Audit the P104 index-to-tensor bridge without replaying events.

research/p104-index-tensor-bridge/README.md

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+# Index-to-tensor bridge for the scalar P104 code
+
+**Audit of one published convention. No new κ.** Selected κ stays
+`0.001672660197076918`.
+
+PR #3996 checks 763,392 literal events and, separately, the block algebra of
+`U`. Its proof states the bridge between them and does not execute that
+bridge. This package executes it.
+
+## Scope and evidence
+
+The index in that proof is
+
+```text
+index(bank, i, j) = (bank*104 + i)*104 + j
+```
+
+Axis 0 varies `i` at fixed `j`. Axis 1 varies `j` at fixed `i`. On every
+coefficient of widths 2 and 8, and on one dense width-104 state:
+
+- broadcasting a one-axis map `K` along axis 0 is `K tensor I` (left multiplication);
+- broadcasting it along axis 1 is `I tensor K`, which right-multiplies by `K^t`.
+
+The second identity fails if the column fiber is implemented as right
+multiplication by `K`. The four sweeps `U`, `U^{-1}`, `U^t` and `U^{-t}` of
+the canonical code are checked in that form. The four shears are the block
+maps with factors `A` and `M`: lower/upper `A` use axis 0 and axis 1 of `A`,
+and the coded Gram shears use `M = U U^t`.
+
+On the canonical fixture
+`research/p104-native-channel/inputs/P104-FIXTURE.json`
+(SHA256 `516c06f6ec3cb84be588c546108de897650288576dd5fbf5fe44b9c5546ad8a4`),
+an independent root enumeration rebuilds the 768 signed-half entries. Their
+ASCII digest is
+`88e9a726e8c8aec055bfd7cd024883b5c8ecbda0cd6471e591a08c43a108a535`,
+the same digest PR #3996 binds. For this `U`:
+
+- `A = U^t P U` satisfies `A^2 = 13 A`, and `(I-A)` has an exhibited rational inverse;
+- `M = U U^t` is invertible, and `M` is not `U^t U`;
+- the bank block `P tensor (M - U^t U)` has Frobenius square **18432**;
+- `N - P = U^{-t}(I-A)U^{-1}` is invertible, so each omitted side
+  `(N-P) tensor M` and `M tensor (N-P)` has rational rank **10816**.
+
+The contraction identity
+`||sum c_k A_k tensor B_k||_F^2 = sum c_k c_l <A_k, A_l> <B_k, B_l>`
+was checked against the dense Kronecker matrix at widths 2 and 3, including
+a nonzero sample. The width-104 gap uses that identity. Both factors of an
+omitted side have exhibited inverses. The identity
+`(A tensor B)(A^{-1} tensor B^{-1}) = I` was checked on a 2-by-2 pair. At
+width 104 it is the same entrywise rule, not a stored 10816-square product.
+That is the rank step.
+
+This does **not** replay the 763,392 events, localize a fiber of PR #3979, or
+supply a physical consumer. Algebraic rank is not a native-call price. No
+supplier is admitted.
+
+## Reproduce
+
+Python 3.12, standard library, from the repository root:
+
+```sh
+python3.12 -B research/p104-index-tensor-bridge/verify.py
+python3.12 -B research/p104-index-tensor-bridge/test_verify.py
+python3.12 -B scripts/research_package.py --package research/p104-index-tensor-bridge
+```
+
+Expected markers:
+
+```text
+PASS_P104_INDEX_TENSOR_BRIDGE
+PASS_P104_INDEX_TENSOR_BRIDGE_TESTS
+```
+
+The tests reject a column convention that drops the transpose, and they reject
+a one-entry change to `B2`.
+
+## Open next questions
+
+1. One frozen encoder fiber from PR #3996 should be compared with axis 0 of
+   `U`, without calling that package's checker. The word bytes are on head
+   `b8dd4e04bf8490aca121abc7ba0e503651db6c97`, not on this main checkout.
+2. A repeated physical consumer still has to pay `(N-P) tensor M` or show a
+   different interface. Rank 10816 says the Gram shear is not that payment.
+
+## Credit
+
+The code, the index sentence, and the rank claim under audit are Chris R /
+Clear1nsight's PR #3979, audited by ToikY in PR #3996. The fixture and root
+normalization come from the retained P104 native channel (Rohan Arun, Chafik
+Boukhalfa, Adam Gall, and the native/E8 lineage named there). This package
+does not import either checker's source.
+
+Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.
+No independent human review is claimed.

research/p104-index-tensor-bridge/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "research/p104-native-channel/inputs/P104-FIXTURE.json",
+      "usage": "input",
+      "git_blob": "2e16f99b295bb386fd13bd8fbd57b42ef54143a9",
+      "sha256": "516c06f6ec3cb84be588c546108de897650288576dd5fbf5fe44b9c5546ad8a4"
+    }
+  ]
+}

research/p104-index-tensor-bridge/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "p104-side-correction",
+  "priority_revision": 6,
+  "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f",
+  "original_card": {
+    "id": "p104-side-correction",
+    "question": "Can the proposed P104 joint endpoint flags be realized by a chronological correction program with coefficients, dirty restoration and an affordable complete bill?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/p104-native-channel/README.md",
+      "research/p104-native-channel/PROOF.md",
+      "docs/research/community-efficient1000-review.md",
+      "research/p104-joint-unit-flags/README.md"
+    ],
+    "methods": [
+      "Construct one side-correction word at an explicit chronological cut with the needed frames still available.",
+      "Derive a lower bound on the side correction and hosting costs that decides whether this channel can beat the selected budget."
+    ],
+    "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_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the revision-6 family record and #2981 static joint flags, alongside the reviewed #1991 channel. #2981 is an author-checked source archive, not an independently validated executable correction or a refutation of program-level lifetime floors.",
+      "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission."
+    },
+    "first_experiment": "After checking live handoffs, pin one named collection from #2981 and attach acquisition/delivery times, source dependencies and coefficient requirements. Test legal access and arbitrary dirty restoration; price any completion against the full channel/endpoint/hosting allowance. Stop with the exact missing implication or a scoped counterexample rather than expanding the static cover census.",
+    "bottleneck_link": "Completing an already realized changed channel tests a concrete construction opportunity, instead of refining the incumbent packing. A positive local result still needs global and all-size admission.",
+    "allowed_variations": [
+      "One correction factorization, one chronological cut, or one explicit hosting obstruction.",
+      "A changed correction schedule with an updated full bill and native frame contract."
+    ],
+    "scope_change_triggers": [
+      "Recompiling the already certified low-rank channel without closing a new obligation.",
+      "Treating a pending ancestor, local histogram or unpriced side correction as an admitted global supplier.",
+      "Repeating a correction or physical conversion already supplied by a pending follow-up without adding independent coverage or a different unresolved obligation.",
+      "Repeating the 208-flag static matching or calling a static nested cover a chronological correction program. Independent audit of that certificate is distinct and remains useful."
+    ],
+    "overlap_terms": [
+      "P104",
+      "I-G/2",
+      "side correction",
+      "native channel",
+      "1972",
+      "1991",
+      "2586",
+      "endpoint transport",
+      "physical dual",
+      "relay composition",
+      "2981",
+      "joint unit flags",
+      "acquisition delivery",
+      "static nesting"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #2981 reports static joint endpoint flags and a matching of 208 departure and arrival flags; archival intake is not independent verification.",
+        "evidence": "research/p104-joint-unit-flags/README.md",
+        "remaining": "Independent flag check and a chronological coefficient program with dirty restoration and a complete cost.",
+        "status": "author-checked",
+        "source_commit": "3d24b92d8ba057b57cb2d480170ec407520e6882",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Under the index in PR #3996, do the eight stated local sweeps and shears equal the published tensor factors, and is the omitted identity side full rank?",
+  "scope_change_reason": "The catalogue card asks for a chronological correction program. Discussion #1166 comment 19035716 instead asks for an independent inspection of PR #3996's literal-index-to-tensor bridge. This package answers that audit and does not construct a new correction word.",
+  "bottleneck_link": "No kappa change. The bridge decides whether the scalar code's local maps are the tensors P tensor M and M tensor P with M = U U^t. Replacing M by U^t U changes the coded shear. The omitted identity side stays rank 10816, so the Gram-only saving is not an identity-shear completion.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after the index bridge, the transpose-order gap, and the rank consequence. Do not replay the 763,392 events and do not build a physical consumer.",
+  "outcome": "partial",
+  "evidence": "PASS_P104_INDEX_TENSOR_BRIDGE and PASS_P104_INDEX_TENSOR_BRIDGE_TESTS. The wrong-factor block Frobenius square is 18432/1. Literal events were not replayed.",
+  "author": "unpaidmoon",
+  "ai_assistance": "Cursor Grok 4.7 agent, including the verifier and tests.",
+  "open_questions": [
+    {
+      "question": "Does one frozen fiber of PR #3979's event list implement these eight broadcasts?",
+      "why_it_matters": "This package certifies the operator interpretation of the stated maps. It does not read the 763,392 events, so a wrong event could still fail to be the tensor factor.",
+      "first_step": "Localize one encoder fiber from the frozen PR #3996 word bytes and compare it with axis-0 of U, without calling that package's checker.",
+      "blocked_by": "The word bytes live on PR #3996 head b8dd4e04bf8490aca121abc7ba0e503651db6c97 and are not on this main checkout."
+    },
+    {
+      "question": "Is there one repeated physical consumer whose complete bill keeps the k=2 Gram saving?",
+      "why_it_matters": "Rank 10816 says the identity shear is not the Gram shear. A consumer that pays the omitted side can erase the scalar saving.",
+      "first_step": "Pin one chronological producer/consumer pair and price N-P tensor M with owners, frames, and dirty return before any native expansion.",
+      "blocked_by": "No such pair is fixed. PR #3996 open question 1 is still open."
+    }
+  ]
+}

research/p104-index-tensor-bridge/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/p104-native-channel/inputs/P104-FIXTURE.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Index bridge at widths 2, 8 and 104; A^2=13A; exhibited inverse of N-P; positive transpose-order gap 18432."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/test_verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Wrong column convention and a one-entry B2 mutation both fail closed."
+    }
+  ]
+}

research/p104-index-tensor-bridge/test_verify.py

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+#!/usr/bin/env python3
+"""Failure controls for the index-to-tensor bridge. Standard library only."""
+from __future__ import annotations
+
+import json
+from pathlib import Path
+import sys
+
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+import verify
+
+
+def require(condition, message):
+    if not condition:
+        raise SystemExit("FAIL: " + message)
+
+
+def test_wrong_column_convention():
+    operator = verify.witness(verify.N)
+    state = verify.state_from(verify.N, 4)
+    fiber = verify.axis1_broadcast(operator, state)
+    omitted_transpose = verify.matmul(state, operator)
+    gaps = verify.compare(fiber, omitted_transpose)
+    require(gaps > 0, "omitting K^t must disagree on the non-symmetric witness")
+
+
+def test_mutated_coefficient_breaks_square():
+    b2, _gram = verify.load_b2()
+    mutated = [row[:] for row in b2]
+    mutated[0][0] += 1
+    try:
+        verify.check_geometry(mutated)
+    except SystemExit as exc:
+        require(str(exc).startswith("FAIL:"), "mutation must fail closed")
+        return
+    raise SystemExit("FAIL: mutated B2 was accepted")
+
+
+def test_receipt_shape():
+    b2, gram = verify.load_b2()
+    require(gram[0][0] == 8 and len(b2) == 8 and len(b2[0]) == 96, "fixture shape")
+    require(verify.factored_frobenius_square([(1, [[1]], [[1]])]) == 1, "one-cell contraction")
+
+
+def main():
+    test_wrong_column_convention()
+    test_mutated_coefficient_breaks_square()
+    test_receipt_shape()
+    print("PASS_P104_INDEX_TENSOR_BRIDGE_TESTS " + json.dumps({
+        "groups": 3, "new_kappa": False}, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()