.dump({"head":"ed1a0a83dfe5d28db9a971bcfc1403bcdc03a49b",
+               "invoice_sha256":sha256(source.read_bytes()).hexdigest(),
+               "paid_repairs":repairs,"at_targets":report,
+               "scope":"Raw complex-side screening with optimistically coalesced coordinate idles and fixed native helper targets. Free and rank8 tariffs are hypothetical. No HOST implementation, ordinary cost, BIT, or outer admission."},out,indent=2)
diff --git a/research/fixed-caller-query-and-host-limits/replay/screen_6824_dark_two_contact.py b/research/fixed-caller-query-and-host-limits/replay/screen_6824_dark_two_contact.py
new file mode 100644
index 0000000000..12d1b80b3e
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/screen_6824_dark_two_contact.py
@@ -0,0 +1,123 @@
+"""Screen two-contact repairs whose individual baseline effects vanish."""
+from collections import defaultdict
+from fractions import Fraction as F
+import json
+from pathlib import Path
+
+root=Path(__file__).resolve().parent
+initial=root/"search_6824_host_entrance_contacts.py"
+ns={"__file__":str(initial)}
+exec(initial.read_text().split("after=[None]")[0],ns)
+w,n,N,events,ports,native,columns,sink=(ns[k] for k in ("w","n","N","events","ports","native","outputs","sink"))
+after=[None]*len(events)
+def tag(col):
+    return not col,sink(col)
+for i in range(len(events)-1,-1,-1):
+    op,d,*args=events[i]
+    if op=="MOVE":
+        continue
+    r=args[0] if op in ("ADD","COPY") else d
+    after[i]=(r,tag(columns[r]))
+    if op in ("ADD","COPY"):
+        native.add(columns[r],columns[d],F(args[1]))
+    elif op=="SCALE":
+        columns[d]={k:F(args[0])*v for k,v in columns[d].items()}
+    else:
+        columns[d]={}
+suffix=[tag(v) for v in columns]
+rows=[{r:F(1)} if r<n else {} for r in range(N)]
+frames=w["initial"]+[None]*w["owned_fields"]
+groups=defaultdict(set)
+ordered=sorted(ports)
+bit={port:1<<i for i,port in enumerate(ordered)}
+reachable=[0]*N
+hits={}
+legal_dark_entry=set()
+legal_dark_exit=set()
+def scan(frame,cut):
+    if frame is None:
+        return
+    registers=groups[frame]
+    zero_live=[r for r in registers if not rows[r]]
+    # Look for the second edit before admitting first contacts at this cut.
+    # A same-cut first contact can go directly into the second source, so
+    # check it explicitly after the additions below.
+    dark=[r for r in registers if suffix[r][0]]
+    sources={}
+    for r in registers:
+        if len(rows[r])==1:
+            (i,c),=rows[r].items()
+            if i-112 in bit:
+                sources[r]=bit[i-112]
+    union=0
+    for mask in sources.values():
+        union|=mask
+    if dark:
+        for r in dark:
+            available=union if r not in sources else 0
+            if r in sources:
+                for s,mask in sources.items():
+                    if s!=r:
+                        available|=mask
+            if available:
+                reachable[r]|=available
+                legal_dark_entry.add(r)
+    zero_union=0
+    for r in zero_live:
+        zero_union|=reachable[r]
+    for dst in registers:
+        sig=suffix[dst][1]
+        if not sig:
+            continue
+        port,_=sig
+        if any(r!=dst for r in zero_live):
+            legal_dark_exit.add(port)
+        if zero_union&bit[port] and port not in hits:
+            for src in zero_live:
+                if src!=dst and reachable[src]&bit[port]:
+                    hits[port]=[cut,dst,src]
+                    break
+for r,f in enumerate(frames):
+    if f is not None:
+        groups[f].add(r)
+for f in list(groups):
+    scan(f,0)
+for i,event in enumerate(events):
+    op,d,*args=event
+    affected={frames[d]}
+    if after[i] is not None:
+        affected.add(frames[after[i][0]])
+    if op=="MOVE":
+        groups[frames[d]].remove(d)
+        frames[d]=args[1]
+        groups[frames[d]].add(d)
+    elif op=="CLEAR":
+        groups[frames[d]].remove(d)
+        frames[d]=None
+        rows[d]={}
+        reachable[d]=0
+    elif op=="INIT":
+        frames[d]=args[0]
+        groups[frames[d]].add(d)
+        rows[d]={}
+        reachable[d]=0
+    elif op=="SCALE":
+        rows[d]={k:F(args[0])*v for k,v in rows[d].items()}
+    else:
+        src=args[0]
+        if op=="COPY":
+            reachable[d]=reachable[src]
+        else:
+            reachable[d]|=reachable[src]
+        native.add(rows[d],rows[src],F(args[1]))
+    if after[i] is not None:
+        r,value=after[i]
+        suffix[r]=value
+    affected.add(frames[d])
+    for f in affected:
+        scan(f,i+1)
+with (root/"PR6824-TWO-CONTACT-DARK-REACHABILITY.json").open("x") as f:
+    json.dump({"reachable_ports":hits,"dark_entry_registers":len(legal_dark_entry),
+               "potential_dark_exit_ports":len(legal_dark_exit),"cuts":len(events)+1,
+               "scope":"Necessary path condition. First edit reads pure Y into a baseline suffix-zero register; second edit reads a baseline-zero source into an isolated X+Y suffix. Existing linear dependencies are granted even if their coefficients cancel. Baseline COPY is modeled as transfer with zero destination."},f,indent=2)
+print("dark entries",len(legal_dark_entry),"dark exit ports",len(legal_dark_exit),"reachable",len(hits),flush=True)
diff --git a/research/fixed-caller-query-and-host-limits/replay/screen_6824_mixed_first_order.py b/research/fixed-caller-query-and-host-limits/replay/screen_6824_mixed_first_order.py
new file mode 100644
index 0000000000..896e089b53
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/screen_6824_mixed_first_order.py
@@ -0,0 +1,108 @@
+"""Locate exact nonzero first-order Y->X contacts with both sides mixed."""
+from collections import defaultdict,Counter
+from fractions import Fraction as F
+from pathlib import Path
+import json
+
+root=Path(__file__).resolve().parent
+source=root/"search_6824_host_entrance_contacts.py"
+ns={"__file__":str(source)}
+exec(source.read_text().split("def sink(")[0],ns)
+w,n,N,events,ports,native=(ns[k] for k in ("w","n","N","events","ports","native"))
+suffix=[{i:F(1)} if i<n else {} for i in range(N)]
+after=[None]*len(events)
+for i in range(len(events)-1,-1,-1):
+    op,d,*a=events[i]
+    if op=="MOVE":
+        continue
+    changed=a[0] if op in ("ADD","COPY") else d
+    after[i]=(changed,suffix[changed])
+    if op in ("ADD","COPY"):
+        suffix[changed]=suffix[changed].copy()
+        native.add(suffix[changed],suffix[d],F(a[1]))
+    elif op=="SCALE":
+        suffix[d]={k:F(a[0])*v for k,v in suffix[d].items()}
+    else:
+        suffix[d]={}
+rows=[{i:F(1)} if i<n else {} for i in range(N)]
+frames=w["initial"]+[None]*w["owned_fields"]
+from_y=defaultdict(set)
+to_x=defaultdict(set)
+sample=defaultdict(dict)
+def update(r,removing=False):
+    f=frames[r]
+    if f is None:
+        return
+    for table, values in ((from_y,(i-112 for i in rows[r] if i-112 in ports)),
+                          (to_x,(i for i in suffix[r] if i in ports))):
+        for port in values:
+            if removing:
+                table[port,f].remove(r)
+            else:
+                table[port,f].add(r)
+def save(cut,port,d,s,frame):
+    if d==s:
+        return
+    a,b=rows[s],suffix[d]
+    assert a.get(port+112) and b.get(port)
+    # Keep distinct exact outer-product directions with compact support.
+    # Large supports remain counted, but are not exported as recipes.
+    histogram[port][(min(len(a),32),min(len(b),32))]+=1
+    if len(a)*len(b)>160:
+        return
+    key=(tuple(sorted(a.items())),tuple(sorted(b.items())))
+    sample[port].setdefault(key,(cut,d,s,frame))
+def scan(changed,cut):
+    for r in changed:
+        frame=frames[r]
+        if frame is None:
+            continue
+        for y in rows[r]:
+            if y-112 in ports:
+                for dst in to_x[y-112,frame]:
+                    save(cut,y-112,dst,r,frame)
+        for x in suffix[r]:
+            if x in ports:
+                for src in from_y[x,frame]:
+                    save(cut,x,r,src,frame)
+histogram=defaultdict(Counter)
+for i in range(N):
+    update(i)
+scan(range(N),0)
+for i,event in enumerate(events):
+    op,d,*a=event
+    changed={d}
+    if after[i] is not None:
+        changed.add(after[i][0])
+    for r in changed:
+        update(r,True)
+    if op=="MOVE":
+        frames[d]=a[1]
+    elif op=="INIT":
+        frames[d]=a[0]
+        rows[d]={}
+    elif op=="CLEAR":
+        frames[d]=None
+        rows[d]={}
+    elif op=="SCALE":
+        rows[d]={k:F(a[0])*v for k,v in rows[d].items()}
+    else:
+        native.add(rows[d],rows[a[0]],F(a[1]))
+    if after[i] is not None:
+        r,col=after[i]
+        suffix[r]=col
+    for r in changed:
+        update(r)
+    scan(changed,i+1)
+
+def describe(bucket):
+    return [[list(edit),[[k,str(v)] for k,v in a],[[k,str(v)] for k,v in b]]
+            for (a,b),edit in bucket.items()]
+summary={str(port):{"contacts_by_support":[[a,b,count] for (a,b),count in sorted(histogram[port].items())],
+                   "compact_directions":describe(sample[port])}
+         for port in sorted(ports)}
+with (root/"PR6824-MIXED-FIRST-ORDER-HOST-CONTACTS.json").open("x") as f:
+    json.dump({"ports":summary,"scope":"Exact first-order contacts on fixed normalized chronology. Large support contacts counted only. Extra tensor entries and higher-order interactions still have to cancel."},f)
+print("ports with first-order effect",sum(bool(histogram[p]) for p in ports),
+      "ports with compact directions",sum(bool(sample[p]) for p in ports),
+      "compact directions",sum(map(len,sample.values())),flush=True)
diff --git a/research/fixed-caller-query-and-host-limits/replay/screen_6824_two_edit_mixed.py b/research/fixed-caller-query-and-host-limits/replay/screen_6824_two_edit_mixed.py
new file mode 100644
index 0000000000..6a3dda28b6
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/screen_6824_two_edit_mixed.py
@@ -0,0 +1,157 @@
+"""Screen necessary tensor-factor cancellations for two coframe repairs."""
+from collections import defaultdict
+from fractions import Fraction as F
+from pathlib import Path
+import json
+
+root=Path(__file__).resolve().parent
+initial=root/"search_6824_host_entrance_contacts.py"
+ns={"__file__":str(initial)}
+exec(initial.read_text().split("def sink(")[0],ns)
+w,n,N,events,ports,native,B=(ns[k] for k in ("w","n","N","events","ports","native","outputs"))
+A=[{i:F(1)} if i<n else {} for i in range(N)]
+frames=w["initial"]+[None]*w["owned_fields"]
+after=[None]*len(events)
+for i in range(len(events)-1,-1,-1):
+    op,d,*a=events[i]
+    if op=="MOVE":
+        continue
+    r=a[0] if op in ("ADD","COPY") else d
+    after[i]=r,B[r]
+    if op in ("ADD","COPY"):
+        B[r]=B[r].copy()
+        native.add(B[r],B[d],F(a[1]))
+    elif op=="SCALE":
+        B[r]={k:v*F(a[0]) for k,v in B[r].items()}
+    else:
+        B[r]={}
+groups=defaultdict(set)
+for i,f in enumerate(frames):
+    if f is not None:
+        groups[f].add(i)
+
+def pure_y(row):
+    if len(row)==1:
+        i=next(iter(row))
+        if i-112 in ports:
+            return i-112
+    return None
+
+def isolated(row):
+    if len(row)==2:
+        p=min(row)
+        if p in ports and row.get(p+112)==row[p]:
+            return p
+    return None
+
+def canon(row):
+    if not row:
+        return ()
+    p=row[min(row)]
+    return tuple(sorted((k,v/p) for k,v in row.items()))
+
+# If first suffix is zero, later baseline donor must cancel the first
+# donor's non-Y terms. If later donor is zero, earlier baseline suffix
+# must supply the residual after subtracting the second suffix's X part.
+dark_prefix=defaultdict(dict)
+pure_suffix=defaultdict(dict)
+out_A={}
+out_B={}
+count_A=set()
+count_B=set()
+cache={}
+def norm_suffix(d):
+    v=B[d]
+    if d not in cache or cache[d][0] is not v:
+        cache[d]=(v,canon(v))
+    return cache[d][1]
+
+def scan(affected,changed,cut):
+    for f in sorted(affected):
+        registers=groups[f]
+        for dst in sorted(registers):
+            if not B[dst]:
+                for src in sorted(registers-{dst}):
+                    if src not in changed and dst not in changed:
+                        continue
+                    a=A[src]
+                    for y in a:
+                        p=y-112
+                        if p in ports:
+                            key=canon({k:v for k,v in a.items() if k!=y})
+                            dark_prefix[p].setdefault(key,(cut,src,dst))
+        # Add all newly available first contacts from pure Y donors.
+        for r in sorted(registers&changed):
+            p=pure_y(A[r])
+            if p is not None:
+                for dst in registers-{r}:
+                    if B[dst]:
+                        pure_suffix[p].setdefault(norm_suffix(dst),(cut,r,dst))
+            if B[r]:
+                for src in registers-{r}:
+                    p=pure_y(A[src])
+                    if p is not None:
+                        pure_suffix[p].setdefault(norm_suffix(r),(cut,src,r))
+
+    for f in sorted(affected):
+        registers=groups[f]
+        zero={r for r in registers if not A[r]}
+        for dst in sorted(registers):
+            p=isolated(B[dst])
+            if p is not None and p not in out_A:
+                for src in sorted(registers-{dst}):
+                    a=A[src]
+                    if not a or p+112 in a:
+                        continue
+                    count_A.add(p)
+                    key=canon(a)
+                    if key in dark_prefix[p]:
+                        out_A[p]=(dark_prefix[p][key],(cut,src,dst))
+                        break
+            if not zero-{dst}:
+                continue
+            for p,b in B[dst].items():
+                if p not in ports or p in out_B:
+                    continue
+                count_B.add(p)
+                residual={i:-v/b for i,v in B[dst].items()}
+                residual[p]+=1
+                residual[p+112]=residual.get(p+112,0)+1
+                key=canon({i:v for i,v in residual.items() if v})
+                if key and key in pure_suffix[p]:
+                    out_B[p]=(pure_suffix[p][key],(cut,min(zero-{dst}),dst))
+scan(set(groups),set(range(N)),0)
+for i,event in enumerate(events):
+    op,d,*a=event
+    changed={d}
+    if after[i]:
+        changed.add(after[i][0])
+    affected={frames[r] for r in changed}
+    if op=="MOVE":
+        groups[frames[d]].remove(d)
+        frames[d]=a[1]
+        groups[frames[d]].add(d)
+    elif op=="INIT":
+        frames[d]=a[0]
+        groups[frames[d]].add(d)
+        A[d]={}
+    elif op=="CLEAR":
+        groups[frames[d]].remove(d)
+        frames[d]=None
+        A[d]={}
+    elif op=="SCALE":
+        A[d]={k:F(a[0])*v for k,v in A[d].items()}
+    else:
+        native.add(A[d],A[a[0]],F(a[1]))
+    if after[i]:
+        r,v=after[i]
+        B[r]=v
+    affected.update(frames[r] for r in changed)
+    scan(affected-{None},changed,i+1)
+
+with (root/"PR6824-TWO-EDIT-MIXED-CANCELLATION.json").open("x") as out:
+    json.dump({"prefix_signature_counts":{p:len(x) for p,x in dark_prefix.items()},
+               "tested_later_isolated_sink_ports":len(count_A),"tested_later_zero_source_ports":len(count_B),
+               "first_suffix_zero_candidates":out_A,"second_donor_zero_candidates":out_B,
+               "scope":"Necessary temporal cancellation matches for the one-zero-factor cases of two coframe ADDs. Transfer amplitude, COPY legality and full endpoint replay still required for survivors. Both-zero dark path tested separately."},out,indent=2)
+print("tested",len(count_A),len(count_B),"cancellation candidates",len(out_A),len(out_B),flush=True)
diff --git a/research/fixed-caller-query-and-host-limits/replay/screen_7000_central_query_rank.py b/research/fixed-caller-query-and-host-limits/replay/screen_7000_central_query_rank.py
new file mode 100644
index 0000000000..3ea987a5fb
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/screen_7000_central_query_rank.py
@@ -0,0 +1,63 @@
+"""Rank obstruction to compressing each caller's central four-query block."""
+from pathlib import Path
+from hashlib import sha256
+import json,random
+root=Path(__file__).resolve().parent
+path=root/"PR7000-CALLER.json"
+digest=sha256(path.read_bytes()).hexdigest()
+assert digest=="3828d53e80ea97e8b866320f081af20b6b93bfebd58b95b56b85a7afe151af5e"
+data=json.loads(path.read_bytes())
+src=(root/"jclib_6936.py").read_text()
+ns={"__file__":str(root/"jclib_6936.py")}
+exec(src[:src.index("CONST =")]+src[src.index("PM ="):src.index("# ---------------------------------------------------------------- own resynthesis")],ns)
+prime,IM,replay=ns["PM"],ns["IM"],ns["replay_matrix"]
+rng=random.Random(281)
+def rank(A):
+    basis={}
+    for row in A:
+        v=dict((i,x) for i,x in enumerate(row) if x)
+        while v:
+            pivot=min(v)
+            if pivot not in basis:
+                inv=pow(v[pivot],-1,prime)
+                basis[pivot]={j:x*inv%prime for j,x in v.items()}
+                break
+            scale=v[pivot]
+            for j,x in basis[pivot].items():
+                t=(v.get(j,0)-scale*x)%prime
+                if t:v[j]=t
+                else:v.pop(j,None)
+    return len(basis),sorted(basis)
+report={}
+for tag in data["types"]:
+    queries=[i for i,e in enumerate(data["events"]) if e[0]==tag and e[1]=="QUERY"]
+    interval=[e for e in data["events"][queries[0]:queries[-1]+1] if e[0]==tag]
+    assert len(queries)==4
+    assert all(e[0]!="J" for e in data["events"][queries[0]:queries[-1]+1])
+    trial={**data,"events":interval}
+    records=[]
+    for q in (1,IM):
+        for case in range(2):
+            D={j:(1 if case==0 else rng.randrange(2,prime)) for j in range(1,19)}
+            P=replay(trial,q,D)
+            M=replay(trial,-q%prime,D)
+            r,pivots=rank([[(x-y)%prime for x,y in zip(a,b)] for a,b in zip(P,M)])
+            records.append({"q":q,"stage_values":D,"rank":r,"pivot_columns":pivots})
+    omitted=[]
+    for pos,e in enumerate(interval):
+        if e[1]!="QUERY":
+            continue
+        change={**trial,"events":interval[:pos]+interval[pos+1:]}
+        D={j:1 for j in range(1,19)}
+        before=replay(trial,1,D)
+        after=replay(change,1,D)
+        assert before!=after
+        omitted.append(pos)
+    report[tag]={"query_indices":queries,"tested_differences":records,
+                 "fixed_interval_query_lower_bound":max(x["rank"] for x in records),
+                 "literal_omission_negative_controls":omitted}
+    print(tag,"difference ranks",[x["rank"] for x in records],flush=True)
+with (root/"PR7000-CENTRAL-QUERY-SIGN-RANK.json").open("x") as out:
+    json.dump({"source_sha256":digest,"prime":prime,"branches":report,
+               "proof":"Each even ordinary map is equal at q and -q. Each odd query changes its sign, so its two maps differ by a rank-one matrix. A telescoping product difference has rank at most the sum of those ranks. A finite-field specialization where the required difference has rank r proves at least r queries for this fixed interval over the dyadic operator ring.",
+               "scope":"Preserves the full input/output operator of the central interval. Moving a QUERY across a J call, changing the boundary operator or making new sign-sensitive native calls is outside the bound."},out,indent=2)
diff --git a/research/fixed-caller-query-and-host-limits/replay/screen_7000_query_host_contacts.py b/research/fixed-caller-query-and-host-limits/replay/screen_7000_query_host_contacts.py
new file mode 100644
index 0000000000..3ccde9e75a
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/screen_7000_query_host_contacts.py
@@ -0,0 +1,85 @@
+"""Check whether QUERY directions can merge with each other or a retained HOST shear."""
+from collections import defaultdict
+from fractions import Fraction as F
+from pathlib import Path
+import json,random
+
+root=Path(__file__).resolve().parent
+src=(root/"screen_7000_transported_idle_projectors.py").read_text()
+ns={"__file__":str(root/"screen_7000_transported_idle_projectors.py")}
+exec(src[:src.index("def signatures(")],ns)
+data,PM,IM,HALF,mod=map(ns.get,("data","PM","IM","HALF","mod"))
+def normalized(vec):
+    z=next(x for x in vec if x)
+    z=pow(z,-1,PM)
+    return tuple(x*z%PM for x in vec)
+def directions(q,D):
+    n=data["roles"]
+    rows=[[int(i==j) for j in range(n)] for i in range(n)]
+    cols=[r.copy() for r in rows]
+    signature={}
+    def record(key,d,s):
+        signature[key]=(normalized(cols[d]),normalized(rows[s]))
+    def add(d,s,c):
+        rows[d]=[(x+c*y)%PM for x,y in zip(rows[d],rows[s])]
+        cols[s]=[(x-c*y)%PM for x,y in zip(cols[s],cols[d])]
+    def scale(r,c):
+        rows[r]=[x*c%PM for x in rows[r]]
+        cols[r]=[x*pow(c,-1,PM)%PM for x in cols[r]]
+    for i,(tag,op,*a) in enumerate(data["events"]):
+        if tag=="J":
+            s,d,x,y=a[0]
+            record(("A","host",i,0),d,s)
+            add(d,s,pow(q,-1,PM))
+            record(("A","host",i,1),x,y)
+            add(x,y,mod(data["types"]["A"]["alpha2"])*q%PM)
+            for r in a[0]: scale(r,D[op])
+            s,t,alpha,beta=a[1]
+            record(("B","host",i,0),s,t)
+            add(s,t,mod(alpha)*q%PM)
+            record(("B","host",i,1),t,s)
+            add(t,s,mod(beta)*pow(q,-1,PM)%PM)
+            for r in (s,t):scale(r,D[op])
+        elif op in ("ADD","QUERY"):
+            d,s,c=a
+            if op=="QUERY":
+                record((tag,"query",i,0),d,s)
+            add(d,s,mod(c) if op=="ADD" else pow(q,c%4,PM))
+        elif op=="SWAP":
+            s,d=a
+            rows[s],rows[d]=rows[d],rows[s]
+            cols[s],cols[d]=cols[d],cols[s]
+        elif op=="SCALE":
+            scale(a[0],mod(a[1]))
+        elif op=="LAMBDA":
+            v=a[1]
+            scale(a[0],((1+v*IM)+(1-v*IM)*q*q)*HALF%PM)
+        elif op=="IDLE_ONE":
+            value=1
+            for j in a[1]:value=value*D[j]%PM
+            scale(a[0],value)
+        else:raise ValueError(op)
+    assert rows==ns["ns"]["replay_matrix"](data,q,D)
+    return signature
+rng=random.Random(722)
+all_sigs=defaultdict(list)
+for q in (1,IM,PM-1,PM-IM)*2:
+    D={j:rng.randrange(2,PM) for j in range(1,19)}
+    for key,pair in directions(q,D).items():
+        all_sigs[key].append(pair)
+matches=[]
+tested=0
+for first,a in all_sigs.items():
+    if first[1]!="query":continue
+    for second,b in all_sigs.items():
+        if second==first or second[0]!=first[0] or (second[1]=="query" and second<first):
+            continue
+        tested+=1
+        v=all(x[0]==y[0] for x,y in zip(a,b))
+        u=all(x[1]==y[1] for x,y in zip(a,b))
+        if v or u:matches.append({"query":first,"other":second,"same_range":v,"same_source":u})
+with (root/"PR7000-QUERY-HOST-TRANSPORT-CONTACTS.json").open("x") as out:
+    json.dump({"tested_pairs":tested,"matches":matches,"sample_count":8,
+               "scope":"Conjugated shear image and source directions at the original prefixes in the fixed operator word. Exact finite-field evaluations exclude proportionality over the dyadic formal ring if any evaluation differs. General resynthesis is outside this screen."},out,indent=2)
+print("pairs tested",tested,"range or source matches",len(matches))
+for x in matches:print(x)
diff --git a/research/fixed-caller-query-and-host-limits/replay/screen_7000_transported_idle_projectors.py b/research/fixed-caller-query-and-host-limits/replay/screen_7000_transported_idle_projectors.py
new file mode 100644
index 0000000000..92178e55a2
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/screen_7000_transported_idle_projectors.py
@@ -0,0 +1,88 @@
+"""Find equal transported IDLE projections in the full public caller."""
+from collections import defaultdict
+from fractions import Fraction as F
+from pathlib import Path
+import json,random
+
+root=Path(__file__).resolve().parent
+data=json.loads((root/"PR7000-CALLER.json").read_bytes())
+src=(root/"jclib_6936.py").read_text()
+ns={"__file__":str(root/"jclib_6936.py")}
+exec(src[:src.index("CONST =")]+src[src.index("PM ="):src.index("# ---------------------------------------------------------------- own resynthesis")],ns)
+PM,IM,HALF=(ns[k] for k in ("PM","IM","HALF"))
+def mod(value):
+    x=F(value)
+    return x.numerator*pow(x.denominator,-1,PM)%PM
+def signatures(q,ds):
+    n=data["roles"]
+    eye=[[int(i==j) for j in range(n)] for i in range(n)]
+    rows=[r.copy() for r in eye]
+    columns=[r.copy() for r in eye]
+    out={}
+    qi=pow(q,-1,PM)
+    a2=mod(data["types"]["A"]["alpha2"])
+    def add(d,s,c):
+        rows[d]=[(x+c*y)%PM for x,y in zip(rows[d],rows[s])]
+        columns[s]=[(x-c*y)%PM for x,y in zip(columns[s],columns[d])]
+    def scale(r,c):
+        rows[r]=[x*c%PM for x in rows[r]]
+        ci=pow(c,-1,PM)
+        columns[r]=[x*ci%PM for x in columns[r]]
+    for i,(tag,op,*a) in enumerate(data["events"]):
+        if tag=="J":
+            s,d,x,y=a[0]
+            add(d,s,qi)
+            add(x,y,a2*q%PM)
+            for r in a[0]:
+                scale(r,ds[op])
+            s,t,al,be=a[1]
+            alpha,beta=mod(al),mod(be)
+            add(s,t,alpha*q%PM)
+            add(t,s,beta*qi%PM)
+            scale(s,ds[op])
+            scale(t,ds[op])
+        elif op=="ADD":
+            add(a[0],a[1],mod(a[2]))
+        elif op=="SWAP":
+            s,d=a
+            rows[s],rows[d]=rows[d],rows[s]
+            columns[s],columns[d]=columns[d],columns[s]
+        elif op=="SCALE":
+            scale(a[0],mod(a[1]))
+        elif op=="LAMBDA":
+            s=a[1]
+            scale(a[0],((1+s*IM)+(1-s*IM)*q*q)*HALF%PM)
+        elif op=="QUERY":
+            add(a[0],a[1],pow(q,a[2]%4,PM))
+        elif op=="IDLE_ONE":
+            r,labels=a
+            pivot=next(x for x in rows[r] if x)
+            out[i]=(tuple(x*pow(pivot,-1,PM)%PM for x in rows[r]),tuple(x*pivot%PM for x in columns[r]))
+            c=1
+            for stage in labels:
+                c=c*ds[stage]%PM
+            scale(r,c)
+        else:
+            raise ValueError(op)
+    assert rows==ns["replay_matrix"](data,q,ds)
+    assert all(sum(x*y for x,y in zip(row,col))%PM==(i==j)
+               for i,row in enumerate(rows) for j,col in enumerate(columns))
+    return out
+rnd=random.Random(931)
+groups=defaultdict(list)
+points=[(q,{stage:rnd.randrange(2,PM) for stage in range(1,19)}) for q in (1,IM,PM-1,PM-IM)*2]
+keys=defaultdict(list)
+for q,ds in points:
+    for i,sig in signatures(q,ds).items():
+        keys[i].append(sig)
+for i,values in keys.items():
+    groups[(data["events"][i][0],tuple(values))].append(i)
+matches=[]
+for group in groups.values():
+    if len(group)<2:
+        continue
+    matches.append([{"index":i,"event":data["events"][i]} for i in group])
+with (root/"PR7000-TRANSPORTED-IDLE-PROJECTORS.json").open("x") as out:
+    json.dump({"sample_points":len(points),"jobs":len(keys),"potential_equal_projector_groups":matches,
+               "scope":"Exact finite-field full caller prefix/inverse propagation across all four q roots and two D tuples. If two projections differ in any sampled field evaluation they cannot be identical over the pinned dyadic formal ring. Coincidence only gives a candidate."},out,indent=2)
+print("idle jobs",len(keys),"projector matches",len(matches),flush=True)
diff --git a/research/fixed-caller-query-and-host-limits/replay/search_6824_host_entrance_contacts.py b/research/fixed-caller-query-and-host-limits/replay/search_6824_host_entrance_contacts.py
new file mode 100644
index 0000000000..bebf65d5c6
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/search_6824_host_entrance_contacts.py
@@ -0,0 +1,136 @@
+"""Find one coframed scalar insertion realizing the HOST entrance transvection."""
+from collections import defaultdict
+from fractions import Fraction as F
+import gzip, hashlib, json
+from pathlib import Path
+import sys
+
+root=Path(__file__).resolve().parent
+src=root/"supplier6824"/"F6824.json.gz"
+sys.path.insert(0,str(src.parent))
+import native
+w=json.loads(gzip.decompress(src.read_bytes()))
+replay=native.replay(w)
+expected=json.loads((root/"connected7002/inputs/base_invoice.json").read_text())
+assert {str(k):v for k,v in replay["paid"].items()}==expected["local_paid"]
+assert {str(k):v for k,v in replay["helpers"].items()}==expected["helpers"]
+n=w["public"]
+N=n+w["owned_fields"]
+events=w["program"]
+ports=set(w["live"])
+outputs=[{i:F(1)} if i<n else {} for i in range(N)]
+def sink(row):
+    if len(row)!=2:
+        return None
+    x=min(row)
+    if x in ports and row.get(x+112)==row[x]:
+        return x,row[x]
+    return None
+
+after=[None]*len(events)
+for i in range(len(events)-1,-1,-1):
+    e=events[i]
+    op,d=e[:2]
+    changed=e[2] if op in ("ADD","COPY") else d if op!="MOVE" else None
+    if changed is None:
+        continue
+    after[i]=changed,sink(outputs[changed])
+    if op in ("ADD","COPY"):
+        native.add(outputs[changed],outputs[d],F(e[3]))
+    elif op=="SCALE":
+        outputs[d]={k:v*F(e[2]) for k,v in outputs[d].items()}
+    else:
+        outputs[d]={}
+back=[sink(row) for row in outputs]
+assert all(back[x]==(x,1) for x in ports)
+
+def donor(row):
+    if len(row)!=1:
+        return None
+    (r,c),=row.items()
+    return (r-112,c) if r-112 in ports else None
+
+rows=[{i:F(1)} if i<n else {} for i in range(N)]
+frames=w["initial"]+[None]*w["owned_fields"]
+by_donor=defaultdict(set)
+by_sink=defaultdict(set)
+def add_keys(reg):
+    frame=frames[reg]
+    if frame is None:
+        return
+    s=donor(rows[reg])
+    if s is not None:
+        by_donor[s[0],frame].add((reg,s[1]))
+    z=back[reg]
+    if z is not None:
+        by_sink[z[0],frame].add((reg,z[1]))
+
+def remove_keys(reg):
+    frame=frames[reg]
+    if frame is None:
+        return
+    s=donor(rows[reg])
+    if s is not None:
+        by_donor[s[0],frame].remove((reg,s[1]))
+    z=back[reg]
+    if z is not None:
+        by_sink[z[0],frame].remove((reg,z[1]))
+
+def candidates(changed,cut):
+    for reg in changed:
+        f=frames[reg]
+        if f is None:
+            continue
+        s=donor(rows[reg])
+        z=back[reg]
+        if s is not None:
+            for dst,beta in by_sink[s[0],f]:
+                if reg!=dst:
+                    coeff=-1/(s[1]*beta)
+                    if coeff.denominator&(coeff.denominator-1)==0 and abs(coeff)+1<2**16:
+                        yield s[0],(cut,dst,reg,str(coeff),f)
+        if z is not None:
+            for src,alpha in by_donor[z[0],f]:
+                if reg!=src:
+                    coeff=-1/(alpha*z[1])
+                    if coeff.denominator&(coeff.denominator-1)==0 and abs(coeff)+1<2**16:
+                        yield z[0],(cut,reg,src,str(coeff),f)
+
+hits=defaultdict(set)
+for i in range(N):
+    add_keys(i)
+for port,edit in candidates(range(N),0):
+    hits[port].add(edit)
+for i,e in enumerate(events):
+    op,d=e[:2]
+    changed={d}
+    if after[i] is not None:
+        changed.add(after[i][0])
+    for reg in changed:
+        remove_keys(reg)
+    if op=="MOVE":
+        frames[d]=e[3]
+    elif op=="INIT":
+        frames[d]=e[2]
+        rows[d]={}
+    elif op=="CLEAR":
+        frames[d]=None
+        rows[d]={}
+    elif op=="SCALE":
+        rows[d]={k:F(e[2])*v for k,v in rows[d].items()}
+    else:
+        native.add(rows[d],rows[e[2]],F(e[3]))
+    if after[i] is not None:
+        b,back_after=after[i]
+        back[b]=back_after
+    for reg in changed:
+        add_keys(reg)
+    for port,edit in candidates(changed,i+1):
+        hits[port].add(edit)
+assert frames[:n]==w["final"]
+assert all(row==({i:F(1),i-112:F(1)} if i-112 in ports else {i:F(1)} if i<n else {}) for i,row in enumerate(rows))
+with (root/"PR6824-FREE-HOST-ENTRANCE-CONTACTS.json").open("x") as f:
+    json.dump({"source_sha256":hashlib.sha256(src.read_bytes()).hexdigest(),"native_head":"2a7ca44fbda3abaa4df355b183ed7d7478eef7c1",
+               "ports":len(ports),"cuts":len(events)+1,"hits":{str(port):sorted(edits) for port,edits in sorted(hits.items())},
+               "scope":"Normalized arbitrary-input word. A single ADD whose donor is a scalar times pure Y and whose suffix response is a scalar times (X+Y) realizes exactly the desired entrance shear. Composed and physical claims require further replay."},f,indent=2)
+print("cuts",len(events)+1,"hit ports",len(hits),"hits",sum(map(len,hits.values())))
diff --git a/research/fixed-caller-query-and-host-limits/replay/search_7002_idle_projector_order.py b/research/fixed-caller-query-and-host-limits/replay/search_7002_idle_projector_order.py
new file mode 100644
index 0000000000..d0adab4a9e
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/search_7002_idle_projector_order.py
@@ -0,0 +1,53 @@
+"""Search independent valid projector allocations under different greedy orders."""
+from collections import Counter
+from decimal import Decimal as D, getcontext
+from pathlib import Path
+import json
+import random
+
+root=Path(__file__).resolve().parent
+p=root/"construct_7002_noncoordinate_idle.py"
+src=p.read_text()
+pre=src[:src.index("intervals=sorted(")]
+allocation=src[src.index("chosen=[]"):src.index("# Replay explicit projection")]
+ns={"__file__":str(p)}
+exec(pre,ns)
+stages=ns["stages"]
+masks=ns["masks"]
+count=len(stages)
+ns["Counter"]=Counter
+pairs=[(i,j) for i in range(count) for j in range(i+1,count)]
+getcontext().prec=32
+prices={r:D(r)**D(".995") for r in range(8,8*count+1,8)}
+base_jobs=sum(len(mask)-2 for mask in masks)
+def bill(chosen):
+    bins=Counter(8*(j-i+1) for i,j,_,_ in chosen)
+    bins[8]=base_jobs-sum(r*c//8 for r,c in bins.items())
+    return sum(prices[r]*c for r,c in bins.items()),bins
+results=[]
+best=None
+for seed in range(22):
+    rnd=random.Random(seed)
+    perturb={p:rnd.random() for p in pairs}
+    strength=0 if seed<2 else (seed-1)/3
+    order=sorted(pairs,key=lambda x:(x[0]-x[1]+strength*perturb[x],(-1 if seed==1 else 1)*x[0]))
+    ns["intervals"]=order
+    exec(allocation,ns)
+    chosen=ns["chosen"]
+    value,bins=bill(chosen)
+    results.append({"seed":seed,"strength":strength,"paid_moment_diagnostic":str(value),"jobs":sum(bins.values())})
+    if best is None or value<best[0]:
+        best=(value,chosen,bins,seed)
+        print("best",seed,"moment",str(value),"jobs",sum(bins.values()),flush=True)
+value,chosen,bins,seed=best
+ns["chosen"]=chosen
+exec(src[src.index("def replay("):src.index("profile=Counter(")],ns)
+previous=json.loads((root/"PR7002-NONCOORDINATE-IDLE-WORD.json").read_text())
+reference=sum(prices[int(r)]*c for r,c in previous["idle_rank_profile"].items())
+assert value<=reference
+with (root/"PR7002-IDLE-PROJECTOR-ORDER-SEARCH.json").open("x") as out:
+    json.dump({"trials":results,"best_seed":seed,"rank_histogram":bins,
+               "104_port_advantage_at_005_diagnostic":str(104*(reference-value)),
+               "best_projectors":[[i,j,list(map(str,v)),list(map(str,u))] for i,j,v,u in chosen],
+               "scope":"Bounded deterministic seed/order search on exact projector construction. Exact role-level relocation controls on the best profile; cost comparison diagnostic only."},out,indent=2)
+print("best advantage across 104 ports",104*(reference-value),flush=True)
diff --git a/research/fixed-caller-query-and-host-limits/replay/supplier6824/F6824.json.gz b/research/fixed-caller-query-and-host-limits/replay/supplier6824/F6824.json.gz
new file mode 100644
index 0000000000..06815f76af
Binary files /dev/null and b/research/fixed-caller-query-and-host-limits/replay/supplier6824/F6824.json.gz differ
diff --git a/research/fixed-caller-query-and-host-limits/replay/supplier6824/native.py b/research/fixed-caller-query-and-host-limits/replay/supplier6824/native.py
new file mode 100644
index 0000000000..6f36cbe80d
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/replay/supplier6824/native.py
@@ -0,0 +1,133 @@
+"""Exact native replay and signed physical maps.
+
+Adapted from Ali Romman's independent-helper verifier; native compiler and
+Gaussian interpreter retain their source credit. Inventory, COPY monitor and
+retimed helper extension by @CubeJerry with substantial OpenAI assistance.
+Apache-2.0.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from functools import lru_cache
+from hashlib import sha256
+from pathlib import Path
+import gzip, importlib.util, json, sys
+HERE=Path(__file__).resolve().parent
+def need(ok, why):
+    if not ok:
+        raise ValueError(why)
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw)
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    sys.modules[name] = module
+    spec.loader.exec_module(module)
+    return module
+
+def add(dst, src, q):
+    for k, v in tuple(src.items()):
+        value = dst.get(k, 0) + q*v
+        if value:
+            dst[k] = value
+        else:
+            dst.pop(k, None)
+
+def span(basis):
+    out = {0}
+    for v in basis:
+        need(type(v) is int and 0 < v < 512 and v not in out, 'Independent binary basis')
+        out |= {x ^ v for x in tuple(out)}
+    return frozenset(out)
+
+def replay(w):
+ n=w['public'];N=n+w['owned_fields'];frames=[span(x)for x in w['frames']]
+ need(type(n) is int and len(w['initial'])==len(w['final'])==n, 'Public boundary size')
+ need(len(w['live'])==len(w['ports'])==104, 'Main port inventory')
+ rows=[{r:Q(1)}if r<n else{}for r in range(N)];current=w['initial']+[None]*w['owned_fields']
+ owned=set();paid=Counter();erased=[];peak=0;lifetimes=0;scalar=0;copy=0
+ for i,e in enumerate(w['program']):
+  op,r=e[:2];need(0<=r<N,('role',i))
+  if op=='MOVE':
+   a,b,private=e[2:];need(current[r]==a and private==(r in owned),('move current',i,e,current[r]))
+   need(frames[b]<frames[a]if private else frames[a]<frames[b],('move nesting',i,e))
+   current[r]=b;paid[abs(len(w['frames'][b])-len(w['frames'][a]))]+=1
+  elif op=='INIT':
+   need(r>=n and r not in owned,('init',i));owned.add(r);peak=max(peak,len(owned));lifetimes+=1;rows[r]={};current[r]=e[2];scalar+=2
+  elif op=='CLEAR':
+   need(r in owned and current[r]==e[2],('clear',i));
+   if rows[r]:erased.append(dict(event=i,role=r,frame=e[2]))
+   rows[r]={};current[r]=None;owned.remove(r);scalar+=2
+  else:
+   q,f=Q(e[-2]),e[-1];need(q!=0 and current[r]==f,('scalar frame',i,e,current[r]));a,d=abs(q.numerator),q.denominator
+   need(d&(d-1)==0 and abs(q)+1<2**16,('scalar alphabet',i))
+   if op=='SCALE':
+    need(a&(a-1)==0,('unit',i));rows[r]={k:v*q for k,v in rows[r].items()};scalar+=2*(abs(a.bit_length()-d.bit_length())+int(q<0))
+   else:
+    s=e[2];need(s!=r and 0<=s<N and current[s]==f,('scalar source',i,e,current[s]))
+    if op=='COPY':need(r in owned and not rows[r],('COPY zero',i));copy+=1
+    else:need(op=='ADD',('opcode',i))
+    add(rows[r],rows[s],q);scalar+=2*(3+a.bit_length()-1+a.bit_count()+d.bit_length()-1)
+ need(not owned and current[:n]==w['final'],'exits')
+ for r,row in enumerate(rows):
+  expected={r:Q(1)}if r<n else{}
+  if r-112 in w['live']:expected[r-112]=Q(1)
+  need(row==expected,('endpoint',r,row,expected))
+ main=set(w['live'])|{r+112 for r in w['live']}
+ helpers=Counter()
+ for r in range(n):
+  if r not in main:
+   a,b=w['initial'][r],w['final'][r];need(frames[a]<frames[b],('target nesting',r));helpers[len(w['frames'][b])-len(w['frames'][a])]+=1
+ return dict(public=n,owned_fields=w['owned_fields'],events=len(w['program']),public_inputs=n,owned_lifetimes=lifetimes,peak_owned_fields=peak,real_scalar_allowance=scalar,endpoint_coefficients=N*N,paid=dict(paid),helpers=dict(helpers),erased=erased,peak=peak,lifetimes=lifetimes,scalar=scalar,COPY=copy)
+
+def native(w):
+    n = w['public']
+    C = load(HERE/'retained/native/clifford_exact.py', 'p104_productive_clifford')
+    V = load(HERE/'retained/native/native_verify.py', 'p104_productive_gaussian')
+    @lru_cache(None)
+    def chart(i):
+        return C.canonical_frame(9, tuple(w['frames'][i]))
+    recipes = {}
+    def check(a,b):
+        if (a,b) not in recipes:
+            recipe,_ = C.lower_child(chart(a).adjoint().then(chart(b)))
+            expected = V.adjoint(V.frame(w['frames'][a],9)) + V.frame(w['frames'][b],9)
+            V.equal(V.recipe(recipe),expected,'Native chart change and exact global phase')
+            need(recipe['rank'] == abs(len(w['frames'][a])-len(w['frames'][b])), 'Native boundary rank')
+            recipes[a,b] = recipe
+        return recipes[a,b]
+    for e in w['program']:
+        if e[0] == 'MOVE':
+            check(e[2],e[3])
+    main = set(w['live']) | {r+112 for r in w['live']}
+    helper_profile = Counter()
+    for r in range(n):
+        if r not in main:
+            helper_profile[check(w['initial'][r],w['final'][r])['rank']] += 1
+    adapters = []
+    for r,q in zip(w['live'],w['ports']):
+        need(w['frames'][w['initial'][r]] == [q], 'Literal central port')
+        need(span(w['frames'][w['final'][r+112]]) == frozenset(x for x in range(512) if not (x&q).bit_count()%2), 'Literal output hyperplane')
+        tests = [
+            (C.cgate(9,q,1).adjoint().then(chart(w['initial'][r])), V.adjoint((('C',q,1),))+V.frame(w['frames'][w['initial'][r]],9)),
+            (chart(w['final'][r+112]).adjoint().then(C.cgate(9,q,-1).then(C.fourier(9))), V.adjoint(V.frame(w['frames'][w['final'][r+112]],9))+(('C',q,-1),)+V.fourier(9))]
+        for actual,expected in tests:
+            recipe,_ = C.lower_child(actual)
+            need(recipe['rank'] == 0, 'Free intrinsic main adapter')
+            V.equal(V.recipe(recipe),expected,'Main endpoint phase')
+            adapters.append(recipe)
+    bad = json.loads(json.dumps(next(iter(recipes.values()))))
+    bad['left']['phase'] = (bad['left']['phase']+1)%4
+    a,b = next(iter(recipes))
+    try:
+        V.equal(V.recipe(bad),V.adjoint(V.frame(w['frames'][a],9))+V.frame(w['frames'][b],9),'Wrong phase control')
+    except ValueError:
+        pass
+    else:
+        raise ValueError('Wrong native phase accepted')
+    payload = [[a,b,recipes[a,b]] for a,b in sorted(recipes)] + adapters
+    return {'distinct_maps':len(recipes),'main_adapters':len(adapters),'helper_normalizers':2*sum(helper_profile.values()),
+            'helpers':dict(helper_profile),'recipe_payload_sha256':sha256(json.dumps(payload,sort_keys=True,separators=(',',':')).encode()).hexdigest(),
+            'wrong_phase_rejected':True, 'proof':'Every signed Pauli image and exact global phase; frame induction at every positive tensor width'}
diff --git a/research/fixed-caller-query-and-host-limits/verify.py b/research/fixed-caller-query-and-host-limits/verify.py
new file mode 100644
index 0000000000..ae4883703d
--- /dev/null
+++ b/research/fixed-caller-query-and-host-limits/verify.py
@@ -0,0 +1,55 @@
+"""Replay the submitted, bounded negative checks in a disposable copy."""
+import argparse
+import hashlib
+import json
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+from tempfile import TemporaryDirectory
+
+root = Path(__file__).resolve().parent
+parser = argparse.ArgumentParser(description=__doc__)
+parser.add_argument("suite", choices=("caller", "idle", "host"))
+suite = parser.parse_args().suite
+hashes = json.loads((root / "SHA256.json").read_text())
+for path, expected in hashes.items():
+    assert hashlib.sha256((root / path).read_bytes()).hexdigest() == expected, path
+
+checks = {
+    "caller": [
+        ("screen_7000_central_query_rank", "PR7000-CENTRAL-QUERY-SIGN-RANK"),
+        ("screen_7000_query_host_contacts", "PR7000-QUERY-HOST-TRANSPORT-CONTACTS"),
+        ("price_7004_query_families", "PR7004-QUERY-FAMILY-TARGET-PRICE"),
+        ("certify_7000_sign_query_floor", "PR7000-QUERY-COUNT-SIGN-LOWER-BOUND"),
+    ],
+    "idle": [
+        ("construct_7002_chronological_idle_groups", "PR7002-CHRONOLOGICAL-IDLE-GROUPS"),
+        ("construct_7002_noncoordinate_idle", "PR7002-NONCOORDINATE-IDLE-WORD"),
+        ("search_7002_idle_projector_order", "PR7002-IDLE-PROJECTOR-ORDER-SEARCH"),
+        ("price_7002_75_job_composition", "PR7002-75-JOB-COMPOSITION-PRICE"),
+    ],
+    "host": [
+        ("screen_6824_mixed_first_order", "PR6824-MIXED-FIRST-ORDER-HOST-CONTACTS"),
+        ("screen_6824_two_edit_mixed", "PR6824-TWO-EDIT-MIXED-CANCELLATION"),
+        ("screen_6824_dark_two_contact", "PR6824-TWO-CONTACT-DARK-REACHABILITY"),
+        ("certify_6824_two_add_obstruction", "PR6824-TWO-ADD-HOST-OBSTRUCTION"),
+    ],
+}
+with TemporaryDirectory(prefix="fixed-caller-replay-") as temp:
+    work = Path(temp) / "replay"
+    shutil.copytree(root / "replay", work)
+    for script, receipt in checks[suite]:
+        subprocess.run([sys.executable, "-B", str(work / f"{script}.py")], cwd=work, check=True)
+        name = receipt + ".json"
+        got = json.loads((work / name).read_text())
+        want = json.loads((root / "expected" / name).read_text())
+        assert got == want, f"Replay changed {name}"
+        if receipt == "PR7000-CENTRAL-QUERY-SIGN-RANK":
+            assert [v["fixed_interval_query_lower_bound"] for v in got["branches"].values()] == [4, 4]
+        if receipt == "PR7000-QUERY-HOST-TRANSPORT-CONTACTS":
+            assert got["tested_pairs"] == 300 and got["matches"] == []
+        if receipt == "PR7002-75-JOB-COMPOSITION-PRICE":
+            assert got["jobs_per_port"] == 75
+            assert got["tests"]["1/200"]["remaining_rank_one_equivalents"] == 815
+print(f"PASS_FIXED_CALLER_NEGATIVE_{suite.upper()}")