diff --git a/docs/ci-verification.md b/docs/ci-verification.md
index 63ba3e9aa8..52b62d0481 100644
--- a/docs/ci-verification.md
+++ b/docs/ci-verification.md
@@ -1,8 +1,25 @@
 # CI verification
 
-## Current selected-family replay: #6030
+## Current selected-family replay: #7000 with #7001
 
 The [selected record](../certificates/selected-result.json) binds conditional
+κ = 0.00363005817 to the [application review](research/pr-intake-evidence/pr7000-application/PROOF-REVIEW.md),
+[validation receipts](research/pr-intake-evidence/pr7000-application/VALIDATION.json),
+and [explicit source closure](../certificates/frontier7000-source.json).
+`make frontier7000-verify` follows that exact-source selected replay. The review
+reuses eleven authenticated preceding executions and records seven fresh serial
+application, scalar and complete native-catalogue executions. The earlier
+monolithic timeout is retained separately and is not completed coverage.
+Consult the receipts for exact commands, source heads and limits.
+
+The five inherited framework assumptions remain. No complete uniform word,
+literal multiplier execution, independent human proof or formal-kernel proof
+is asserted. Routine research submissions do not need to rerun this
+selected-family replay. The sections below preserve historical checkpoints.
+
+## Historical selected-family replay: #6030
+
+The [historical checkpoint](../certificates/checkpoints/frontier6030.json) binds conditional
 κ = 0.003125804 to the [proof review](research/pr-intake-evidence/pr6030-audit/PROOF-REVIEW.md),
 [validation receipts](research/pr-intake-evidence/pr6030-audit/VALIDATION.json),
 and [explicit source closure](../certificates/frontier6030-source.json).
diff --git a/research/historical-selected-replay-gap/README.md b/research/historical-selected-replay-gap/README.md
index 55d8cc3b49..36d9a873ca 100644
--- a/research/historical-selected-replay-gap/README.md
+++ b/research/historical-selected-replay-gap/README.md
@@ -69,7 +69,11 @@ python3 -B scripts/research_package.py --package research/historical-selected-re
 
 The direct command prints `PASS_HISTORICAL_SELECTED_REPLAY_GAP`. A registered
 replay prints `PASS_REGISTERED_RESEARCH_PACKAGE`. Both require Git history
-containing the two inspected commits.
+containing the two inspected commits and the source and manifest objects at
+`2485805a6d47f36ea83ddde6327d453ac82d44dc`. The verifier uses a temporary
+sparse checkout of that commit, checks the declared source digests there, and
+uses its planner and manifest inventory. The recorded rejections and selection
+therefore remain reproducible after later changes to the live Makefile or CI guide.
 
 ## Open next questions
 
diff --git a/research/historical-selected-replay-gap/SOURCES.json b/research/historical-selected-replay-gap/SOURCES.json
index c1010eec95..62bb8b3950 100644
--- a/research/historical-selected-replay-gap/SOURCES.json
+++ b/research/historical-selected-replay-gap/SOURCES.json
@@ -4,13 +4,13 @@
   "files": [
     {
       "path": "Makefile",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "0d683a06b9e7ee162496108ce9a7c5d2ee94fccf",
       "sha256": "4f2d4f2dcd15139ec82658a975f85ed300897385f85799218539f4c8d60567da"
     },
     {
       "path": "certificates/partial-swap-network.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "eccafa830c16170c36faf93045ddf1f638f7bcd4",
       "sha256": "4c0b9d37e1034b2076e30a70f8e514416298c462d9ee98bc87fe6556b14df786"
     },
@@ -22,7 +22,7 @@
     },
     {
       "path": "docs/ci-verification.md",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "63ba3e9aa8bdc5e942b56e34244b92b16f854085",
       "sha256": "c7d3027e9ad8bcbff68f07aa9576b30fb2f3c76c44d876d40c7fdbf4a3e2228a"
     },
@@ -34,163 +34,163 @@
     },
     {
       "path": "research/clifford-state-performance/SOURCE.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "6f98a0061a5104dfab82c9e806f819b41811f684",
       "sha256": "396d0f08df24952248140d5c65c51b8c902ef1c580892ff7ea182890530f67ee"
     },
     {
       "path": "research/community-batch1047-audit/CONTENT-COVERAGE.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "5e0f92af463ec12c5e1dcc3effd44081a88af647",
       "sha256": "07a9daeaf2bda308a92e9a4684f13d5fc766c7772d74801fceb7f4599fdab226"
     },
     {
       "path": "research/community-batch1099-audit/CONTENT-COVERAGE.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "9e13266bf85e627f1b7dc225e9530ea69fd2c7f0",
       "sha256": "421e1211fb1897c45621dc6801c276e53f2e6f335583c9c9049e535f87c0a3b1"
     },
     {
       "path": "research/community-batch932-audit/CONTENT-COVERAGE.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "cc4d03eb59b9ab3f952735f7e88ff18c2d15d7af",
       "sha256": "184629cac91a5cfaca50330a88596008b824221433867dcf8117539c913c284a"
     },
     {
       "path": "research/community-batch970-audit/CONTENT-COVERAGE.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "8b9f4111badf7de5d97684799560b55110e9da79",
       "sha256": "23188ed920e38a54006cb883e181585620821c63bf7e8b5e05d32719417cc37e"
     },
     {
       "path": "research/community-frontier741-audit/CONTENT-COVERAGE.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "a5300d4e7a5381a3f443fc54c768ca6f0f236d68",
       "sha256": "3c820fb30e1b4d9bcfc6a7ab524375e5b2abd66b940af2c509146104f0bcd79c"
     },
     {
       "path": "research/community-frontier890-audit/CONTENT-COVERAGE.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "d7ff6d777b01d69b6ce84caf25d3b7e4a4d2f211",
       "sha256": "6b185a9902652f893f3ebd8ada92d2f11b6de6533a9a4d11718a8a4496101128"
     },
     {
       "path": "research/community-hyperplane599-audit/SOURCE.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "546f37d326d10a99910ae8f908e71ef768524d98",
       "sha256": "65099d764bfcc39bda5e4d9966783611b094c3522dbdd1435cd498d657a8ef8e"
     },
     {
       "path": "research/community-k492-audit/SOURCE.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "e538481e4cb16ed936d3195f2dfb5b5a9ca0a76b",
       "sha256": "2c0f4fa5bc150d05658af2e7c54c4d2c337dd52b7efd3d69530ae73bcbdf452a"
     },
     {
       "path": "research/community-reconciliation92-audit/MANIFEST.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "2a2e93685173d5f13cbb5abe740f5d90352e0228",
       "sha256": "5f501f3c118131e7d069f30ad77186eb2ad6961f9680a0ef105f4514ed41808a"
     },
     {
       "path": "research/partial-swap-digest/baseline.py",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "a2f0190704db83bd8ef48e46e723c49b925804fe",
       "sha256": "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34"
     },
     {
       "path": "research/r420-two-sided-basis/SOURCES.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "5d718e11e62f4bcadecf1e02d6b61f87dbe190b0",
       "sha256": "d9810b0d139c5a1211fd2c1f0d142187cc1fca30026e1e7bc4f9ecfacf1596d1"
     },
     {
       "path": "research/skip-clones/SOURCE.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "8d1bb3b9c8189e35e5d8bfdfa632d7473e8be0d5",
       "sha256": "0b68e63e35a97ce6b0cdb6e291b88ebaa8f2dd4afb70b2498f10ee89428258dc"
     },
     {
       "path": "research/split-skip/SOURCE.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "2ab610b6ea2edd2865fda793ef2168b0c76afb4f",
       "sha256": "7c2b4646a3ecfef6f881da5c43e4bd0fa9a4d1b00548b8ab458d897e16735134"
     },
     {
       "path": "scripts/historical-ci-inputs/Makefile",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "aff68409021c9d401a6f8013b9dfd7dbcc30f2a8",
       "sha256": "ea8830dd79da493e2d75baf753d733ff7efbcf2b4794afe41fae0ac8f3055646"
     },
     {
       "path": "scripts/historical-ci-inputs/ledger-batch932-run_isolated_tests.py",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "65db599ab0b1dea0312c4ca048e0bd0f44c3736f",
       "sha256": "96ea543e6c707424afe247e77bd86c82152f90fc76a0773c4232145da5cdf8d1"
     },
     {
       "path": "scripts/historical-ci-inputs/ledger-batch932-test_isolated_test_runner.py",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "34820a8f24678f918f4d0e7a35380d8013fc3495",
       "sha256": "628391b6abfbc8674ceec1751867a4392f2cc0b5b66886243e139af86cf355ac"
     },
     {
       "path": "scripts/historical-ci-inputs/ledger-batch970-verify_selected_result.py",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "c755b76e0d44ba4917aa94440ebe54daefce5b2a",
       "sha256": "d7fd929726b326aeeaf0a3996475adec88eee9aac09ae0bebeeaa0bc1fc8f199"
     },
     {
       "path": "scripts/historical-ci-inputs/ledger-frontier741-ci-verification.md",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "7f3c012504187917a728b9fe87043f0fc8cd006a",
       "sha256": "a854022e0e1d5d4db4d60e586be3ea56005013ef14a1fc06d02bc06e8529c4b0"
     },
     {
       "path": "scripts/historical-ci-inputs/partial-swap-context.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "ad65114886bf34a4fd27e79f3be502389e689faa",
       "sha256": "833a9642f33aeab2ffea17ec9c6b82e0a953f90192b2c82e10bef21538dccba9"
     },
     {
       "path": "scripts/historical-ci-inputs/partial-swap-network.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "52075f2463f60af5e16571347f24274fce73a1ea",
       "sha256": "f3c4be597b2f2136da4ae2cc80c7454f63c90aa01f84e5b8131cee4dd55de815"
     },
     {
       "path": "scripts/partial_swap/shared.py",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "44a0e454c70f9c4b98e258b8443612e6a119904b",
       "sha256": "5a0646a50b9f3e8ea55168620a78e8853b0ab810517cefc8cfb8696aedee278a"
     },
     {
       "path": "scripts/replay_historical_check.py",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "1e92fff2782970ef71378f594f2350d245a4db26",
       "sha256": "5467619c78183d3adc82b0cb55af28e5c1a01fca2b0588677816244b53e2bafd"
     },
     {
       "path": "scripts/research_package.py",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "091b4c8f58bac9a9580d76025b887dc5c873d05f",
       "sha256": "e1256016e7f51827d04fa2179255989f639ae1d97afaa9c16265f85a0c6abd70"
     },
     {
       "path": "scripts/run_isolated_tests.py",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "a96ab35b315ce492e7fbbfd6c5ae211aa066b541",
       "sha256": "49eb56dd0fc0d8d8ffdb209970a7adf2176223580646f575d5c22e59543b381c"
     },
     {
       "path": "scripts/verify_selected_result.py",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "6882a4700e410dec569b51ae2eaf1a19cc019195",
       "sha256": "d6b305eac5b9bdb8172c469ad30a1655a60fa0aceac8b1bf610e1b73f51babd8"
     },
     {
       "path": "tests/test_isolated_test_runner.py",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "343b24abf6719b81805eba5a84c74e57634c8288",
       "sha256": "3a5470d0b139828b90e19bf9583ddeafcd69f8e34f2824664eb3a2958a52e34d"
     }
diff --git a/research/historical-selected-replay-gap/VERIFY.json b/research/historical-selected-replay-gap/VERIFY.json
index 98553e72ed..ab7efa3471 100644
--- a/research/historical-selected-replay-gap/VERIFY.json
+++ b/research/historical-selected-replay-gap/VERIFY.json
@@ -4,36 +4,7 @@
   "python": "3.12",
   "requirements": [],
   "inputs": [
-    "Makefile",
-    "certificates/partial-swap-network.json",
-    "docs/ci-verification.md",
-    "research/clifford-state-performance/SOURCE.json",
-    "research/community-batch1047-audit/CONTENT-COVERAGE.json",
-    "research/community-batch1099-audit/CONTENT-COVERAGE.json",
-    "research/community-batch932-audit/CONTENT-COVERAGE.json",
-    "research/community-batch970-audit/CONTENT-COVERAGE.json",
-    "research/community-frontier741-audit/CONTENT-COVERAGE.json",
-    "research/community-frontier890-audit/CONTENT-COVERAGE.json",
-    "research/community-hyperplane599-audit/SOURCE.json",
-    "research/community-k492-audit/SOURCE.json",
-    "research/community-reconciliation92-audit/MANIFEST.json",
-    "research/partial-swap-digest/baseline.py",
-    "research/r420-two-sided-basis/SOURCES.json",
-    "research/skip-clones/SOURCE.json",
-    "research/split-skip/SOURCE.json",
-    "scripts/historical-ci-inputs/Makefile",
-    "scripts/historical-ci-inputs/ledger-batch932-run_isolated_tests.py",
-    "scripts/historical-ci-inputs/ledger-batch932-test_isolated_test_runner.py",
-    "scripts/historical-ci-inputs/ledger-batch970-verify_selected_result.py",
-    "scripts/historical-ci-inputs/ledger-frontier741-ci-verification.md",
-    "scripts/historical-ci-inputs/partial-swap-context.json",
-    "scripts/historical-ci-inputs/partial-swap-network.json",
-    "scripts/partial_swap/shared.py",
-    "scripts/replay_historical_check.py",
-    "scripts/research_package.py",
-    "scripts/run_isolated_tests.py",
-    "scripts/verify_selected_result.py",
-    "tests/test_isolated_test_runner.py"
+    "scripts/research_package.py"
   ],
   "commands": [
     {
diff --git a/research/historical-selected-replay-gap/verify.py b/research/historical-selected-replay-gap/verify.py
index 83b995941a..9d266c5a4e 100644
--- a/research/historical-selected-replay-gap/verify.py
+++ b/research/historical-selected-replay-gap/verify.py
@@ -6,8 +6,10 @@
 """
 import hashlib
 import importlib.util
+import json
 import subprocess
 import sys
+import tempfile
 from pathlib import Path
 
 ROOT = Path(__file__).resolve().parents[2]
@@ -61,31 +63,47 @@ def require(ok, message):
         raise SystemExit(message)
 
 
-def load_checker():
-    path = ROOT / "scripts/replay_historical_check.py"
-    spec = importlib.util.spec_from_file_location("historical_selected_replay_gap_checker", path)
+def load_module(path):
+    spec = importlib.util.spec_from_file_location(path.stem, path)
     module = importlib.util.module_from_spec(spec)
     spec.loader.exec_module(module)
     return module
 
 
+def checkout_snapshot(snapshot, sources, runner, env):
+    paths = [runner.canonical_relative_path(row["path"]) for row in sources["files"]]
+    git = ["git", "-c", "maintenance.auto=false", "-c", "gc.auto=0",
+           "-c", "core.autocrlf=false"]
+    subprocess.run([*git, "clone", "--quiet", "--shared", "--no-tags", "--no-checkout",
+                    "--", str(ROOT), str(snapshot)], cwd=ROOT, env=env, check=True)
+    subprocess.run([*git, "update-ref", "--no-deref", "HEAD", INSPECTED],
+                   cwd=snapshot, env=env, check=True)
+    # The pinned planner reads omitted manifests from the sparse HEAD/index.
+    patterns = "".join(f"/{path.as_posix()}\n" for path in paths)
+    subprocess.run([*git, "sparse-checkout", "set", "--no-cone", "--stdin"],
+                   cwd=snapshot, env=env, input=patterns.encode("utf-8"), check=True)
+    subprocess.run([*git, "read-tree", "-mu", "HEAD"], cwd=snapshot, env=env, check=True)
+    for path, row in zip(paths, sources["files"], strict=True):
+        require(hashlib.sha256((snapshot / path).read_bytes()).hexdigest() == row["sha256"],
+                "historical checkout source digest changed: " + path.as_posix())
+
+
 def entries(checker):
     for name, config in checker.CONFIG.items():
         for entry in [config, *config.get("additional_inputs", [])]:
             yield name, entry
 
 
-def reject(checker, entry):
+def reject(root, checker, entry):
     try:
-        checker.authenticated_input(ROOT, entry)
+        checker.authenticated_input(root, entry)
     except ValueError as exc:
         return str(exc)
     raise SystemExit("historical input was admitted: " + entry["path"])
 
 
-def main():
-    require(not sys.flags.optimize, "assertions must stay enabled")
-    checker = load_checker()
+def check_snapshot(root, env):
+    checker = load_module(root / "scripts/replay_historical_check.py")
     selected = [entry for name, entry in entries(checker)
                 if name == "tooling-ledger" and entry["path"] == SELECTED_PATH]
     require(len(selected) == 1, "selected-result checker overlay is not unique")
@@ -94,7 +112,7 @@ def main():
     require(entry["accepted_live_sha256"] == [SELECTED_ACCEPTED],
             "accepted selected-checker successors changed")
     frozen = (checker.INPUTS / entry["input"]).read_bytes()
-    live = (ROOT / SELECTED_PATH).read_bytes()
+    live = (root / SELECTED_PATH).read_bytes()
     require(hashlib.sha256(frozen).hexdigest() == SELECTED_PIN, "frozen selected checker bytes changed")
     require(hashlib.sha256(live).hexdigest() == SELECTED_LIVE, "live selected checker digest changed")
     require(SELECTED_LIVE not in (SELECTED_PIN, SELECTED_ACCEPTED), "live checker was already admitted")
@@ -102,7 +120,7 @@ def main():
     # live successor, not a broken comparison.
     require(SELECTED_PIN in (SELECTED_PIN, *entry["accepted_live_sha256"]),
             "pin membership control failed")
-    require(reject(checker, entry) == REJECTIONS[SELECTED_PATH][1],
+    require(reject(root, checker, entry) == REJECTIONS[SELECTED_PATH][1],
             "selected checker rejection text changed")
 
     counts = {path: 0 for path in REJECTIONS}
@@ -110,7 +128,7 @@ def main():
     for _name, item in entries(checker):
         if item["path"] not in REJECTIONS:
             continue
-        message = reject(checker, item)
+        message = reject(root, checker, item)
         counts[item["path"]] += 1
         messages.setdefault(item["path"], message)
     for path, (count, message) in REJECTIONS.items():
@@ -118,20 +136,31 @@ def main():
         require(messages[path] == message, "rejection text changed for " + path)
     require(sum(counts.values()) == 19, "rejection total changed")
     ci = [item for _name, item in entries(checker) if item["path"] == CI_PATH]
-    require(len(ci) == 1 and hashlib.sha256((ROOT / CI_PATH).read_bytes()).hexdigest() == CI_LIVE,
+    require(len(ci) == 1 and hashlib.sha256((root / CI_PATH).read_bytes()).hexdigest() == CI_LIVE,
             "selected CI note digest changed")
 
     diff = subprocess.check_output(
-        ["git", "diff", "--name-only", PARENT, INSPECTED], cwd=ROOT, text=True)
+        ["git", "diff", "--name-only", PARENT, INSPECTED], cwd=root, env=env, text=True)
     changed = sorted(name for name in diff.splitlines() if name)
     require(changed == CHANGED, "inspected commit diff changed")
-    sys.path.insert(0, str(ROOT / "scripts"))
-    from research_package import plan_details
-    details = plan_details(ROOT, set(changed))
+    planner = load_module(root / "scripts/research_package.py")
+    details = planner.plan_details(root, set(changed))
     require([row["package"] for row in details] == PLAN_PACKAGES, "helper plan selection changed")
     matched = {name for row in details for names in row["causes"].values() for name in names}
     require(sorted(set(changed) - matched) == UNMATCHED, "unmatched plan paths changed")
-    require(plan_details(ROOT, set()) == [], "empty change set selected a package")
+    require(planner.plan_details(root, set()) == [], "empty change set selected a package")
+
+
+def main():
+    require(not sys.flags.optimize, "assertions must stay enabled")
+    sources = json.loads(Path(__file__).with_name("SOURCES.json").read_bytes())
+    require(sources["base_commit"] == INSPECTED, "historical checkout base changed")
+    runner = load_module(ROOT / "scripts/research_package.py")
+    env = runner.git_source_env()
+    with tempfile.TemporaryDirectory(prefix="historical-selected-replay-") as temporary:
+        snapshot = Path(temporary) / "snapshot"
+        checkout_snapshot(snapshot, sources, runner, env)
+        check_snapshot(snapshot, env)
     print("PASS_HISTORICAL_SELECTED_REPLAY_GAP")
     print("selected_checker_live=" + SELECTED_LIVE)
     print("rejections=19 distinct_paths=7 plan_packages=9")
diff --git a/research/p104-frontier-7156-application-review/APPLICATION.md b/research/p104-frontier-7156-application-review/APPLICATION.md
new file mode 100644
index 0000000000..5fbb77cb82
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/APPLICATION.md
@@ -0,0 +1,206 @@
+# Exact-source application of the selected conditional framework
+
+The conclusion under the five inherited premises is
+`T(n) = O(n (log n)^(1-0.003644407895539))` on the same bit-complexity
+model as the selected result. This proof specializes the
+[#7000/#7001 application](../../docs/research/pr-intake-evidence/pr7000-application/PROOF-REVIEW.md)
+to the exact #7156 word and exact #7113 caller. [RESULT.json](RESULT.json)
+gives the rational parameters and independent numerical checks.
+
+## Native word, arbitrary inputs and absolute phase
+
+The input to the chart-306 construction is the exact #7155 word. Reverse
+propagation of the five timed gather coefficients gives
+`c = -5e1029/2 - 4e349 - 2e1025 + 2e334`. Forward propagation of all
+seven injections gives
+`d = -e349/2 + e1021/2 - e831/2 - e334/2`, with all other public, owned
+and guarded suffix coordinates zero. The pairing is `c d = 1`. Both
+supports are in the same helper boundary group. The pivot is 831 at
+cut 36,772. The contact-free paths retain the literal contacts and paid
+ranks except that role 1,034's rank-eight MOVE is replaced by the nested
+`9 → 306 → 127` path of ranks three and five. Its midpoint is reached
+in time for the later observation. The causal two-buffer identity in
+[#7156's proof](https://github.com/CrocSwap/integer-mult-bounds/blob/b44944c3058d522cbff17836e16240d40d77a927/research/p104-temporal-chart306-continuation/PROOF.md)
+returns the new arbitrary helper and preserves all other endpoints. The
+whole-word exact forward and adjoint checks check that transfer independently
+of the discovery search.
+
+For a live field with frame U, write its physical contents as
+`T_U^(tensor f) z`. A MOVE is the exact quotient between frames. All
+scalar contacts are between equal frames. A nested quotient factors as
+`L C_r R` and its tensor product gives one rank-`rf` child with both
+monomial adapters. Its absolute phase `i^a` becomes `i^(af)`.
+Rational coefficients stay outside tensor products, so the full scalar
+identity applies to arbitrary arrays at every positive column multiplicity
+under the retained native premise. The catalogue compares complete signed
+Pauli actions and one nonzero Gaussian state scalar for each Clifford
+comparison. The former fixes the quotient up to phase, and the latter
+fixes that phase. The cold run also checks all 512 columns on the affected
+chart pairs. The word has 400 main slots, 1,098 independent helpers,
+61 owned labels, 64 lifetimes, peak 47 and owned ascent rank mass 56.
+Owned fields remain subject to complete initialization, return and
+retirement under the selected erasure premise.
+
+Deleting the literal injection at zero-based event 37,799 keeps the
+new helper's unit pulse correct while corrupting 24 other public outputs.
+The independent checker rejects the altered complete endpoint. A synthetic
+dirty COPY followed by erasure has a correct final endpoint and fails the
+interior zero guard. The actual word's COPY is covered by the whole-word
+exact replay.
+
+## Signed caller and complete paid ownership
+
+Bind the 104 ports to 96 type-A and eight type-B ports, each with 36 root
+roles. Each of 17 occurrences has separate owned and helper labels.
+Main owners are the literal distinct caller roles, with all 400 contacts
+bound injectively per invocation. The independent census rejects a repeated
+A owner even though counts are unchanged. Each physical boundary includes
+its phase translation and fixes external spectators. The cold replay uses
+the selected physical-checker source with counted substitutions for the new
+occurrence geometry and signed idle. Its 104 main boundary pairs compare
+the complete maps up to exact signed Pauli action and absolute phase.
+
+Use the same formal substitution as in the selected proof in the ring
+`Q(i)[q,D_1,...,D_17]/(q^4-1)`. The signed caller replay compares every
+final role with its signed diagonal row. Its packed body encoding uses
+radix 256 with per-stage degree bounded by 35. In the physical application,
+the stage factors act on distinct eight-axis blocks and commute with the
+central Q of order four. Thus the formal caller equality applies at
+every column multiplicity. A signed idle `Q_f^-1 D_s` is one positive
+rank-nine child `Q_f D_s` with the charged translation `Q_f^2`. The
+source phase-polynomial checker applies the same absolute-phase rule to
+negative root targets, QUERY and contact boundaries. It checks both
+directions and the complete coordinate map.
+
+For s equal to +1 or -1 the caller's LAMBDA is the whole operator
+`((1+is)I+(1-is)Q_f^2)/2 = P_+ + is P_-`, where
+`P_± = (I ± Q_f^2)/2`. This is unitary and uses a complete ordinary
+translation and scalar mix, with one full initialized serial scratch
+shared with QUERY. At multiplicity two take the tensor square of
+`v=(1,-1)`, on which the one-axis C has eigenvalue i. Whole LAMBDA
+with s=+1 acts as +1 there. Applying the one-axis LAMBDA independently
+on each axis acts as -1. The exact control protects the whole-factor
+interpretation.
+
+The 3,744 main root targets and 18,666 fresh helpers total 22,410 productive
+fields. There are 110,502 paid positions, 13,600 translated native
+boundaries and no empty-root credits. The independent rank census checks
+the complete signed old and new histograms. The supplier's fresh physical
+receipt covers the detailed owner, phase and spectator bindings. The signed
+rank surplus is 1,424.
+
+## Exact scalar service and common root format
+
+The exact per-native-call scale is 1125 with fractional depth 25.
+The caller uses the separately charged scale 675. The fresh source-bound
+prefix and pre-product checks bind both conversions and their reciprocals,
+the odd and binary divisibility at every affected operation, and the
+whole LAMBDA numerator before halving. A completed normalized output is
+dyadic, so the terminal divisions by the two odd scales are exact. Scales
+are attached to the actual occurrences and their lifetimes.
+
+For a reduced fixed scalar a/b the selected product transducer has carry
+in `[0, |a|]`. The quotient scan uses remainder in `[0,b)`, updating it
+from `2r+u` on input bit u. A zero final remainder proves the exact
+quotient. These two invariants give the same linear scan for every
+component width, with finite control compiled from each literal a and b.
+The selected source census's 19-bit denominator bound was specific to
+that word. This word has a 20-bit denominator in `-97039/655360` and still
+has numerator width at most 24. A fixed larger remainder state space
+preserves the per-bit scan and the tape alphabet. Padding depends on
+the product and subsequent signed addition, for which 26 temporary
+bits suffice. The retained reference scans pass 95,482 exact cases over
+7,079 distinct literal rational components and reject 6,703 nonexact
+remainders. These finite tests supplement the transducer invariant.
+
+Keep the whole original D-bit root factor throughout descent. Only external
+ROW is partitioned into roles. With complete, source-bound endpoints,
+a finished child joins the accumulated Clifford and resets its extra
+exterior debt relative to its entrance. The fresh bounds give height 406
+and coefficient-mass bits 1,215 per unfinished context, so use
+`c=2 max(406,1215)=2430`. At the funded carrier `N=2^H`,
+`4096 K* < N` with `K*=1920·153^1920·(H+1)^2`. The retained depth bound
+gives `t≤K* floor(log_N D)`. For D≥N use `N ell≤N^ell≤D` with
+`ell=floor(log_N D)` to get `2430t<D`. For D<N there is no unfinished
+ordinary nesting. The fixed-root Clifford denominator and norm bounds
+then give the same `F=p+D`, `W=p+h+2D+3` and `W+26` temporary format.
+Induction on the finite ideal tree gives the exact numerical simulation
+with complete returns. The selected root preprocessing, final H0 factors
+and single truncation in #7000 §5 apply on that format and supply the
+same input to analytic recovery.
+
+## Finite tariff, storage and funding
+
+The 781,880,696 ordinary source-unit total includes the signed idle,
+scalar surcharges and both sets of boundary conversions. The physical
+bit-tape bound charges 43,689,280 complete scalar services, each within
+the selected allowance of `2^20` steps per padded component bit.
+It also charges 298,672 complete monomial maps, including both sides of
+paid and productive jobs, all native contacts, idle, QUERY, LAMBDA and
+the extra signed-idle translations. With 145 actual ambient axes,
+`4(145+1)^2` elementary records per map gives 25,465,969,408 records.
+The two tariffs retain their own units and the selected primitive movement
+and setup constants. One raw unit reserves `17·61=1,037` native banks and
+one serial QUERY/LAMBDA bank. Full capacities and returns are charged.
+
+In the finite compiler use its actual compiled productive width W,
+paid count P, carrier N and complete setup/route/scalar bill G.
+For raw occurrence count U and native occurrence count J take
+`O=61J+U+O_aux`, with unique occurrence ownership and the retained
+compiler, discarded-target and primitive reserves in `O_aux`.
+Substitute these into `Z=W+O`, `E0=64(Z+N+P+G+1)^3`,
+`B0=P+E0` and `C0=32 N B0²`, and use the actual W in
+`W^(2+ceil(log_N d))`. Include the simultaneous completed BIT stock.
+The compiler applies the same ambient bound `153^1920` and uses
+the same complete-factor depth-first parking. These new finite
+constants and the smaller positive margins enter the eventual cutoffs
+through the explicit fixed-polynomial threshold construction in #7000 §6.
+
+The exact funded price is `C=κ+7g=0.00364440789553907`,
+`g=10^-17`. The new signed moment has a strict positive lower bound
+at C, and #7155 has a strict negative upper bound at the proposed κ.
+The directed gate brackets the raw crossing and checks its derivative.
+Product power 1,920, cutoff 11, completion floor 12 and tail offset 1/7
+satisfy the retained separated funding inequalities. The written
+logarithmic power is 2,237. Integer comparison gives
+`(H+1)^2237 < 2^(gH)` for `H=16510400000000000000000` and rejects the
+preceding grid point. The input-lift derivative with respect to exponent
+`p=1-κ` is uniformly negative on the checked interval. Equivalently the
+saving-coordinate derivative is positive. The lift vanishes at κ=0 and
+is strictly positive at both proposed prices.
+
+The nine-stage equal-target packing law in
+[the local-word ceiling](../complex-local-word-ceiling/README.md) has
+different hypotheses. For this fixed mixed target histogram and 17
+fixed native words, hold the remaining paid rank mass 109,088 constant
+and allow fractional remainder at any rank at most 145. For positive x,
+`r^(-x)` decreases in r, so assigning all remaining mass to rank 145
+is the favorable relaxation. The certified relaxed moment crosses in
+`[0.00580448601471, 0.00580448601473]` and decreases on `[0,1/32]`.
+Within that fixed-profile relaxation the proposed κ is about 62.7861%
+of the raw packing ceiling. This bound concerns the fixed histograms,
+mass and ambient cap.
+
+## Outer conclusion and admission boundary
+
+Use complex uniform saving `κ+6g` at `N=2^H`. The authenticated
+selected BIT data and completed cover supply `0.00385248`, which exceeds
+the retained weaker premise `0.00376669`. The selected outer formula
+evaluator gives all 54 strict and four functional inequalities with
+minimum guard `10^-18`. Its nine named savings exceed κ. The limiting
+slack is `299635559210446097/10^34`. Substituting BIT at and just below
+the effective saving into the actual evaluator rejects both. The analytic
+decomposition, simultaneous stocks, fine-prime avoidance and exact
+recovery now use the same outer framework with the new rational parameters.
+
+The five inherited premises are `native_all_columns`, `owned_erasure`,
+`compiler`, `precision_tape` and `analytic_recovery`. The candidate
+cold execution and hosted supplier job cover the changed complex source.
+The selected recorded evidence supplies the unchanged BIT and framework
+sources. One inherited intermediate receipt carries the earlier
+same-native scope sentence. The exact adapters, complete fresh native
+replay and current phase, precision and physical receipts are the
+evidence for the changed word. The intermediate BIT fault marker is
+supplemented by the actual outer-evaluator mutation above. The result
+remains conditional and requires maintainer mathematical review for
+repository selection.
diff --git a/research/p104-frontier-7156-application-review/INPUTS.json b/research/p104-frontier-7156-application-review/INPUTS.json
new file mode 100644
index 0000000000..e43c02b770
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/INPUTS.json
@@ -0,0 +1,94 @@
+{
+  "sources": [
+    {
+      "pr": 7156,
+      "commit": "b44944c3058d522cbff17836e16240d40d77a927",
+      "path": "research/p104-temporal-chart306-continuation/WORD.json.gz",
+      "file": "inputs/pr7156/WORD.json.gz",
+      "git_blob": "d05462ff386d710b6ec3e4d7ebdbfdba1da496cf",
+      "sha256": "e950eab5cc3f3fc8a2554e488114d788741d3262381459688ebaea08cd0a4d50",
+      "bytes": 380570
+    },
+    {
+      "pr": 7156,
+      "commit": "b44944c3058d522cbff17836e16240d40d77a927",
+      "path": "research/p104-temporal-chart306-continuation/WITNESS.json",
+      "file": "inputs/pr7156/WITNESS.json",
+      "git_blob": "5abaa48c8078744013d091281237c87b53d03403",
+      "sha256": "d48dac72cf9b6d07e6903db5d0c00f903e74256815c5f9af79e734f540b79d6d",
+      "bytes": 2088
+    },
+    {
+      "pr": 7156,
+      "commit": "b44944c3058d522cbff17836e16240d40d77a927",
+      "path": "research/p104-temporal-chart306-continuation/PATHS.json",
+      "file": "inputs/pr7156/PATHS.json",
+      "git_blob": "a33773333cf0c9736e14145503132784b22f2666",
+      "sha256": "60195cf6db4faa98a3e2b7ce5d1b00cd6345a4b87ab43030c9066da23f91e4a7",
+      "bytes": 1714
+    },
+    {
+      "pr": 7156,
+      "commit": "b44944c3058d522cbff17836e16240d40d77a927",
+      "path": "research/p104-temporal-chart306-continuation/RESULT.json",
+      "file": "inputs/pr7156/RESULT.json",
+      "git_blob": "b27ddf273c75cb67d10603594904d5019d1d4cd1",
+      "sha256": "88fba8e4b5a6965545d4e32889be4c4c25db9d9b5d70c45147d20db4d56f1985",
+      "bytes": 79518
+    },
+    {
+      "pr": 7156,
+      "commit": "b44944c3058d522cbff17836e16240d40d77a927",
+      "path": "research/p104-temporal-chart306-continuation/NATIVE-RESULT.json",
+      "file": "inputs/pr7156/NATIVE-RESULT.json",
+      "git_blob": "3d84a6fa5f2a0f80f01ef7d17aaec3cef66765c7",
+      "sha256": "69664f6939c0ec4507ee4b849a289dbe4ede0b5c33d9dc95ae319827fc43af0d",
+      "bytes": 75496
+    },
+    {
+      "pr": 7156,
+      "commit": "b44944c3058d522cbff17836e16240d40d77a927",
+      "path": "research/p104-temporal-chart306-continuation/NOTICE",
+      "file": "inputs/pr7156/NOTICE",
+      "git_blob": "45ae369fa941ebc0dba6f2a956220ad4b4b0e339",
+      "sha256": "f86fdd80256d606ed8d8b441fcf62ede86d1dd41df96c612d1a4758aa03ab1fe",
+      "bytes": 1527
+    },
+    {
+      "pr": 7155,
+      "commit": "594d57036057f88f8bacc82e9c203bd4cb3276b9",
+      "path": "research/p104-temporal-237-595-composition/WORD.json.gz",
+      "file": "inputs/pr7155/WORD.json.gz",
+      "git_blob": "7de0c810805462f27c371e20d09e0bcb1f70e317",
+      "sha256": "ba1d4315fb4fcf8f73d63a8a22a223bb139bbae1bab0eab2eb92d61a54cc4c23",
+      "bytes": 380290
+    },
+    {
+      "pr": 7155,
+      "commit": "594d57036057f88f8bacc82e9c203bd4cb3276b9",
+      "path": "research/p104-temporal-237-595-composition/NOTICE",
+      "file": "inputs/pr7155/NOTICE",
+      "git_blob": "c5466006c2fddd09e3e88abee58726357fdacb50",
+      "sha256": "a9fe84d751db2dc6cada5b267e2ff84ce5705880aab5d0a2515413cc15187060",
+      "bytes": 1223
+    },
+    {
+      "pr": 7113,
+      "commit": "07a76c5e2738882c0cb322278e56f6cae3c9885d",
+      "path": "research/signed-caller-8x9/expected/ODD-TYPE-AB-CALLER.json",
+      "file": "inputs/pr7113/CALLER.json",
+      "git_blob": "9451ceaf6e8e037894680b549f3ef41c21b260d7",
+      "sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc",
+      "bytes": 117156
+    },
+    {
+      "pr": 7113,
+      "commit": "07a76c5e2738882c0cb322278e56f6cae3c9885d",
+      "path": "research/signed-caller-8x9/LICENSE",
+      "file": "inputs/pr7113/LICENSE",
+      "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64",
+      "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+      "bytes": 11357
+    }
+  ]
+}
diff --git a/research/p104-frontier-7156-application-review/NOTICE b/research/p104-frontier-7156-application-review/NOTICE
new file mode 100644
index 0000000000..9a8aed91a5
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/NOTICE
@@ -0,0 +1,17 @@
+Prepared for Clear1nsight with substantial OpenAI Codex and ChatGPT Pro
+assistance. New review code and text are Apache-2.0.
+
+Rohan Arun supplied the chart-306 continuation and the signed 17-stage
+caller. Clear1nsight supplied #7155 and this application review. Ali Romman
+supplied the causal-history owned-buffer identity. Jerry Chen / CubeJerry
+supplied contact-free retiming, temporal verification and common-grid
+review. dillona supplied the chart-595 source and temporal replay
+adaptation. Matarener supplied complete helper kernels. ToikY supplied
+the directed pricing lineage and chart leads.
+
+Douglas Colkitt and the #7000/#7001 reviewers supplied the selected
+exact-scalar, physical and application review. The outer evaluator
+retains zxv's #4359 endpoint, Jacob Alan Sussman's mixed-target flow,
+Cinna Davis's #4470 and intqwq's #4610 instantiation. The selected BIT,
+compiler and phase sources retain all original credit. The exact #7155
+and #7156 notices and the #7113 license are kept alongside their inputs.
diff --git a/research/p104-frontier-7156-application-review/README.md b/research/p104-frontier-7156-application-review/README.md
new file mode 100644
index 0000000000..8b649e0726
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/README.md
@@ -0,0 +1,82 @@
+# Application review for conditional κ = 0.003644407895539
+
+[PR #7156](https://github.com/CrocSwap/integer-mult-bounds/pull/7156) supplies the
+chart-306 continuation of [#7155](https://github.com/CrocSwap/integer-mult-bounds/pull/7155).
+This review supplies an exact-head cold replay, separate checks of the
+affected application, and a written transfer of the five selected #7000
+premises. The proposed bound is **κ = 0.003644407895539**, an increase of
+0.000014349725539 over the selected #7000/#7001 record and 0.000000140810139 over
+#7155. Selection requires maintainer mathematical review under the
+[repository's frontier lane](../../docs/research/research-archive-intake.md).
+
+The exact proposed parameters, both uniform savings, all nine outer savings
+and the limiting slack are in the `proposed` object of [RESULT.json](RESULT.json).
+[APPLICATION.md](APPLICATION.md) gives the proof and its scope. The application
+uses the unchanged signed [#7113 caller](https://github.com/CrocSwap/integer-mult-bounds/pull/7113),
+with 17 native invocations on ambient 145. The complete invoice has 110,502
+paid positions, 22,410 productive fields and rank surplus 1,424 with zero
+empty-root credit. The proof retains the compiler's conservative ambient
+cap of 153.
+
+## Reproduce
+
+```sh
+python3.12 -I -B research/p104-frontier-7156-application-review/verify.py
+python3.12 scripts/research_package.py --package research/p104-frontier-7156-application-review
+```
+
+The registered review check matches the complete receipt. It uses Python
+3.12 and the standard library. It independently recomputes the temporal
+certificate, literal rank invoice, fixed-tape counts, directed numerical
+bounds and exact outer predicates. It invokes the pinned selected
+carry/remainder implementation on all literal coefficients. The cold supplier
+check is a separate replay.
+
+```sh
+# In an isolated checkout of PR #7156 at b44944c3058d522cbff17836e16240d40d77a927
+python3.12 scripts/research_package.py --package research/p104-temporal-chart306-continuation
+```
+
+The supplier replay exited zero in 819.98 seconds and used 662,444 KiB peak
+RSS. It checked the complete normalized native and signed caller endpoints,
+all 3,037 catalogue maps, all 104 main boundary pairs, precision, physical
+binding and the outer gates. See the
+[cold replay](evidence/CANDIDATE-REGISTERED-COLD.log) and
+[exact commit check](evidence/CANDIDATE-GIT-CHECK.log). The exact-head
+[hosted supplier job](https://github.com/CrocSwap/integer-mult-bounds/actions/runs/42947927760/job/130286697795)
+also passed. Its sibling
+[historical replay](https://github.com/CrocSwap/integer-mult-bounds/actions/runs/42947927760/job/130286697696)
+failed on the historical package's Makefile source pin.
+
+[SOURCES.json](SOURCES.json) pins selected main inputs.
+[INPUTS.json](INPUTS.json) binds the small frozen PR review inputs by commit,
+path, Git blob, SHA256 and length. The registered check authenticates the
+vendored bytes offline. To verify their provenance, fetch the named
+`refs/pull/<number>/head` refs separately, ensure the recorded commits are
+available, and compare each row against
+`git --no-replace-objects ls-tree <commit> -- <path>` and
+`git --no-replace-objects cat-file blob <git_blob>`. The local cold review
+compared the complete 32-member #7155 archive and the 30-member #7113
+review slice against the directly fetched PR trees. The
+[source audit](evidence/SOURCE-AUTHENTICATION.json) also binds the selected
+BIT data and the selected physical checker by byte equality. The
+[closure comparison](evidence/SELECTED-CLOSURE-DELTA.json) and
+[recorded-evidence check](evidence/SELECTED-RECORDED-EVIDENCE.log) bind the
+unchanged selected 220-path scientific closure and its 18 recorded executions.
+
+## Open next questions
+
+- Review this application for conditional frontier selection. The next step
+  is a maintainer's reading of the common-grid, stock and outer proof
+  against the pinned source and the preserved receipts. The five inherited
+  framework assumptions remain. This package gives finite evidence and a
+  mathematical application argument. A materialized uniform word, literal
+  multiplier execution and independent human or formal proof remain outside
+  this contribution.
+
+## Credit
+
+Rohan Arun supplied #7156 and the #7113 signed caller. Clear1nsight supplied
+#7155 and this exact-source application review with substantial OpenAI Codex
+and ChatGPT Pro assistance. The [notice](NOTICE) records the inherited work.
+Coordination is in the [P104 board](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19533717).
diff --git a/research/p104-frontier-7156-application-review/RESULT.json b/research/p104-frontier-7156-application-review/RESULT.json
new file mode 100644
index 0000000000..8cbf48f0e1
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/RESULT.json
@@ -0,0 +1,179 @@
+{
+  "aliased_main_rejected": true,
+  "chart": {
+    "c": {
+      "1025": "-2",
+      "1029": "-5/2",
+      "334": "2",
+      "349": "-4"
+    },
+    "collateral": [
+      303,
+      334,
+      349,
+      356,
+      408,
+      774,
+      781,
+      797,
+      842,
+      849,
+      859,
+      864,
+      1020,
+      1025,
+      1026,
+      1051,
+      1064,
+      1066,
+      1122,
+      1128,
+      1146,
+      1176,
+      1229,
+      1328
+    ],
+    "d": {
+      "1021": "1/2",
+      "334": "-1/2",
+      "349": "-1/2",
+      "831": "-1/2"
+    },
+    "erased_dirty_copy_rejected": true,
+    "gather_count": 5,
+    "injection_count": 7,
+    "omitted_injection": 37799,
+    "pulse": 1497
+  },
+  "exact_scalars": {
+    "distinct": 7079,
+    "divisor_bits": 20,
+    "exact_cases": 95482,
+    "numerator_bits": 24,
+    "remainder_controls": 6703,
+    "wide_divisor_example": "-97039/655360"
+  },
+  "finite_bill": {
+    "ambient": 145,
+    "compiler_cap": 153,
+    "elementary_records": 25465969408,
+    "main": 3744,
+    "monomial_maps": 298672,
+    "native_banks": 1037,
+    "native_contacts": 13600,
+    "native_helpers": 18666,
+    "ordinary": 781880696,
+    "paid": 110502,
+    "precision_c": 2430,
+    "productive": 22410,
+    "scalar_coefficient": 45811530465280,
+    "scalar_services": 43689280,
+    "serial_scratch": 1,
+    "surplus": 1424
+  },
+  "numeric": {
+    "H": 16510400000000000000000,
+    "alpha_upper": "1461501637330901174391114548731906406717566317231/1461501637330902918203684832716283019655932542976",
+    "delta_upper": "331042476128062423085715414609860363362278457145/365375409332725729550921208179070754913983135744",
+    "fraction_of_packing_ceiling_lower": "3644407895539/5804486014730",
+    "fraction_of_packing_ceiling_upper": "3644407895539/5804486014710",
+    "gamma_upper": "687464245122367855205498926463248907990241479735/730750818665451459101842416358141509827966271488",
+    "input_lift_p_derivative_upper": "-1344482878675397912478266815118544434586450215/1461501637330902918203684832716283019655932542976",
+    "log_power": 2237,
+    "packing_raw_bracket": [
+      "580448601471/100000000000000",
+      "580448601473/100000000000000"
+    ],
+    "paid_remainder_rank_mass": 109088,
+    "previous_margin_upper": "-79813320214798272070250310261518955454037760665/1461501637330902918203684832716283019655932542976",
+    "raw_bracket": [
+      "36444078955399752291473031465479/10000000000000000000000000000000000",
+      "911101973884993807286825786637/250000000000000000000000000000000"
+    ],
+    "tested_margin_lower": "513077818990190852818553055832036810081/1461501637330902918203684832716283019655932542976"
+  },
+  "proposed": {
+    "admitted_bit_saving": "12039/3125000",
+    "assumptions": [
+      {
+        "id": "native_all_columns",
+        "statement": "Retained native operators, phase conventions, spectators and whole-job adapters work at every positive column multiplicity."
+      },
+      {
+        "id": "owned_erasure",
+        "statement": "Owned streams and suspended centers obey the retained allocation, erasure and ownership contracts."
+      },
+      {
+        "id": "compiler",
+        "statement": "The finite mixed-target compiler and chronological product, completion and splitting satisfy the retained uniform closure contract."
+      },
+      {
+        "id": "precision_tape",
+        "statement": "Retained fixed-tape movement and precision/storage prescriptions apply to the new fixed finite template."
+      },
+      {
+        "id": "analytic_recovery",
+        "statement": "Analytic decomposition, fine-prime avoidance and exact integer recovery follow the retained upstream/outer framework."
+      }
+    ],
+    "bit_at_and_below_effective_rejected": true,
+    "complex_bit_premise": "376669/100000000",
+    "complex_uniform": {
+      "actual_raw_ambient": 145,
+      "compiler_raw_ambient_cap": 153,
+      "rank_encoding": "2^16510400000000000000000",
+      "saving": "182220394776953/50000000000000000"
+    },
+    "delta_over_pr7155": "140810139/1000000000000000",
+    "delta_over_selected": "14349725539/1000000000000000",
+    "functional_count": 4,
+    "kappa": "3644407895539/1000000000000000",
+    "minimum_guard": "1/1000000000000000000",
+    "nine_outer_savings": {
+      "boundary_algebraic_matrix": "36444078955390399635559210446097/10000000000000000000000000000000000",
+      "fused_gaussian": "36444078955390398906677631338291/10000000000000000000000000000000000",
+      "global_coordinate_router": "22777549347119/6250000000000000",
+      "group_bit_router": "2277754934711906181667351958643/625000000000000000000000000000000",
+      "group_scans": "49999999999999999/50000000000000000",
+      "main_transform": "36444078955390299635559210446097/10000000000000000000000000000000000",
+      "microbox_face_corrections": "1925000000000000001/25000000000000000",
+      "polynomial_products": "99999999999999999/100000000000000000",
+      "sparse_union_movement": "4098944078955390399635559210446097/10000000000000000000000000000000000"
+    },
+    "outer_parameters": {
+      "a": "22777549347119/6250000000000000",
+      "b": "72888157910781/20000000000000000",
+      "beta": "99999999999999997/100000000000000000",
+      "bit_saving": "376669/100000000",
+      "complex_uniform_saving": "182220394776953/50000000000000000",
+      "d": "1/100000000000000000",
+      "epsilon": "99999999999999999/100000000000000000",
+      "kappa": "3644407895539/1000000000000000",
+      "layout": "1/100000000000000000",
+      "q": "364440789553903/100000000000000000",
+      "r0": "1/1000000000000000000",
+      "stop": "1/100000000000000000",
+      "tested_saving": "364440789553907/100000000000000000"
+    },
+    "retained_bit_before_cover": {
+      "ambient": 134,
+      "family": "BIT before cover",
+      "rank_encoding": "2^296630000000000",
+      "saving": "38525299/10000000000"
+    },
+    "schema": "conditional-frontier-proposal/1",
+    "source_heads": {
+      "pr7113": "07a76c5e2738882c0cb322278e56f6cae3c9885d",
+      "pr7155": "594d57036057f88f8bacc82e9c203bd4cb3276b9",
+      "pr7156": "b44944c3058d522cbff17836e16240d40d77a927"
+    },
+    "strict_count": 54,
+    "strict_limiting_slack": "299635559210446097/10000000000000000000000000000000000",
+    "tested_complex_price": "364440789553907/100000000000000000"
+  },
+  "status": "PASS_SOURCE_BOUND_7156_APPLICATION_REVIEW",
+  "whole_lambda": {
+    "axiswise": "-1",
+    "whole": "+1"
+  }
+}
diff --git a/research/p104-frontier-7156-application-review/SOURCES.json b/research/p104-frontier-7156-application-review/SOURCES.json
new file mode 100644
index 0000000000..a52c7140bb
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/SOURCES.json
@@ -0,0 +1,60 @@
+{
+  "schema_version": 1,
+  "base_commit": "e54523517d0f03e58352e647c403a5af3e525a57",
+  "files": [
+    {
+      "path": "certificates/frontier7000-source.json",
+      "usage": "provenance",
+      "git_blob": "8bef362348070bbaff01db24d976cfbd7a18ac61",
+      "sha256": "f437972e07c734bf37f6baf3a32c636cf528e26966510b439417211ce60a9826"
+    },
+    {
+      "path": "certificates/frontier7000/CLAIM.json",
+      "usage": "input",
+      "git_blob": "c9b816f8445be9dc19b2259e03e9d8709d18c87a",
+      "sha256": "3f8add8252adb223b60418ec69351a69b6b5edfe601ec1c6b4b65cd9e2afd9b2"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "75d77b328ea02ded535e7f23aee5b1e55d0bb1a8",
+      "sha256": "154c3d30455d778fd3343b6b4851f0fa4665f0f7625b0adb3675e2bafbbf6bf1"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "docs/research/pr-intake-evidence/pr7000-application/PROOF-REVIEW.md",
+      "usage": "provenance",
+      "git_blob": "3dd1af2285e597676725e85ad4f65e7ad326d695",
+      "sha256": "4501502c2ceb9759b20372435fe4beb51082c5a5e2910c1fd5dbe6edca415055"
+    },
+    {
+      "path": "docs/research/pr-intake-evidence/pr7000-application/check_exact_scalar.py",
+      "usage": "input",
+      "git_blob": "72dc728777162fbc90992878657127f7177810eb",
+      "sha256": "f83e506617a92027b3ff82f28bc043e34e890951eb7f3bd930e08c6c02a04a9d"
+    },
+    {
+      "path": "research/final4610-independent-admission/checks/outer.py",
+      "usage": "input",
+      "git_blob": "39e62cac780b662903582cb5f8684990fa779bb3",
+      "sha256": "196be1bc2329500f2c7c995deaf5a82aecc5e27f0fef7805470cb65d187bb1c0"
+    },
+    {
+      "path": "research/odd-native-common-grid/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "edea8e98a082f4513aedbfb7bd55f32063e32b38",
+      "sha256": "b710cc953163ebe282fce7cf0a426744c155a0d5acbfb9bf7d67e81195b66a1e"
+    },
+    {
+      "path": "research/p104-shared-native-helper-splits/retained/compiler/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "f5ef0d2e8289adfb6c5e73c4b58970da462d7df2",
+      "sha256": "95cc9e31bc030ec94b04decddcca2d28ee98cfec0ca7803b54666b2b76a5c9ab"
+    }
+  ]
+}
diff --git a/research/p104-frontier-7156-application-review/TASK.json b/research/p104-frontier-7156-application-review/TASK.json
new file mode 100644
index 0000000000..80b58e838b
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/TASK.json
@@ -0,0 +1,117 @@
+{
+  "schema_version": 1,
+  "task_id": "p104-side-correction",
+  "priority_revision": 8,
+  "base_commit": "e54523517d0f03e58352e647c403a5af3e525a57",
+  "original_card": {
+    "id": "p104-side-correction",
+    "question": "Can joint helper bases and a legal causal split improve the complete P104 productive/paid invoice?",
+    "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",
+      "research/p104-helper-subspace-splits/README.md",
+      "research/dyadic-helper-channel-capacity/README.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": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "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": "Start with the selected #5599 emitted word and review pending #5718 distinct input/output bases plus #5717/#5719 coverage before claiming work. Pick one uncovered source word, helper group and cut region. Prove the arbitrary-input relation and legal entry/exit corrections, then compare full target and paid profiles. Reject if completion, owned lifetimes or consumer costs repay the gain. A static pairing rank alone is not a physical split.",
+    "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": [
+      "P104",
+      "helper basis",
+      "helper split",
+      "5718",
+      "dyadic capacity"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4133: literal-slot defect",
+        "evidence": "research/p104-literal-slot-defect/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4136: uniform commutation gap",
+        "evidence": "research/p104-uniform-commutation-gap/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4140: uniform encoding gap",
+        "evidence": "research/p104-uniform-encoding-gap/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance",
+        "evidence": "research/p104-source-chart-shortcut/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4154: fiber-tag seam mismatch",
+        "evidence": "research/p104-fiber-tag-seam/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0",
+        "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": "Review the exact chart-306 application of #7156 at b44944c3058d522cbff17836e16240d40d77a927 with the signed 17-stage #7113 caller, including complete supplier replay, exact proof application and conditional frontier proposal.",
+  "scope_change_reason": "The live P104 board already had the chart-306 construction. Review its exact arbitrary-input contract and full composed invoice rather than duplicate that construction.",
+  "bottleneck_link": "Bind the strongest direct signed-caller continuation to the selected framework, including the changed native and signed caller, complete costs, common grid, BIT and all outer savings.",
+  "budget_minutes": 90,
+  "stop_rule": "One exact candidate head and one predecessor/caller lineage. Complete the cold and independent checks, record a concrete rejection if any assumption fails, and hand off for maintainer review.",
+  "outcome": "partial",
+  "evidence": "APPLICATION.md and RESULT.json give the source-specific conditional application, full budget, nine outer savings and negative controls. evidence/CANDIDATE-REGISTERED-COLD.log records the full source-bound replay.",
+  "author": "Clear1nsight",
+  "ai_assistance": "OpenAI Codex did source review, implementation and replay. ChatGPT Pro supplied an adversarial review and suggested controls; local checks verified the reported results.",
+  "open_questions": [
+    {
+      "question": "Should the exact #7156 conditional claim be selected?",
+      "why_it_matters": "The published evidence supplies a larger conditional bound with the same five inherited assumptions.",
+      "first_step": "Review APPLICATION.md and compare the exact RESULT.json parameters with the supplier and selected receipts.",
+      "blocked_by": "Maintainer mathematical review and selection."
+    }
+  ]
+}
diff --git a/research/p104-frontier-7156-application-review/VERIFY.json b/research/p104-frontier-7156-application-review/VERIFY.json
new file mode 100644
index 0000000000..6ffc66fd99
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/VERIFY.json
@@ -0,0 +1,23 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "certificates/frontier7000/CLAIM.json",
+    "docs/research/pr-intake-evidence/pr7000-application/check_exact_scalar.py",
+    "research/final4610-independent-admission/checks/outer.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 90,
+      "checks": "Literal source pins, independent timed gather/injection and corruption controls, physical paid invoice, scalar scans, complete finite tariff, directed compiler price and packing relaxation, BIT and all 54+4 outer predicates."
+    }
+  ]
+}
diff --git a/research/p104-frontier-7156-application-review/evidence/CANDIDATE-GIT-CHECK.log b/research/p104-frontier-7156-application-review/evidence/CANDIDATE-GIT-CHECK.log
new file mode 100644
index 0000000000..45b56fbd09
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/evidence/CANDIDATE-GIT-CHECK.log
@@ -0,0 +1 @@
+PASS_RESEARCH_COMMIT_BYTES {"commit": "b44944c3058d522cbff17836e16240d40d77a927", "files": 33, "package": "research/p104-temporal-chart306-continuation", "executable_modes_checked": true, "source_history_commits": ["e54523517d0f03e58352e647c403a5af3e525a57"]}
diff --git a/research/p104-frontier-7156-application-review/evidence/CANDIDATE-REGISTERED-COLD.log b/research/p104-frontier-7156-application-review/evidence/CANDIDATE-REGISTERED-COLD.log
new file mode 100644
index 0000000000..321b0edce9
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/evidence/CANDIDATE-REGISTERED-COLD.log
@@ -0,0 +1,77 @@
+CHECK Complete source reconstruction, exact arbitrary-input adjoint, owned inventory and both directed17-stage prices; every early receipt field.
+PASS_EXACT_NATIVE_AND_PRICE_ONLY 0.003644407895539
+CHECK Complete source/operator, fresh forward/adjoint and minimal1125/F25 grid, exact owned census64/47/61, timed coefficient certificate and corruption controls, ingredient pricing, ordinary/precision, all affected512-column charts, absolute phase and finite physical replay.
+PASS whole source/operator, forward/adjoint, causal charts and fresh native grid
+caller 0 terms 77
+caller 500 terms 621
+caller 1000 terms 2648
+caller 1500 terms 3619
+caller 2000 terms 1590
+caller 2500 terms 398
+caller 3000 terms 1918
+caller 3500 terms 1797
+caller 4000 terms 1817
+caller 4500 terms 912
+caller 5000 terms 167
+PASS full ingredient invoice, ordinary, precision, both prices and outer gates
+events 76220 public 1498 owned roles 61 paid {1: 3998, 2: 853, 3: 829, 4: 225, 5: 344, 6: 14, 7: 10, 8: 5} owned UP {1: 10, 2: 4, 3: 1, 4: 6, 5: 1, 6: 1} helpers {1: 17, 2: 21, 3: 47, 4: 222, 5: 78, 6: 43, 7: 19, 8: 35, 9: 616}
+endpoint bad rows 0 odd certificate S 1125
+PASS_HOST3 decoupled ports 96 hosted ports 8
+gate interpreter agrees with the library on 4 exact state vectors
+replayed 76220 events, 2950 chart pairs, 35s
+prime 1000000009 seed 11: helper rows bad 0 (of 1098), X rows bad 0, Y rows bad 0, X2 rows bad 0, Y2 rows bad 0 (of 104 ports; 96 with second mains)
+tableau on 104 ports: XX!=D 0 YY!=D 0 YX!=Q^-1D 0 XY!=QD 0 | controls matching (must be 0): 0 0
+PASS_PHYSICAL 47s
+PASS affected Gaussian chart columns, phase, corruption controls and finite physical replay
+PASS_TEMPORAL_CHART306_NATIVE 3643791910661/1000000000000000
+CHECK Full unchanged17-stage caller, complete paid/helper catalogue and104 main boundaries; fresh grid, precision, ordinary/physical/fixed-tape costs, two directed prices and54+4 outer conditions; every frozen application field.
+PASS two reconstructed invoices and both exact price engines 0.003644407895539
+RUN emit_odd_type_b.py
+caller 0 terms 41
+caller 500 terms 1178
+caller 1000 terms 2699
+caller 1500 terms 1262
+caller 2000 terms 881
+caller 2500 terms 2484
+caller 3000 terms 765
+caller 3500 terms 640
+caller 0 terms 41
+caller 500 terms 1178
+caller 1000 terms 2701
+caller 1500 terms 1264
+caller 2000 terms 881
+caller 2500 terms 2485
+caller 3000 terms 765
+caller 3500 terms 641
+PASS exact short type B 3877 events Counter({8: 34, 9: 4, 56: 4, 48: 4, 40: 4, 32: 4, 24: 4, 16: 4, 64: 2})
+RUN emit_odd_type_ab.py
+caller 0 terms 73
+caller 500 terms 1076
+caller 1000 terms 2476
+caller 1500 terms 1334
+caller 2000 terms 2078
+caller 2500 terms 1235
+caller 3000 terms 2978
+caller 3500 terms 2335
+caller 4000 terms 1046
+caller 4500 terms 299
+PASS exact short A+B 4783 events 3752 ['36444078955399752291473031465479/10000000000000000000000000000000000', '911101973884993807286825786637/250000000000000000000000000000000']
+RUN check_odd_caller_exact_grid.py
+PASS odd caller grid [381, 69, 62] [381, 3, 2] scale bits 10 checked 176874
+RUN check_odd_physical_binding.py
+PASS exact physical binding 110502 13600 22410
+RUN check_odd_precision.py
+PASS short precision 406 1215 2430
+RUN check_odd_partial_admission.py
+ordinary bill 781880696
+PASS partial signed short gates 781880696 3644407895539/1000000000000000 {'strict_count': 54, 'functional_count': 4, 'minimum_margin': '1/1000000000000000000', 'BIT_just_below_effective_rejected': True}
+RUN check_odd_fixed_tape_counts.py
+PASS finite tariff substitution 43689280 25465969408 precision 2430
+RUN complete catalogue 0 1000
+RUN complete catalogue 1000 2000
+RUN complete catalogue 2000 3000
+RUN complete catalogue 3000 3037
+PASS complete 8+9 component application checks 3644407895539/1000000000000000 3037 110502
+PASS_TEMPORAL_CHART306_CONTINUATION 3644407895539/1000000000000000
+PASS_REGISTERED_RESEARCH_PACKAGE research/p104-temporal-chart306-continuation outcome=partial
+elapsed_seconds=819.98 peak_RSS_kib=662444 exit=0
diff --git a/research/p104-frontier-7156-application-review/evidence/SELECTED-CLOSURE-DELTA.json b/research/p104-frontier-7156-application-review/evidence/SELECTED-CLOSURE-DELTA.json
new file mode 100644
index 0000000000..3d87cd67ba
--- /dev/null
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diff --git a/research/p104-frontier-7156-application-review/inputs/pr7113/LICENSE b/research/p104-frontier-7156-application-review/inputs/pr7113/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/inputs/pr7113/LICENSE
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+                                 Apache License
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diff --git a/research/p104-frontier-7156-application-review/inputs/pr7155/NOTICE b/research/p104-frontier-7156-application-review/inputs/pr7155/NOTICE
new file mode 100644
index 0000000000..c5466006c2
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/inputs/pr7155/NOTICE
@@ -0,0 +1,20 @@
+Prepared for Clear1nsight with substantial OpenAI Codex and ChatGPT Pro
+assistance. Apache-2.0.
+
+Rohan Arun: chart-237 witness, signed application and endpoint construction.
+dillona: complete chart-595 source, width repair and temporal replay adaptation.
+Ali Romman: causal-history owned-buffer identity and helper bases
+(https://github.com/CrocSwap/integer-mult-bounds/discussions/5600#discussioncomment-19209322).
+Jerry Chen / CubeJerry: contact-free retiming, exact temporal histories and
+verification. Matarener: complete helper kernels. ToikY: price engines and
+earlier chart leads. Cinna Davis / 1337isnot1337, Dugongue, DreamingOfClouds,
+Douglas Colkitt/#7000 reviewers and all authors in the source closure retain
+their credit.
+
+The complete #7148 package, original notices, and all nested sources are
+retained verbatim inside its archive. #7147 contributes eight exact source
+files, including its NOTICE, not a second duplicate source closure. The
+local copies of derive_grid.py, split.py, support.py and temporal_construct.py
+are byte-identical to #7148 and checked against it before use. Local replay
+adapters are credited in their headers. The separate CI navigation prerequisite
+is reused verbatim from #7147.
diff --git a/research/p104-frontier-7156-application-review/inputs/pr7155/WORD.json.gz b/research/p104-frontier-7156-application-review/inputs/pr7155/WORD.json.gz
new file mode 100644
index 0000000000..7de0c81080
Binary files /dev/null and b/research/p104-frontier-7156-application-review/inputs/pr7155/WORD.json.gz differ
diff --git a/research/p104-frontier-7156-application-review/inputs/pr7156/NATIVE-RESULT.json b/research/p104-frontier-7156-application-review/inputs/pr7156/NATIVE-RESULT.json
new file mode 100644
index 0000000000..3d84a6fa5f
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/inputs/pr7156/NATIVE-RESULT.json
@@ -0,0 +1,3113 @@
+{
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+    "vectors": {
+      "c": {
+        "1025": "-2",
+        "1029": "-5/2",
+        "334": "2",
+        "349": "-4"
+      },
+      "d": {
+        "1021": "1/2",
+        "334": "-1/2",
+        "349": "-1/2",
+        "831": "-1/2"
+      }
+    }
+  },
+  "word_canonical_sha256": "b012295cfe44d204c2724fe544731ac17aa969e06e33043496ac7a1c91a912b3"
+}
diff --git a/research/p104-frontier-7156-application-review/inputs/pr7156/NOTICE b/research/p104-frontier-7156-application-review/inputs/pr7156/NOTICE
new file mode 100644
index 0000000000..45ae369fa9
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/inputs/pr7156/NOTICE
@@ -0,0 +1,22 @@
+Prepared for Clear1nsight with substantial OpenAI Codex and ChatGPT Pro
+assistance. Apache-2.0.
+
+Rohan Arun: chart-237 witness, signed application and endpoint construction.
+dillona: complete chart-595 source, width repair and temporal replay adaptation.
+Ali Romman: causal-history owned-buffer identity and helper bases
+(https://github.com/CrocSwap/integer-mult-bounds/discussions/5600#discussioncomment-19209322).
+Jerry Chen / CubeJerry: contact-free retiming, exact temporal histories and
+verification. Matarener: complete helper kernels. ToikY: price engines and
+earlier chart leads. Cinna Davis / 1337isnot1337, Dugongue, DreamingOfClouds,
+Douglas Colkitt/#7000 reviewers and all authors in the source closure retain
+their credit.
+
+The complete #7148 package, original notices, and all nested sources are
+retained verbatim inside its archive. #7147 contributes eight exact source
+files, including its NOTICE, not a second duplicate source closure. The
+local copies of derive_grid.py, split.py, support.py and temporal_construct.py
+are byte-identical to #7148 and checked against it before use. Local replay
+adapters are credited in their headers. The separate CI navigation prerequisite
+is reused verbatim from #7147.
+
+New chart306 timed instance: Rohan Arun with substantial OpenAI Codex assistance. Retains Ali Romman causal-history identity, CubeJerry temporal/verification methods, Matarener kernels, dillona source instances, Clear1nsight guarded composition, ToikY pricing and all nested source notices. Apache-2.0.
diff --git a/research/p104-frontier-7156-application-review/inputs/pr7156/PATHS.json b/research/p104-frontier-7156-application-review/inputs/pr7156/PATHS.json
new file mode 100644
index 0000000000..a33773333c
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/inputs/pr7156/PATHS.json
@@ -0,0 +1,145 @@
+[
+  {
+    "role": 781,
+    "lo": 36822,
+    "hi": 37777,
+    "frame": 306,
+    "moves": [
+      37776
+    ],
+    "frames": [
+      306,
+      517
+    ]
+  },
+  {
+    "role": 831,
+    "lo": 36275,
+    "hi": 36785,
+    "frame": 306,
+    "moves": [
+      36784
+    ],
+    "frames": [
+      304,
+      306
+    ]
+  },
+  {
+    "role": 831,
+    "lo": 37218,
+    "hi": 45479,
+    "frame": 306,
+    "moves": [
+      45478
+    ],
+    "frames": [
+      306,
+      267
+    ]
+  },
+  {
+    "role": 864,
+    "lo": 37218,
+    "hi": 48031,
+    "frame": 306,
+    "moves": [
+      48030
+    ],
+    "frames": [
+      306,
+      127
+    ]
+  },
+  {
+    "role": 1020,
+    "lo": 36772,
+    "hi": 36800,
+    "frame": 306,
+    "moves": [
+      36799
+    ],
+    "frames": [
+      299,
+      306
+    ]
+  },
+  {
+    "role": 1020,
+    "lo": 36823,
+    "hi": 37783,
+    "frame": 306,
+    "moves": [
+      37782
+    ],
+    "frames": [
+      306,
+      518
+    ]
+  },
+  {
+    "role": 1021,
+    "lo": 36815,
+    "hi": 56953,
+    "frame": 306,
+    "moves": [
+      56952
+    ],
+    "frames": [
+      306,
+      127
+    ]
+  },
+  {
+    "role": 1023,
+    "lo": 32458,
+    "hi": 36789,
+    "frame": 306,
+    "moves": [
+      36788
+    ],
+    "frames": [
+      300,
+      306
+    ]
+  },
+  {
+    "role": 1025,
+    "lo": 36769,
+    "hi": 36798,
+    "frame": 306,
+    "moves": [
+      36797
+    ],
+    "frames": [
+      298,
+      306
+    ]
+  },
+  {
+    "role": 1025,
+    "lo": 36824,
+    "hi": 57114,
+    "frame": 306,
+    "moves": [
+      57113
+    ],
+    "frames": [
+      306,
+      127
+    ]
+  },
+  {
+    "role": 1029,
+    "lo": 36301,
+    "hi": 36802,
+    "frame": 306,
+    "moves": [
+      36801
+    ],
+    "frames": [
+      302,
+      306
+    ]
+  }
+]
\ No newline at end of file
diff --git a/research/p104-frontier-7156-application-review/inputs/pr7156/RESULT.json b/research/p104-frontier-7156-application-review/inputs/pr7156/RESULT.json
new file mode 100644
index 0000000000..b27ddf273c
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/inputs/pr7156/RESULT.json
@@ -0,0 +1,1599 @@
+{
+  "adapter": {
+    "adapted_sha256": {
+      "check_odd_partial_admission.py": "7610f7a66e8de47c6e4fc500e1873f735389261d02a28d6cebaa99ea00e9d158",
+      "check_odd_precision.py": "32f9af21c64dcf407a3ba94fa12a1c2ad06f4c303e981dbc7084845b11240c77",
+      "emit_odd_type_ab.py": "6fd9f61f9ba6c726524d1a585d0201b0eac61829ccae6be598f0f0fc1cb64f1a"
+    },
+    "edits": [
+      {
+        "file": "emit_odd_type_ab.py",
+        "new": "invoice=json.loads((root/\"COHORT-PRICE.json\").read_text())",
+        "old": "invoice=next(x for x in json.loads((root/\"SHORT-CALLER-RAW-PRICE.json\").read_text())[\"rows\"] if tuple(x[\"shape\"])==shape)"
+      },
+      {
+        "file": "check_odd_partial_admission.py",
+        "new": "actual_native=ind.native(w)\nassert actual_native==N and not N[\"bad_inputs\"], \"Fresh complete native inventory and arbitrary-input adjoint\"",
+        "old": "previous=json.loads((root/\"SHORT-ADMISSION-PARTIAL.json\").read_text())\nassert previous[\"native_sha256\"]==digest and not N[\"bad_inputs\"]"
+      },
+      {
+        "file": "check_odd_partial_admission.py",
+        "new": "claim=Q('0.003644407895539')",
+        "old": "claim=Q(\".00363797977\")"
+      },
+      {
+        "file": "check_odd_partial_admission.py",
+        "new": "tested=claim+Q(7,10**17)\nwhile tested>=Q(reference[\"raw_bracket\"][0]):\n    tested=claim+(tested-claim)/10",
+        "old": "tested=claim+Q(7,10**17)"
+      },
+      {
+        "file": "check_odd_partial_admission.py",
+        "new": "g=gate(invoice,claim,tested,*bracket,r[\"gate\"][\"BIT_pin\"])\ntry:\n    gate(invoice,claim,Q(bracket[0]),*bracket,r[\"gate\"][\"BIT_pin\"])\nexcept AssertionError:\n    crossing_probe_rejected=True\nelse:\n    raise AssertionError(\"Probe at lower crossing unexpectedly accepted\")",
+        "old": "g=gate(invoice,claim,tested,*bracket,r[\"gate\"][\"BIT_pin\"])"
+      },
+      {
+        "file": "check_odd_partial_admission.py",
+        "new": "\"crossing_probe_rejected\":crossing_probe_rejected,\"scope\":\"Reuse exact same native word all-column adjoint;",
+        "old": "\"scope\":\"Reuse exact same native word all-column adjoint;"
+      },
+      {
+        "file": "check_odd_precision.py",
+        "new": "patch('(life, peak, owned_count) == (54, 43, 51)','(life, peak, owned_count) == (64, 47, 61)')\nenv=ModuleType(\"short_envelope\")",
+        "old": "env=ModuleType(\"short_envelope\")"
+      },
+      {
+        "file": "check_odd_precision.py",
+        "new": "",
+        "old": "previous=json.loads((root/\"SHORT-PRECISION.json\").read_text())"
+      },
+      {
+        "file": "check_odd_precision.py",
+        "new": "assert grid_receipt[\"caller_sha256\"]==sha256(cpath.read_bytes()).hexdigest()",
+        "old": "assert previous[\"native_sha256\"]==sha and grid_receipt[\"caller_sha256\"]==sha256(cpath.read_bytes()).hexdigest()"
+      },
+      {
+        "file": "check_odd_precision.py",
+        "new": "wg=grid.word_run(w, frac=25)\nwp,wr=env.native_envelope(w)\nwg=json.loads(json.dumps(wg,default=str));wr=json.loads(json.dumps(wr,default=str))\nassert wg==r[\"precision\"][\"word\"] and wr==r[\"precision\"][\"rounded_native\"], \"Fresh changed-native grid and envelope\"",
+        "old": "wg=previous[\"native_grid\"]\nwr=previous[\"rounded_native\"]\nwp={key:(Q(v[\"exact\"]),v[\"witness\"]) for key,v in wr[\"bounds\"].items()}"
+      }
+    ]
+  },
+  "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc",
+  "catalogue": [
+    {
+      "catalogue_digest": "8a6d5341f689488e8ef09eba8396d2152312b59ab0756edbd6b86890d2c44a85",
+      "catalogue_size": 3037,
+      "checked_maps": 1000,
+      "distinct_helper_maps": 188,
+      "distinct_paid_maps": 2950,
+      "exact_recipe_digest": "74c6f1c5717989bb3d3a993bc915321585c9524e98477fbd6a6f0a25d463bba5",
+      "main_boundary_digest": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
+      "main_boundary_pairs": 0,
+      "phase_control_rejected": true,
+      "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.",
+      "slice_start": 0,
+      "slice_stop": 1000,
+      "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE",
+      "word_sha256": "e950eab5cc3f3fc8a2554e488114d788741d3262381459688ebaea08cd0a4d50"
+    },
+    {
+      "catalogue_digest": "8a6d5341f689488e8ef09eba8396d2152312b59ab0756edbd6b86890d2c44a85",
+      "catalogue_size": 3037,
+      "checked_maps": 1000,
+      "distinct_helper_maps": 188,
+      "distinct_paid_maps": 2950,
+      "exact_recipe_digest": "5796317772e8b26cb6118de671c511683cdc6ba8129379580b2f7058ac9912be",
+      "main_boundary_digest": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
+      "main_boundary_pairs": 0,
+      "phase_control_rejected": true,
+      "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.",
+      "slice_start": 1000,
+      "slice_stop": 2000,
+      "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE",
+      "word_sha256": "e950eab5cc3f3fc8a2554e488114d788741d3262381459688ebaea08cd0a4d50"
+    },
+    {
+      "catalogue_digest": "8a6d5341f689488e8ef09eba8396d2152312b59ab0756edbd6b86890d2c44a85",
+      "catalogue_size": 3037,
+      "checked_maps": 1000,
+      "distinct_helper_maps": 188,
+      "distinct_paid_maps": 2950,
+      "exact_recipe_digest": "af93e262513853d9e484dbc68719e195853ecc5a16a446293afecc4e671746c4",
+      "main_boundary_digest": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
+      "main_boundary_pairs": 0,
+      "phase_control_rejected": true,
+      "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.",
+      "slice_start": 2000,
+      "slice_stop": 3000,
+      "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE",
+      "word_sha256": "e950eab5cc3f3fc8a2554e488114d788741d3262381459688ebaea08cd0a4d50"
+    },
+    {
+      "catalogue_digest": "8a6d5341f689488e8ef09eba8396d2152312b59ab0756edbd6b86890d2c44a85",
+      "catalogue_size": 3037,
+      "checked_maps": 37,
+      "distinct_helper_maps": 188,
+      "distinct_paid_maps": 2950,
+      "exact_recipe_digest": "cec6af5c26e0d918bb4965d54ccfd8835b82b1eed025bc92bbb56a1a1a61e012",
+      "main_boundary_digest": "ad959887c990b8862a0e60db3f53d5195a1c9d667c1593f0101adc8db18f27fa",
+      "main_boundary_pairs": 104,
+      "phase_control_rejected": true,
+      "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.",
+      "slice_start": 3000,
+      "slice_stop": 3037,
+      "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE",
+      "word_sha256": "e950eab5cc3f3fc8a2554e488114d788741d3262381459688ebaea08cd0a4d50"
+    }
+  ],
+  "checks": {
+    "ODD-8X9-APPLICATION-CHECKS.json": {
+      "assumptions": [
+        "native_all_columns",
+        "owned_erasure",
+        "compiler",
+        "precision_tape",
+        "analytic_recovery"
+      ],
+      "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc",
+      "candidate": "3644407895539/1000000000000000",
+      "catalogue": [
+        {
+          "catalogue_digest": "8a6d5341f689488e8ef09eba8396d2152312b59ab0756edbd6b86890d2c44a85",
+          "catalogue_size": 3037,
+          "checked_maps": 1000,
+          "distinct_helper_maps": 188,
+          "distinct_paid_maps": 2950,
+          "exact_recipe_digest": "74c6f1c5717989bb3d3a993bc915321585c9524e98477fbd6a6f0a25d463bba5",
+          "log_sha256": "3a86a9ff8b95e5a44c9cb6816869c2f6a309b79ee1b2aa3a2e4215f3c24f4787",
+          "main_boundary_digest": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
+          "main_boundary_pairs": 0,
+          "phase_control_rejected": true,
+          "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.",
+          "slice_start": 0,
+          "slice_stop": 1000,
+          "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE",
+          "word_sha256": "e950eab5cc3f3fc8a2554e488114d788741d3262381459688ebaea08cd0a4d50"
+        },
+        {
+          "catalogue_digest": "8a6d5341f689488e8ef09eba8396d2152312b59ab0756edbd6b86890d2c44a85",
+          "catalogue_size": 3037,
+          "checked_maps": 1000,
+          "distinct_helper_maps": 188,
+          "distinct_paid_maps": 2950,
+          "exact_recipe_digest": "5796317772e8b26cb6118de671c511683cdc6ba8129379580b2f7058ac9912be",
+          "log_sha256": "285840d1c7cd4d6f376889d9ca8ab80008a365e852cd872eb35a4ddfc72e022d",
+          "main_boundary_digest": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
+          "main_boundary_pairs": 0,
+          "phase_control_rejected": true,
+          "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.",
+          "slice_start": 1000,
+          "slice_stop": 2000,
+          "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE",
+          "word_sha256": "e950eab5cc3f3fc8a2554e488114d788741d3262381459688ebaea08cd0a4d50"
+        },
+        {
+          "catalogue_digest": "8a6d5341f689488e8ef09eba8396d2152312b59ab0756edbd6b86890d2c44a85",
+          "catalogue_size": 3037,
+          "checked_maps": 1000,
+          "distinct_helper_maps": 188,
+          "distinct_paid_maps": 2950,
+          "exact_recipe_digest": "af93e262513853d9e484dbc68719e195853ecc5a16a446293afecc4e671746c4",
+          "log_sha256": "0d0ca112a31760170d47241b6a4a5febca757e80cf46a77621ffbf433cfffb4e",
+          "main_boundary_digest": "4f53cda18c2baa0c0354bb5f9a3ecbe5ed12ab4d8e11ba873c2f11161202b945",
+          "main_boundary_pairs": 0,
+          "phase_control_rejected": true,
+          "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.",
+          "slice_start": 2000,
+          "slice_stop": 3000,
+          "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE",
+          "word_sha256": "e950eab5cc3f3fc8a2554e488114d788741d3262381459688ebaea08cd0a4d50"
+        },
+        {
+          "catalogue_digest": "8a6d5341f689488e8ef09eba8396d2152312b59ab0756edbd6b86890d2c44a85",
+          "catalogue_size": 3037,
+          "checked_maps": 37,
+          "distinct_helper_maps": 188,
+          "distinct_paid_maps": 2950,
+          "exact_recipe_digest": "cec6af5c26e0d918bb4965d54ccfd8835b82b1eed025bc92bbb56a1a1a61e012",
+          "log_sha256": "177709115f5c77c51a6698c9efa17f6f22390a7ba60b0ae0cd6b741845560087",
+          "main_boundary_digest": "ad959887c990b8862a0e60db3f53d5195a1c9d667c1593f0101adc8db18f27fa",
+          "main_boundary_pairs": 104,
+          "phase_control_rejected": true,
+          "scope": "Complete signed Pauli action plus exact Gaussian global phase; for Clifford maps these determine every matrix column. Generic tensor-product and physical grammar application is written in the review. No random-field substitution.",
+          "slice_start": 3000,
+          "slice_stop": 3037,
+          "status": "PASS_CURRENT_NATIVE_CATALOGUE_SLICE",
+          "word_sha256": "e950eab5cc3f3fc8a2554e488114d788741d3262381459688ebaea08cd0a4d50"
+        }
+      ],
+      "fixed_tape_counts": {
+        "H": 16510400000000000000000,
+        "Kstar_bits": 14093,
+        "actual_ambient": 145,
+        "caller_odd_scale": 675,
+        "caller_sha256": "255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc",
+        "common_grid": {
+          "fractional": "p+D",
+          "signed_width": "p+h+2D+3",
+          "temp_padding": 26
+        },
+        "compiler_ambient_cap": 153,
+        "context_bound_bits": 14104,
+        "context_c": 2430,
+        "elementary_records_per_map_upper": 85264,
+        "elementary_records_upper": 25465969408,
+        "log_power": 2237,
+        "max_scalar_numerator_bits": 24,
+        "monomial_map_slots": 298672,
+        "native_invocations": 17,
+        "native_sha256": "b012295cfe44d204c2724fe544731ac17aa969e06e33043496ac7a1c91a912b3",
+        "owned_banks_per_raw_occurrence": 1037,
+        "scalar_macro_inputs": {
+          "caller": 117856,
+          "conversions": 58420,
+          "native": 1189014
+        },
+        "scalar_services_upper": 43689280,
+        "scalar_steps_coefficient": 45811530465280,
+        "scope": "Exact finite-cost and common-format substitutions in the selected #7000 conditional application proof, using the conservative primitive movement and scalar constants there. The premise is the complete signed native/physical binding and retained compiler, BIT, stock, and outer contracts. This script counts the raw occurrence, not an enumerated top-level compiled multiplier.",
+        "tested_claim": "3644407895539/1000000000000000"
+      },
+      "native_archive_sha256": "e950eab5cc3f3fc8a2554e488114d788741d3262381459688ebaea08cd0a4d50",
+      "native_canonical_sha256": "b012295cfe44d204c2724fe544731ac17aa969e06e33043496ac7a1c91a912b3",
+      "numeric_gate": {
+        "BIT_margin": "12228210446093/100000000000000000",
+        "BIT_pin": "376669/100000000",
+        "H": "16510400000000000000000",
+        "alpha": [
+          0.9999999999999988,
+          0.9999999999999988
+        ],
+        "claim": "3644407895539/1000000000000000",
+        "compiler_gap": "1/100000000000000000",
+        "delta": [
+          0.9060338152823023,
+          0.9060338152823023
+        ],
+        "derivative_upper": -381743.11655566044,
+        "gamma": [
+          0.9407642489923767,
+          0.9407642489923767
+        ],
+        "input_lift": {
+          "derivative_upper_on_required_interval": "-2299831290525933154178526076272396899996972093654613095735772838275432653960006518819/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "interval_kappa_cap": "376669/100000000",
+          "margins": {
+            "3644407895539/1000000000000000": [
+              "124340413725381578436168433909673800828712847806542525942299871259053399949237/100000000000000000000000000000000000000000000000000000000000000000000000000000000",
+              "124340413725381578436168433909673800828712847806542525942299871259053399951213/100000000000000000000000000000000000000000000000000000000000000000000000000000000"
+            ],
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+      "raw_bracket": [
+        "0.0036444078955399752291473031465479",
+        "0.003644407895539975229147303146548"
+      ]
+    }
+  },
+  "status": "PASS_TEMPORAL_CHART306_CONTINUATION"
+}
diff --git a/research/p104-frontier-7156-application-review/inputs/pr7156/WITNESS.json b/research/p104-frontier-7156-application-review/inputs/pr7156/WITNESS.json
new file mode 100644
index 0000000000..5abaa48c80
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/inputs/pr7156/WITNESS.json
@@ -0,0 +1,136 @@
+{
+  "frame": 306,
+  "cut": 36772,
+  "pivot": 831,
+  "ranks": [
+    4,
+    5
+  ],
+  "c": {
+    "1029": "-5/2",
+    "349": "-4",
+    "1025": "-2",
+    "334": "2"
+  },
+  "d": {
+    "349": "-1/2",
+    "1021": "1/2",
+    "831": "-1/2",
+    "334": "-1/2"
+  },
+  "gathers": [
+    {
+      "cut": 36772,
+      "role": 1020,
+      "frame": 306,
+      "path": 4,
+      "coefficient": "1"
+    },
+    {
+      "cut": 32458,
+      "role": 1023,
+      "frame": 306,
+      "path": 7,
+      "coefficient": "-2"
+    },
+    {
+      "cut": 36769,
+      "role": 1025,
+      "frame": 306,
+      "path": 8,
+      "coefficient": "-1"
+    },
+    {
+      "cut": 36301,
+      "role": 1029,
+      "frame": 306,
+      "path": 10,
+      "coefficient": "-1/2"
+    },
+    {
+      "cut": 36275,
+      "role": 831,
+      "frame": 306,
+      "path": 1,
+      "coefficient": "1/2"
+    }
+  ],
+  "injections": [
+    {
+      "cut": 37777,
+      "role": 781,
+      "frame": 306,
+      "path": 0,
+      "coefficient": "1/2"
+    },
+    {
+      "cut": 37783,
+      "role": 1020,
+      "frame": 306,
+      "path": 5,
+      "coefficient": "1/2"
+    },
+    {
+      "cut": 57114,
+      "role": 1025,
+      "frame": 306,
+      "path": 9,
+      "coefficient": "-1"
+    },
+    {
+      "cut": 48586,
+      "role": 1034,
+      "frame": 306,
+      "paid_path": 0,
+      "coefficient": "1"
+    },
+    {
+      "cut": 45479,
+      "role": 831,
+      "frame": 306,
+      "path": 2,
+      "coefficient": "1/2"
+    },
+    {
+      "cut": 48031,
+      "role": 864,
+      "frame": 306,
+      "path": 3,
+      "coefficient": "-1/2"
+    },
+    {
+      "cut": 56953,
+      "role": 1021,
+      "frame": 306,
+      "path": 6,
+      "coefficient": "-1/2"
+    }
+  ],
+  "paid_delta": {
+    "3": 1,
+    "5": 1,
+    "8": -1
+  },
+  "paid_path": 0,
+  "path": {
+    "role": 1034,
+    "lo": 37857,
+    "hi": 48586,
+    "frame": 306,
+    "moves": [
+      48585
+    ],
+    "old": 9,
+    "new": 127,
+    "old_paid": [
+      8
+    ],
+    "new_paid": [
+      3,
+      5
+    ],
+    "cost": 0.01916802320250266,
+    "gain": 0.022380282076957414,
+    "private": false
+  }
+}
\ No newline at end of file
diff --git a/research/p104-frontier-7156-application-review/inputs/pr7156/WORD.json.gz b/research/p104-frontier-7156-application-review/inputs/pr7156/WORD.json.gz
new file mode 100644
index 0000000000..d05462ff38
Binary files /dev/null and b/research/p104-frontier-7156-application-review/inputs/pr7156/WORD.json.gz differ
diff --git a/research/p104-frontier-7156-application-review/moments.py b/research/p104-frontier-7156-application-review/moments.py
new file mode 100644
index 0000000000..346db4cb11
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/moments.py
@@ -0,0 +1,130 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Directed rational price, tail, input-lift and fixed-profile bounds."""
+
+from fractions import Fraction as Q
+from functools import lru_cache
+
+from word import require
+
+GRID = 2**160
+
+
+def enclose(lo, hi):
+    return Q(lo * GRID // 1, GRID), Q(-(-hi * GRID // 1), GRID)
+
+
+def log_near_one(x):
+    t = (x - 1) / (x + 1)
+    term, lo = t, Q(0)
+    for j in range(64):
+        lo += 2 * term / (2 * j + 1)
+        term *= t * t
+    return lo, lo + 2 * term / (129 * (1 - t * t))
+
+
+@lru_cache(None)
+def log(r):
+    k = r.bit_length() - 1
+    lo, hi = log_near_one(Q(r, 2**k))
+    a, b = log_near_one(Q(2))
+    return enclose(lo + k*a, hi + k*b)
+
+
+def exp_minus(x):
+    # Odd truncation is a lower bound and the next even one is an upper bound.
+    s, t = Q(1), Q(1)
+    for j in range(1, 46):
+        t *= -x / j
+        s += t
+    return s, s - t*x/46
+
+
+@lru_cache(None)
+def power(r, saving):
+    lo, hi = log(r)
+    lo, hi = enclose(abs(saving)*lo, abs(saving)*hi)
+    require(0 <= lo <= hi < 1, "Alternating exponential domain")
+    a, b = enclose(exp_minus(hi)[0], exp_minus(lo)[1])
+    return enclose(r/b, r/a) if saving < 0 else (r*a, r*b)
+
+
+def moment(hist, saving):
+    lo = hi = Q(0)
+    for r, count in hist.items():
+        a, b = power(r, saving)
+        lo += count * (a if count >= 0 else b)
+        hi += count * (b if count >= 0 else a)
+    return lo, hi
+
+
+def derivative_upper(hist, cap):
+    result = Q(0)
+    for r, count in hist.items():
+        lo, hi = log(r)
+        if count < 0:
+            result -= count * r * hi
+        else:
+            result -= count * power(r, cap)[0] * lo
+    return result
+
+
+def certified_price(paid, target, prior, native_paid, physical_cap, gate):
+    k, C = Q(gate["claim"]), Q(gate["tested"])
+    lo, hi = map(Q, gate["raw_bracket"])
+    bit = Q(gate["BIT_pin"])
+    signed = {r: target.get(r, 0) - paid.get(r, 0) for r in target.keys() | paid.keys()}
+    left, right = moment(signed, lo)[0], moment(signed, hi)[1]
+    tested = moment(signed, C)[0]
+    previous = moment(prior, k)[1]
+    require(0 < k < C < lo < hi < bit and tested > 0 and left > 0 > right,
+            "Directed raw crossing and tested price")
+    require(previous < 0 and derivative_upper(signed, bit) < 0, "Source rejects new price; directed derivative")
+
+    lower_target = moment(target, C)[0]
+    alpha = moment(paid, C)[1] / lower_target
+    gamma = moment(paid, C-Q(1, 7))[1] / (11 / power(11, Q(1, 7))[1] * lower_target)
+    delta = sum(target.values()) * 12 / (11 / power(11, C)[1] * lower_target)
+    reserve, decay, v = Q(1, 10**27), Q(31, 32), 1920
+    require(alpha < 1-reserve and gamma < decay and delta < decay, "Tail and completion margins")
+    require(1/(1+v*reserve) + 4*decay**v < 1, "Separated paid ceiling and target floor")
+    require(11**64 < 12**63 and 2*(11**v)**64 <= (153**v)**63, "Completion geometry")
+
+    a, b = [x/153 for x in power(153, C)]
+    eta = (1-C)*a**v, (1-C)*b**v
+    log_power = gate["written_log_power"]
+    require(eta[1] <= Q(63, 64)**(log_power-2) and eta[0] > Q(63, 64)**(log_power-1)
+            and a**(-v) < 2**log_power, "Minimum and written logarithmic powers")
+    H, g = int(gate["H"]), (C-k)/7
+    require(g.numerator == 1 and H % g.denominator == 0, "Integer funding comparison")
+    h = H // g.denominator
+    require((H+1)**log_power < 2**h and (H-g.denominator+1)**log_power >= 2**(h-1),
+            "Funded integer carrier and preceding grid point")
+
+    # L'(p) for p = 1-saving. This upper bound is negative uniformly on
+    # [1-bit, 1]; the derivative in the saving coordinate is positive.
+    lift = {7: 1, 3: 1, 5: 1, 9: -1, 4: -1, 1: -2}
+    slope_at_one = sum(count * r * log(r)[int(count > 0)] for r, count in lift.items())
+    curvature = sum(abs(count) * r * log(r)[1]**2 for r, count in lift.items())
+    require(sum(count*r for r, count in lift.items()) == 0 and slope_at_one + bit*curvature < 0
+            and min(moment(lift, s)[0] for s in (k, C)) > 0, "Directed input-lift interval")
+
+    # Nine-stage equal-target coverage does not apply here. Hold this exact
+    # mixed target invoice and all 17 native calls fixed. The most favorable
+    # paid remainder concentrates its fixed rank mass at the ambient cap.
+    remainder = paid.copy()
+    remainder.subtract(native_paid)
+    require(all(count >= 0 and r <= physical_cap for r, count in remainder.items()), "Paid remainder")
+    mass = sum(r * count for r, count in remainder.items())
+    relaxation = {r: target.get(r, 0) - native_paid.get(r, 0) for r in target.keys() | native_paid.keys()}
+    relaxation[physical_cap] = relaxation.get(physical_cap, 0) - Q(mass, physical_cap)
+    cap_lo, cap_hi = Q(".00580448601471"), Q(".00580448601473")
+    require(0 < cap_lo < cap_hi < Q(1, 32)
+            and moment(relaxation, cap_lo)[0] > 0 > moment(relaxation, cap_hi)[1]
+            and derivative_upper(relaxation, Q(1, 32)) < 0, "Ambient fixed-profile packing bound")
+    return dict(tested_margin_lower=tested, previous_margin_upper=previous,
+                raw_bracket=[lo, hi], alpha_upper=enclose(alpha, alpha)[1],
+                gamma_upper=enclose(gamma, gamma)[1], delta_upper=enclose(delta, delta)[1],
+                input_lift_p_derivative_upper=enclose(slope_at_one+bit*curvature, slope_at_one+bit*curvature)[1],
+                H=H, log_power=log_power, paid_remainder_rank_mass=mass,
+                packing_raw_bracket=[cap_lo, cap_hi], fraction_of_packing_ceiling_lower=k/cap_hi,
+                fraction_of_packing_ceiling_upper=k/cap_lo)
diff --git a/research/p104-frontier-7156-application-review/verify.py b/research/p104-frontier-7156-application-review/verify.py
new file mode 100644
index 0000000000..46fbd22b9a
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/verify.py
@@ -0,0 +1,291 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Check the literal #7156 application delta and proposed conditional claim."""
+
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as Q
+from hashlib import sha1, sha256
+from pathlib import Path
+import gzip
+import json
+import runpy
+import sys
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+sys.path.insert(0, str(HERE))
+from moments import certified_price
+from word import chart_checks, require, trace
+
+
+def load(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == ".gz" else raw)
+
+
+def canonical(value):
+    return json.dumps(value, sort_keys=True, separators=(",", ":")).encode()
+
+
+def authenticate():
+    index = load(HERE / "INPUTS.json")["sources"]
+    files = {p["file"] for p in index}
+    require(len(files) == len(index) and files == {p.relative_to(HERE).as_posix() for p in
+            (HERE / "inputs").rglob("*") if p.is_file()}, "Complete replay input inventory")
+    for p in index:
+        raw = (HERE / p["file"]).read_bytes()
+        git_blob = sha1(b"blob " + str(len(raw)).encode() + b"\0" + raw).hexdigest()
+        require((len(raw), sha256(raw).hexdigest(), git_blob) == (p["bytes"], p["sha256"], p["git_blob"]),
+                "Exact input bytes for " + p["path"])
+
+
+def invoice(word, caller, native):
+    types = caller["types"]
+    require(types["A"]["ports"] == word["hosted"]["Dports"] and
+            sorted(types["A"]["ports"] + types["B"]["ports"]) == list(range(104)), "Disjoint exact ports")
+    stages = caller["stages"]
+    require(stages == 17 and caller["ambient_rank"] == 9 + 8*stages, "Seventeen disjoint stage planes")
+    require([(types[t]["offset"], types[t]["roles"]) for t in ("A", "B")] == [(0, 36), (36, 36)],
+            "Separate caller role sets")
+    stage_order = []
+    paid, target, macro = Counter(), Counter(), Counter()
+    for e in caller["events"]:
+        if e[0] == "J":
+            _, s, a, b = e
+            require(a == [s, 0, 18, 18+s] and b == [36, 37, "-1", "1/2"], "Exact A/B stage owners")
+            stage_order.append(s)
+            paid.update(native["paid"])
+            target.update(native["helpers"])
+            continue
+        ty, op = e[:2]
+        t = types[ty]
+        ports = len(t["ports"])
+        macro[op] += ports
+        require(op in ("ADD", "SCALE", "SWAP", "LAMBDA", "QUERY", "IDLE_ONE", "IDLE_ODD"), "Caller alphabet")
+        if op in ("IDLE_ONE", "IDLE_ODD"):
+            slots = e[3]
+            require(slots and len(set(slots)) == len(slots) and all(1 <= s <= stages for s in slots), "Valid idle stages")
+            if op == "IDLE_ODD":
+                require(ty == "B" and len(slots) == 1 and e[4:] == [-1], "One negative odd child")
+            paid[8*len(slots)+(op == "IDLE_ODD")] += ports
+        elif op == "QUERY":
+            require(e[-1] in (-1, 1), "Signed query")
+            paid[1] += ports
+        elif op == "LAMBDA":
+            require(e[-1] in (-1, 1), "Signed whole LAMBDA")
+    require(stage_order == list(range(1, stages+1)), "Each stage called once in chronological order")
+    for t in types.values():
+        require(len(t["diagonal"]) == t["roles"], "All main fields have target rows")
+        for sign, spare, *bits in t["diagonal"]:
+            require(sign == -1 and spare == 0 and len(bits) == stages and set(bits) <= {0, 1} and any(bits),
+                    "Signed nonempty root diagonal")
+            target[abs(sign)+8*sum(bits)] += len(t["ports"])
+    return paid, target, macro
+
+
+def whole_lambda_control():
+    # With X the exchange of the two coordinates, on v=(1,-1) the
+    # Gaussian numerator (1+i)v+(1-i)Xv is 2i*v.
+    v = (1, -1)
+    numerator = [(v[j]+v[1-j], v[j]-v[1-j]) for j in range(2)]
+    require(numerator == [(0, 2*x) for x in v], "One-axis eigenvalue i")
+
+    def eigen_lambda(power_of_i):
+        q_squared = 1 if power_of_i % 2 == 0 else -1
+        return (1+q_squared)//2, (1-q_squared)//2
+
+    whole, single = eigen_lambda(2), eigen_lambda(1)
+    tensor = (single[0]**2-single[1]**2, 2*single[0]*single[1])
+    require(whole == (1, 0) and tensor == (-1, 0), "Whole LAMBDA differs at multiplicity two")
+    return {"whole": "+1", "axiswise": "-1"}
+
+
+def scalars(word, caller, native_scale, caller_scale):
+    engine = runpy.run_path(str(ROOT / "docs/research/pr-intake-evidence/pr7000-application/check_exact_scalar.py"))
+    rational = engine["rational"]
+    stages = caller["stages"]
+    coefficients = Counter()
+    for e in word["program"]:
+        if e[0] in ("ADD", "COPY", "SCALE"):
+            coefficients[Q(e[-2])] += stages
+    for e in caller["events"]:
+        if e[0] == "J":
+            coefficients.update({Q(e[3][2]): len(caller["types"]["B"]["ports"]),
+                                 Q(e[3][3]): len(caller["types"]["B"]["ports"])})
+        elif e[1] in ("ADD", "SCALE"):
+            coefficients[Q(e[-1])] += len(caller["types"][e[0]]["ports"])
+        elif e[1] == "LAMBDA":
+            # Real and imaginary components of the complete Gaussian factors.
+            ports = len(caller["types"][e[0]]["ports"])
+            coefficients[Q(1, 2)] += 2*ports
+            coefficients[Q(1, 2)*e[-1]] += ports
+            coefficients[-Q(1, 2)*e[-1]] += ports
+    for scale, fields in [(native_scale, stages*word["public"]),
+                          (caller_scale, sum(t["roles"]*len(t["ports"]) for t in caller["types"].values()))]:
+        coefficients[Q(scale)] += fields
+        coefficients[Q(1, scale)] += fields
+    coefficients.update({Q(-1): 1, Q(1): 1})  # real/imaginary signs and unit phases
+    num_bits = max(abs(q.numerator).bit_length() for q in coefficients)
+    div_bits = max(q.denominator.bit_length() for q in coefficients)
+    require((num_bits, div_bits) == (24, 20) and word["program"][2322][-2] == "-97039/655360",
+            "Literal numerator and divisor bounds")
+    valid = invalid = 0
+    for q in sorted(coefficients):
+        b = q.denominator
+        for width in (1, 7, 25, 65):
+            limit = (2**width-1)//b
+            for m in {0, min(1, limit), limit//2, limit, -limit}:
+                x = m*b
+                require(rational(x, q, width) == x*q and abs(x*q.numerator) < 2**(width+24),
+                        "All literal fixed coefficients and padded product bound")
+                valid += 1
+        if b > 1:
+            try:
+                rational(1, q, b.bit_length())
+            except ValueError as error:
+                require(str(error) == "nonzero exact-division remainder", "Expected exact-division guard")
+                invalid += 1
+            else:
+                raise ValueError("Nonexact quotient accepted")
+    return dict(distinct=len(coefficients), exact_cases=valid, remainder_controls=invalid,
+                numerator_bits=num_bits, divisor_bits=div_bits, wide_divisor_example="-97039/655360")
+
+
+def finite_bill(word, caller, paid, target, macro, result, native, numeric):
+    checks = result["checks"]
+    geometry = checks["ODD-PHYSICAL-BINDING.json"]["occurrence_and_geometry"]
+    fixed = checks["ODD-FIXED-TAPE-COUNTS.json"]
+    precision = checks["ODD-PRECISION.json"]
+    stages = caller["stages"]
+    n = caller["ambient_rank"]
+    main = sum(len(t["ports"])*t["roles"] for t in caller["types"].values())
+    native_helpers = stages*sum(native["helpers"].values())
+    contacts = 4*stages*(len(caller["types"]["A"]["ports"]) + sum(len(t["ports"]) for t in caller["types"].values()))
+    banks = stages*native["labels"]
+    surplus = sum(r*(target.get(r, 0)-paid.get(r, 0)) for r in paid.keys() | target.keys())
+    signed_idle = macro["IDLE_ODD"]
+    require((n, sum(paid.values()), sum(target.values()), surplus, contacts, native_helpers, banks) ==
+            (145, 110502, 22410, 1424, 13600, 18666, 1037), "Exact physical size and surplus")
+    require((contacts, native_helpers, banks) ==
+            (geometry["native_contact_boundaries"], geometry["fresh_helpers"], geometry["reserved_native_banks"])
+            and geometry["reserved_serial_query_lambda_bank"] == 1 and native_helpers + main == sum(target.values()),
+            "Physical receipt and stocks")
+    require(macro["QUERY"] == geometry["query_uses"] and macro["LAMBDA"] == geometry["lambda_uses"]
+            and macro["IDLE_ONE"]+signed_idle == geometry["idle_uses"], "Every paid or ordinary outer macro counted")
+    native_admin = stages*(len(word["program"])-sum(native["paid"].values()))
+    conversions = 2*(stages*word["public"]+main)
+    services = 32*(native_admin+sum(macro.values())+conversions)
+    maps = 2*(sum(paid.values())+sum(target.values())) + contacts + 2*geometry["idle_uses"]
+    maps += 3*macro["QUERY"] + macro["LAMBDA"] + signed_idle
+    records = maps*4*(n+1)**2
+    require((services, services*2**20, maps, records) ==
+            (fixed["scalar_services_upper"], fixed["scalar_steps_coefficient"],
+             fixed["monomial_map_slots"], fixed["elementary_records_upper"]), "Full finite-tape tariff")
+    require(fixed["common_grid"] == dict(fractional="p+D", signed_width="p+h+2D+3", temp_padding=26),
+            "One common field and padded format")
+    H = numeric["H"]
+    context = precision["context_c"]
+    K_star = 1920*153**1920*(H+1)**2
+    require(context == fixed["context_c"] == 2430 <= 4096 and (4096*K_star).bit_length() < H,
+            "Precision context fits funded carrier")
+    require(all(v["strict_power_of_two"] < H for v in precision["rounded_caller"]["bounds"].values()),
+            "Rounded caller envelope")
+    ordinary = checks["ODD-ADMISSION-PARTIAL.json"]["ordinary"]
+    source_units = sum(ordinary[k] for k in ("raw_upper", "per_input_conversion", "lambda_second_charge",
+                                             "all_caller_scalar_surcharge", "charged_caller_odd_conversions"))
+    require(source_units == ordinary["conservative_total"] == 781880696 < 10**9, "Complete source-unit ordinary bill")
+    return dict(ambient=n, compiler_cap=153, paid=sum(paid.values()), productive=sum(target.values()), surplus=surplus,
+                main=main, native_helpers=native_helpers, native_contacts=contacts, native_banks=banks,
+                serial_scratch=1, ordinary=source_units, scalar_services=services, scalar_coefficient=services*2**20,
+                monomial_maps=maps, elementary_records=records, precision_c=context)
+
+
+def outer_claim(gate, selected, sources):
+    outer = runpy.run_path(str(ROOT / "research/final4610-independent-admission/checks/outer.py"))
+    k, C = Q(gate["claim"]), Q(gate["tested"])
+    params = outer["parameters"](k, C)
+    params["bit_saving"] = Q(gate["BIT_pin"])
+    bit = Q(selected["admitted_BIT_saving"])
+    require(params["bit_saving"] == Q(selected["complex_BIT_premise"]) and bit > params["bit_saving"] > C,
+            "Exact retained BIT supplies the weaker premise")
+    checks = outer["evaluate"](params)
+    require(checks["all_positive"] and len(checks["strict_checks"]) == 54 and
+            len(checks["functional_checks"]) == 4, "All strict and functional outer guards")
+    effective = params["a"]
+    for cap in (effective, effective-Q(1, 10**12)):
+        reject = outer["evaluate"](params | {"bit_saving": cap})
+        require(not reject["all_positive"] and reject["strict_checks"]["actual_bit_above_effective"] == cap-effective,
+                "Actual outer gate rejects BIT at or below effective price")
+    before = Q(selected["kappa"])
+    previous = Q(".003644267085400")
+    require(before < previous < k, "Both exact comparisons")
+    limiting = min(checks["margins"].values())
+    return dict(schema="conditional-frontier-proposal/1", source_heads=sources, kappa=k,
+                delta_over_selected=k-before, delta_over_pr7155=k-previous,
+                tested_complex_price=C, complex_uniform=dict(saving=params["complex_uniform_saving"],
+                    rank_encoding="2^"+gate["H"], actual_raw_ambient=145, compiler_raw_ambient_cap=153),
+                retained_bit_before_cover=selected["uniform_templates"][1], admitted_bit_saving=bit,
+                complex_bit_premise=params["bit_saving"], outer_parameters=params,
+                nine_outer_savings=checks["margins"], strict_limiting_slack=limiting-k,
+                strict_count=54, functional_count=4, minimum_guard=min(
+                    *checks["strict_checks"].values(), *checks["functional_checks"].values()),
+                bit_at_and_below_effective_rejected=True, assumptions=selected["assumptions"])
+
+
+def main():
+    authenticate()
+    word, parent = [load(HERE / "inputs" / pr / "WORD.json.gz") for pr in ("pr7156", "pr7155")]
+    caller_file = HERE / "inputs/pr7113/CALLER.json"
+    caller = load(caller_file)
+    receipt = load(HERE / "inputs/pr7156/RESULT.json")
+    native_receipt = load(HERE / "inputs/pr7156/NATIVE-RESULT.json")
+    require(sha256(caller_file.read_bytes()).hexdigest() == receipt["caller_sha256"] and
+            sha256(canonical(word)).hexdigest() == native_receipt["word_canonical_sha256"] == receipt["price"]["new_native"]
+            and sha256(canonical(parent)).hexdigest() == receipt["price"]["old_native"], "Complete input and receipt bindings")
+    native, base = trace(word), trace(parent)
+    require((len(word["program"]), word["public"], native["labels"], native["lifetimes"], native["owned_peak"],
+             native["owned_ascent_mass"]) == (76220, 1498, 61, 64, 47, 56), "Native census")
+    chart = chart_checks(parent, word, load(HERE / "inputs/pr7156/WITNESS.json"),
+                         load(HERE / "inputs/pr7156/PATHS.json"))
+    paid, target, macro = invoice(word, caller, native)
+    old_paid, old_target, _ = invoice(parent, caller, base)
+    mutant = deepcopy(caller)
+    row = next(e for e in mutant["events"] if e[0] == "J")
+    row[2][0] = row[2][1]
+    try:
+        invoice(word, mutant, native)
+    except ValueError as error:
+        require(str(error) == "Exact A/B stage owners", "Expected aliased owner rejection")
+    else:
+        raise ValueError("Aliased main owners accepted")
+    for p, t, name in [(paid, target, "after"), (old_paid, old_target, "before")]:
+        price = receipt["price"][name]
+        require(price["empty_root_credits"] == 0 and json.loads(canonical(p)) == price["P"]
+                and json.loads(canonical(t)) == price["T"], "Complete "+name+" signed rank invoice")
+    prior = old_target.copy()
+    prior.subtract(old_paid)
+    gate = receipt["price"]["gate"]
+    num = certified_price(paid, target, prior, Counter({r: caller["stages"]*q for r, q in native["paid"].items()}),
+                          caller["ambient_rank"], gate)
+    grid = receipt["checks"]["ODD-FIXED-TAPE-COUNTS.json"]["caller_odd_scale"]
+    native_grid = native_receipt["derived_grid"]
+    require((grid, native_grid["odd_scale"], native_grid["fractional_bits"]) == (675, 1125, 25), "Two exact grids")
+    scalar = scalars(word, caller, native_grid["odd_scale"], grid)
+    bill = finite_bill(word, caller, paid, target, macro, receipt, native, num)
+    sources = {f"pr{x['pr']}": x["commit"] for x in load(HERE / "INPUTS.json")["sources"]}
+    selected = load(ROOT / "certificates/frontier7000/CLAIM.json")
+    proposed = outer_claim(gate, selected, sources)
+    report = dict(status="PASS_SOURCE_BOUND_7156_APPLICATION_REVIEW", chart=chart, numeric=num,
+                  exact_scalars=scalar, finite_bill=bill, whole_lambda=whole_lambda_control(),
+                  aliased_main_rejected=True, proposed=proposed)
+    normalized = json.loads(json.dumps(report, default=str, sort_keys=True))
+    if sys.argv[1:] == ["--write"]:
+        (HERE / "RESULT.json").write_text(json.dumps(normalized, indent=2, sort_keys=True)+"\n")
+    else:
+        require(not sys.argv[1:] and normalized == load(HERE / "RESULT.json"), "Full frozen review receipt")
+    print(report["status"], str(proposed["kappa"]), "54+4", len(chart["collateral"]), scalar["divisor_bits"])
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/p104-frontier-7156-application-review/word.py b/research/p104-frontier-7156-application-review/word.py
new file mode 100644
index 0000000000..351935607b
--- /dev/null
+++ b/research/p104-frontier-7156-application-review/word.py
@@ -0,0 +1,216 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Sparse scalar witnesses and a separate census of the literal paid word."""
+
+from collections import Counter, defaultdict
+from fractions import Fraction
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def bump(vector, role, increment):
+    value = vector.get(role, 0) + increment
+    if value:
+        vector[role] = value
+    else:
+        vector.pop(role, None)
+
+
+def frame_spaces(word):
+    spaces = []
+    for basis in word["frames"]:
+        span = {0}
+        for v in basis:
+            require(0 < v < 512 and v not in span, "Independent native axes")
+            span |= {v ^ w for w in span}
+        spaces.append(span)
+    return spaces
+
+
+def trace(word):
+    """Check the literal frames and ownership, and count every MOVE."""
+    n = word["public"]
+    require(len(word["initial"]) == len(word["final"]) == n, "Complete boundaries")
+    spaces = frame_spaces(word)
+    active = dict(enumerate(word["initial"]))
+    paid, rises = Counter(), Counter()
+    labels = set()
+    peak = lifetimes = 0
+    for e in word["program"]:
+        op, r = e[:2]
+        if op == "INIT":
+            require(n <= r < n + word["owned_fields"] and r not in active, "Fresh owned label")
+            active[r] = e[2]
+            labels.add(r)
+            lifetimes += 1
+            peak = max(peak, len(active) - n)
+        elif op == "CLEAR":
+            require(r >= n and active[r] == e[2], "Clear only a live owned field")
+            del active[r]
+        elif op == "MOVE":
+            a, b, owned = e[2:]
+            require(active[r] == a and owned == (r >= n), "Literal MOVE source and ownership")
+            upward = spaces[a] < spaces[b]
+            require(upward or (owned and spaces[b] < spaces[a]), "Strict nested MOVE")
+            rank = abs(len(word["frames"][b]) - len(word["frames"][a]))
+            paid[rank] += 1
+            if upward and owned:
+                rises[rank] += 1
+            active[r] = b
+        else:
+            require(op in ("ADD", "COPY", "SCALE") and active[r] == e[-1], "Literal scalar target")
+            if op != "SCALE":
+                require(r != e[2] and active[e[2]] == e[-1], "Literal scalar source")
+    require(active == dict(enumerate(word["final"])), "All final frames and owned retirement")
+    require(len(labels) == word["owned_fields"], "All owned labels charged")
+
+    main = set(word["live"]) | {r + 112 for r in word["live"]}
+    main.update(word["hosted"]["X2"])
+    main.update(word["hosted"]["Y2"])
+    helpers = Counter()
+    for r in set(range(n)) - main:
+        a, b = word["initial"][r], word["final"][r]
+        require(spaces[a] < spaces[b], "Productive helper boundary")
+        helpers[len(word["frames"][b]) - len(word["frames"][a])] += 1
+    return dict(paid=paid, helpers=helpers, lifetimes=lifetimes, owned_peak=peak,
+                labels=len(labels), owned_ascent_mass=sum(k * v for k, v in rises.items()))
+
+
+def timed_vector(word, witness, *, suffix):
+    """Gather covector backwards, or inject one perturbation forwards.
+
+    In these coordinates MOVE changes the frame and preserves the scalar
+    vector. The source phase/frame proof supplies that identification.
+    """
+    cut = witness["cut"]
+    events = word["program"]
+    field = "injections" if suffix else "gathers"
+    schedule = defaultdict(dict)
+    for row in witness[field]:
+        t, r = row["cut"], row["role"]
+        require((cut <= t <= len(events)) if suffix else (0 <= t <= cut), "Causal schedule")
+        coefficient = Fraction(row["coefficient"])
+        require(row["frame"] == witness["frame"] and r not in schedule[t] and coefficient,
+                "Distinct nonzero timed observations in the declared frame")
+        schedule[t][r] = coefficient
+    state = {}
+    if suffix:
+        for t in range(cut, len(events) + 1):
+            for r, q in schedule[t].items():
+                bump(state, r, q)
+            if t < len(events):
+                step(state, events[t])
+        return state
+    for t in range(cut, -1, -1):
+        if t < cut:
+            op, r, *args = events[t]
+            if op in ("INIT", "CLEAR"):
+                state.pop(r, None)
+            elif op == "SCALE":
+                bump(state, r, (Fraction(args[0]) - 1) * state.get(r, 0))
+            elif op in ("ADD", "COPY"):
+                bump(state, args[0], Fraction(args[1]) * state.get(r, 0))
+                if op == "COPY":
+                    state.pop(r, None)
+        for r, q in schedule[t].items():
+            bump(state, r, q)
+    require(all(r < word["public"] for r in state), "No pre-initialized owned input")
+    return state
+
+
+def step(state, e, *, guard_copy=True):
+    op, r = e[:2]
+    if op in ("INIT", "CLEAR"):
+        state.pop(r, None)
+    elif op == "SCALE":
+        bump(state, r, (Fraction(e[2]) - 1) * state.get(r, 0))
+    elif op in ("ADD", "COPY"):
+        if op == "COPY":
+            require(not guard_copy or not state.get(r, 0), "Nonzero COPY destination")
+            state.pop(r, None)
+        bump(state, r, Fraction(e[3]) * state.get(e[2], 0))
+
+
+def check_paths(word, witness, paths):
+    events = word["program"]
+    f = witness["frame"]
+    spaces = frame_spaces(word)
+    paid = witness["path"]
+    covered = set()
+    for path in [*paths, paid]:
+        r, lo, hi = path["role"], path["lo"], path["hi"]
+        require(0 <= lo < hi <= len(events) and path["frame"] == f, "Path interval")
+        contacts = [i for i in range(lo, hi) if events[i][1] == r
+                    or (events[i][0] in ("ADD", "COPY") and events[i][2] == r)]
+        require(contacts == path["moves"] and not covered.intersection(contacts), "Complete contact-free paths")
+        covered.update(contacts)
+        moves = [events[i] for i in contacts]
+        require(moves and all(e[0] == "MOVE" for e in moves), "Retimed operations are MOVEs")
+        frames = [moves[0][2], *(e[3] for e in moves)]
+        require(frames[:-1] == [e[2] for e in moves], "Continuous source path")
+        if path is paid:
+            a, b = frames[0], frames[-1]
+            require((a, b) == (paid["old"], paid["new"]) and spaces[a] < spaces[f] < spaces[b],
+                    "Strictly nested paid midpoint")
+            require((len(spaces[f]).bit_length() - len(spaces[a]).bit_length(),
+                     len(spaces[b]).bit_length() - len(spaces[f]).bit_length()) == (3, 5),
+                    "Paid replacement ranks")
+        else:
+            require(frames == path["frames"] and f in frames, "Retained neutral path")
+    for row in witness["gathers"] + witness["injections"]:
+        path = paths[row["path"]] if "path" in row else paid
+        require(row["role"] == path["role"] and path["lo"] <= row["cut"] <= path["hi"],
+                "Observation belongs to the retimed path")
+
+
+def pulse(word, skip=None):
+    state = {word["public"] - 1: Fraction(1)}
+    for i, e in enumerate(word["program"]):
+        if i != skip:
+            step(state, e)
+    return state
+
+
+def chart_checks(parent, word, witness, paths):
+    check_paths(parent, witness, paths)
+    c = timed_vector(parent, witness, suffix=False)
+    d = timed_vector(parent, witness, suffix=True)
+    vectors = [{int(r): Fraction(q) for r, q in witness[k].items()} for k in ("c", "d")]
+    require([c, d] == vectors and sum(q * d.get(r, 0) for r, q in c.items()) == 1,
+            "Complete c and d, including all collateral coordinates, and unit pairing")
+    pivot, frame = witness["pivot"], witness["frame"]
+    a, b = parent["initial"][pivot], parent["final"][pivot]
+    main = set(parent["live"]) | {r+112 for r in parent["live"]}
+    main.update(parent["hosted"]["X2"] + parent["hosted"]["Y2"])
+    group = set(c) | set(d) | {pivot}
+    require(not group.intersection(main) and all((parent["initial"][r], parent["final"][r]) == (a, b) for r in group),
+            "One helper boundary group")
+    spaces = frame_spaces(parent)
+    ranks = [len(parent["frames"][j])-len(parent["frames"][i]) for i, j in ((a, frame), (frame, b))]
+    require(spaces[a] < spaces[frame] < spaces[b] and witness["ranks"] == ranks == [4, 5],
+            "Strict productive midpoint")
+    mut = 37799
+    require(word["program"][mut] == ["ADD", 781, 1558, "1/2", 306], "Literal injection under test")
+    z = word["public"] - 1
+    full, omitted = pulse(word), pulse(word, skip=mut)
+    require(full == {z: 1}, "New arbitrary helper pulse returns without collateral")
+    collateral = {r: q for r, q in omitted.items() if r != z}
+    require(omitted.get(z) == 1 and len(collateral) == 24 and max(collateral) < word["public"],
+            "Omitted injection leaves 24 wrong public outputs with the helper still correct")
+
+    toy = [["INIT", 1, 0], ["ADD", 1, 0, "1", 0], ["COPY", 1, 0, "1", 0], ["CLEAR", 1, 0]]
+    unguarded, guarded = {0: 1}, {0: 1}
+    for e in toy:
+        step(unguarded, e, guard_copy=False)
+    require(unguarded == {0: 1}, "Dirty COPY control is invisible at the endpoint")
+    try:
+        for e in toy:
+            step(guarded, e)
+    except ValueError as error:
+        require(str(error) == "Nonzero COPY destination", "Expected interior COPY failure")
+    else:
+        raise ValueError("Dirty COPY accepted")
+    return dict(c=c, d=d, gather_count=len(witness["gathers"]), injection_count=len(witness["injections"]),
+                pulse=z, omitted_injection=mut, collateral=sorted(collateral), erased_dirty_copy_rejected=True)