Route one marked CRT payload fiber from encoded source

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).

research/encoded-crt-leaf-payload/INPUT-PINS.json

@@ -0,0 +1,115 @@
+{
+  "base": "e54523517d0f03e58352e647c403a5af3e525a57",
+  "canonical": [
+    {
+      "path": "research/r437-preparation-composition/predecessor4025/source/words.py",
+      "sha256": "5c37f57708ba3131bdcb03139f9dbc29886bee44569c09cbba51b68f75acd7f9",
+      "git_blob": "8d4ba37e2778acb35b34e0719df2caf138fbeb50",
+      "bytes": 13794
+    },
+    {
+      "path": "research/r437-preparation-composition/predecessor4025/source/records.py",
+      "sha256": "0c9c4b23e998597fb877bb1a29da69ac869b68262abe635b162b4dba9c69b372",
+      "git_blob": "4f00467a0ff580954ad2fd0c7380240c753ddef3",
+      "bytes": 9888
+    },
+    {
+      "path": "research/encoded-crt-entry-lifecycle/entry.py",
+      "sha256": "0537ec98f306270c8ff6a424841886cf53f675d9947029347090c7dc779616d7",
+      "git_blob": "1fa2b0cb88320d4f5b623554bb0fc6de332b773c",
+      "bytes": 6377
+    },
+    {
+      "path": "research/encoded-current-crt/producer.py",
+      "sha256": "88dab4ca02a92164a67826db361214fa1405e4b4a588f8c4279a21bcee95ab76",
+      "git_blob": "a327b0161eca57a1cc44ec2aa8e3defed2167ddc",
+      "bytes": 7891
+    },
+    {
+      "path": "research/crt-persistent-numerical-owner/owner.py",
+      "sha256": "1d73f432f8de9c791260c43335eb207d82bbb3f5b190cc76d0d914a4db076f41",
+      "git_blob": "20ef3519b6fef691ec92b7315e320b5e8ce9bf18",
+      "bytes": 2980
+    },
+    {
+      "path": "research/crt-mixed-row-entry/bridge.py",
+      "sha256": "89c38638c0d66da731566c903c32e7fa1ad31088d29cfd2634fce823dd07c1f9",
+      "git_blob": "57f6853e262a6136bc616f1e47a31d0ace28495c",
+      "bytes": 3864
+    },
+    {
+      "path": "research/crt-current-row-query/join.py",
+      "sha256": "11c9ac1175a45edae80869b22c041e31a1b5cc75f4389ec2e073de37e547bf35",
+      "git_blob": "676582b4a376db375237ec52df84a3ddaf231827",
+      "bytes": 9955
+    },
+    {
+      "path": "research/crt-encoded-benes-rom-producer/microcode.py",
+      "sha256": "d4af5350854a87b67484840800b94e1e53cff82c78ec0f2a91753fed9ea70af7",
+      "git_blob": "052b01a83bc910c176b83a012b9f46f0e9525b9d",
+      "bytes": 23823
+    },
+    {
+      "path": "research/crt-uniform-rom-query/machine.py",
+      "sha256": "46ee6a635251e498ee9a5d4aff8c0e2a7f1ef2ff951e5b6a2a8953316e9cd02d",
+      "git_blob": "88292ce98d31d540c7dba6960bfe4c19f06a8077",
+      "bytes": 12431
+    },
+    {
+      "path": "research/crt-binary-key-port/binary.py",
+      "sha256": "50a3dea7fc087715b4e605e85629566ed31903026540f916df6b8cbaa536182d",
+      "git_blob": "ec574f26d6f64ead00d7c2cf5b808c0498b460cf",
+      "bytes": 5658
+    },
+    {
+      "path": "research/crt-binary-radix-consumer/radix.py",
+      "sha256": "f4200a495d9c445474275214254d46e9a8e03967a635263905a4c9192bb36f1f",
+      "git_blob": "f558019fe70c46bcb2f087464c1d2aa021b7188d",
+      "bytes": 4072
+    },
+    {
+      "path": "research/crt-paid-row-reentry/RESULT.json",
+      "sha256": "d818bffac4647dffaf525ed68dbb79dc575a00303af3315c6d4fe39b60f49a13",
+      "git_blob": "832d3312df223d1b151e5c620cc3d4e295f49e05",
+      "bytes": 15482
+    }
+  ],
+  "retained": [
+    {
+      "path": "research/encoded-balanced-crt-inverse/source/research/encoded-balanced-crt-entry/frontend.py",
+      "sha256": "6ec9aab626a9d7a229b6f13ce6863e1ca77fa30ef65a4a66ae03a6ffaf2ee78c",
+      "git_blob": "8adbe2cfef74da9854ed0b70b6c221f5746efa9f",
+      "bytes": 10737,
+      "file": "frontend.py",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "8c0e55c9ba25ff2c8199b01539a4d56ae71a1473"
+    },
+    {
+      "path": "research/encoded-balanced-crt-inverse/source/research/encoded-balanced-crt-endpoint/endpoint.py",
+      "sha256": "c24ae2c90d175d276120438809e7c7401b8a8c04dec139f1b7345e9778984ced",
+      "git_blob": "b084d893bdb2ce5571ef00196a9ec6a60e723964",
+      "bytes": 6038,
+      "file": "endpoint.py",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "8c0e55c9ba25ff2c8199b01539a4d56ae71a1473"
+    },
+    {
+      "path": "research/encoded-balanced-crt-inverse/inverse_frontend.py",
+      "sha256": "0e5f4c9450372c90000f5ebf3c22dfbe7241dd53da9ae9bcce310af859b009ef",
+      "git_blob": "17abfb8500043bcdeb656094bb0213d911d986fc",
+      "bytes": 2167,
+      "file": "inverse_frontend.py",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "8c0e55c9ba25ff2c8199b01539a4d56ae71a1473"
+    },
+    {
+      "path": "research/encoded-balanced-crt-inverse/inverse_producer.py",
+      "sha256": "6acdebee7134fbc8e2d121060286bd05e7282900da8a28a78c80937dde7ea178",
+      "git_blob": "46bf6ef4e2dfa53bca17ac668914b1a842eaba9e",
+      "bytes": 8041,
+      "file": "inverse_producer.py",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "8c0e55c9ba25ff2c8199b01539a4d56ae71a1473"
+    }
+  ]
+}

research/encoded-crt-leaf-payload/README.md

@@ -0,0 +1,125 @@
+# Route a marked payload from an encoded CRT leaf
+
+The live encoded CRT leaf now drives the existing Beneš row query and
+literal binary radix mover for one padded right-axis fiber. On the
+retained non-root fixture, slots 0 and 1 exchange their payloads and
+padded slots 2 and 3 preserve theirs. The inverse restores the same
+physical payload tape, its keys, the encoded source, and their heads.
+
+| Boundary | Source coordinates | Payload tags in physical order |
+| --- | --- | --- |
+| Input | (3, 2, 1, 1) | 293, 730, 905, 3681 |
+| Forward | (3, 2, 1, 0) | 730, 293, 905, 3681 |
+| Inverse | (3, 2, 1, 1) | 293, 730, 905, 3681 |
+
+The input uses moduli (5, 7, 3, 2) and declared widths (3, 3, 2, 2) from
+the `nonroot_roundtrip` case of [#5625](https://github.com/CrocSwap/integer-mult-bounds/pull/5625).
+Each payload is an opaque 12-bit record in the binary radix format.
+The replay checks the entire frame, including its two-bit position
+keys and its physical backing identity. It also checks the source's
+metadata and inaccessible historical tail.
+
+## Source and payload join
+
+1. Acquire the retained encoded iterator and its clean private roles.
+   Select its last leaf at the level with unary half length one, with
+   a nonempty axis prefix. Retire earlier numerical leases without
+   writing their coordinates. Both directions pay for every visited
+   lease, including the skipped leases.
+2. While the selected lease is live, scan the actual right record for
+   its unary width and modulus and copy the offset from the numerical
+   result stream using the existing precision guide. The measured
+   fields give width 2, modulus 2, precision 5 and offset 1 in both
+   directions. The source and result return to their entry heads
+   with their bytes preserved before source staging.
+3. Run the unchanged encoded Beneš producer on those framed headers.
+   For each physical input slot, follow all produced rows by the
+   existing row-bit query. The adapter keeps the slot address on a
+   binary tape, walks the target bit from low to high and back, and
+   writes the destination as an MSB-first key in the allocated
+   radix cells. It reads the row tape backwards by rows for the
+   inverse, keeping the bits of each row in wire order.
+4. Run the literal radix pass once per unary width mark. Its stable
+   last-bit pass rotates that bit to the front, so two passes sort
+   the two-bit destination keys and return them to their initial
+   orientation. Each tag moves with its key on the actual bit tape.
+   Stage the coordinate result, retire the numerical lease, commit
+   the source and clear the adapter and bucket storage.
+
+For the selected leaf the left modulus and coordinate are 3 and 1.
+The direct CRT oracle solves 3c ≡ 1 modulo 2, giving c = 1. It maps
+valid positions x to (x+c) modulo 2 and fixes the two padded positions.
+The offset depends on the left child, which is preserved here. The
+inverse therefore uses the same offset and the switch layers in reverse
+order. Every switch layer is its own inverse, so the reversed layer
+product undoes the forward product. The independent oracle checks the
+nonidentity forward placement before checking exact restoration.
+
+The input positions are enumerated by an encoded counter. The adapter
+uses the existing key cells for storage and derives its addresses from
+physical positions. Fixture serialization and all independent
+observers are outside the measured runtime.
+
+## Measured work and storage
+
+| Quantity | Forward | Inverse |
+| --- | ---: | ---: |
+| Encoded source symbol actions, including numerical work | 113,295 | 372,489 |
+| Adapter symbol actions | 3,481 | 3,817 |
+| Beneš producer instructions | 2,363,816 | 2,363,816 |
+| Payload adapter bit actions | 1,694 | 1,694 |
+| Literal radix instructions, including finite control | 43,162 | 43,162 |
+| Retained private symbol roles | 136 | 136 |
+| Retained private symbol cells | 2,253 | 2,633 |
+| Retained bucket bit extent | 208 | 208 |
+| Retained radix register bits | 144 | 144 |
+| Retained Beneš registers | 15 | 15 |
+
+The symbol counts include header and key-address preparation, row
+scans, source staging and retirement. The bit counts include the
+physical key writes and bucket initialization and retirement, with
+radix instructions counted separately. Both directions' private roles
+remain retained for the measurement. They share one 57-cell source
+and the original payload tape, whose visited extent is 183 bits.
+These are observations in the respective execution models. A common
+literal tariff for the combined source controller and payload path
+requires further lowering.
+
+## Replay and source credit
+
+From a checkout or an official Git-free export with the declared
+inputs, run:
+
+```sh
+python3.12 -I -B research/encoded-crt-leaf-payload/replay.py
+```
+
+[RESULT.json](RESULT.json) records the observed headers, exact
+endpoints, cost and backing. The checks include a separate direct CRT
+oracle, noncommuting layers that distinguish reverse traversal, a
+truncated layer stream that must fail, and suppressed switches that
+must fail the forward-placement check.
+
+[INPUT-PINS.json](INPUT-PINS.json) binds the runtime to canonical main
+`e54523517d0f03e58352e647c403a5af3e525a57` and four byte-exact
+runtime files from CubeJerry's [#7352](https://github.com/CrocSwap/integer-mult-bounds/pull/7352)
+at `8c0e55c9ba25ff2c8199b01539a4d56ae71a1473`. The forward writer
+is also byte-identical to the one in [#7351](https://github.com/CrocSwap/integer-mult-bounds/pull/7351).
+Ali Romman's [#5625](https://github.com/CrocSwap/integer-mult-bounds/pull/5625)
+supplies the fixture and the paid retirement boundary.
+JoyboyBrian's [#5092](https://github.com/CrocSwap/integer-mult-bounds/pull/5092),
+[#5496](https://github.com/CrocSwap/integer-mult-bounds/pull/5496)
+and [#5015](https://github.com/CrocSwap/integer-mult-bounds/pull/5015)
+supply the encoded producer, physical row query and literal payload
+consumer, respectively. OpenAI Codex and ChatGPT Pro materially assisted
+the work. Pro produced a separate witness with the same placement and
+restoration using different tags and a different input-key policy.
+Apache-2.0.
+
+## Open next questions
+
+A complete balanced payload stage must route all right-axis fibers in
+order, including idle and padded rows. A concrete next test is to
+bind one retained multi-target fixture and check its synchronized
+row and header streams. This package establishes one finite fiber.
+A full integer product and a combined cost proof remain open.

research/encoded-crt-leaf-payload/RESULT.json

@@ -0,0 +1,98 @@
+{
+  "benes_program_instructions": 10648,
+  "control_cases": [
+    "noncommuting rows distinguish traversal order",
+    "truncated width-two layer stream rejected",
+    "suppressed switches fail the forward oracle"
+  ],
+  "fixture": "nonroot_roundtrip",
+  "forward_and_inverse": [
+    {
+      "adapter_symbol_actions": 3481,
+      "benes_instructions": 2363816,
+      "direction": "forward",
+      "encoded_source_symbol_actions": 113295,
+      "observed_headers": {
+        "h": "L01000R",
+        "modulus": "L01000R",
+        "offsets": "L10000|R",
+        "selected_layer": "L00000R",
+        "width": "L11R"
+      },
+      "payload_adapter_bit_actions": 1694,
+      "radix_bit_control_instructions": 43162,
+      "radix_passes": 2,
+      "retained_benes_registers": 15,
+      "retained_bucket_bits": 208,
+      "retained_radix_register_bits": 144,
+      "retained_symbol_cells": 2253,
+      "retained_symbol_roles": 136,
+      "selected_nodes": 1,
+      "skipped_nodes": 1
+    },
+    {
+      "adapter_symbol_actions": 3817,
+      "benes_instructions": 2363816,
+      "direction": "inverse",
+      "encoded_source_symbol_actions": 372489,
+      "observed_headers": {
+        "h": "L01000R",
+        "modulus": "L01000R",
+        "offsets": "L10000|R",
+        "selected_layer": "L00000R",
+        "width": "L11R"
+      },
+      "payload_adapter_bit_actions": 1694,
+      "radix_bit_control_instructions": 43162,
+      "radix_passes": 2,
+      "retained_benes_registers": 15,
+      "retained_bucket_bits": 208,
+      "retained_radix_register_bits": 144,
+      "retained_symbol_cells": 2633,
+      "retained_symbol_roles": 136,
+      "selected_nodes": 1,
+      "skipped_nodes": 2
+    }
+  ],
+  "forward_destinations": [
+    1,
+    0,
+    2,
+    3
+  ],
+  "forward_source": [
+    3,
+    2,
+    1,
+    0
+  ],
+  "forward_tags": [
+    730,
+    293,
+    905,
+    3681
+  ],
+  "input_tags": [
+    293,
+    730,
+    905,
+    3681
+  ],
+  "moduli": [
+    5,
+    7,
+    3,
+    2
+  ],
+  "payload_bits_visited": 183,
+  "radix_program_instructions": 3885,
+  "restored_source_and_payload": true,
+  "source_cells_retained": 57,
+  "status": "PASS_ENCODED_CRT_LEAF_PAYLOAD",
+  "widths": [
+    3,
+    3,
+    2,
+    2
+  ]
+}