Bound endpoint-preserving repairs of PR4633’s BIT quotient (no new κ)

research/pr4633-contract-audit/OVERLAP.json

@@ -0,0 +1,24 @@
+{
+  "checked_after_requested_wait": true,
+  "checked_at_utc": "2026-10-22T14:08:51Z",
+  "coverage": {
+    "recent_prs_all_states": 1000,
+    "recent_discussions": 30,
+    "comments_per_discussion": 20,
+    "latest_handoff_comments": 30,
+    "additional_targeted_pr_search": "repo:CrocSwap/integer-mult-bounds is:pr 4633"
+  },
+  "related": [
+    {
+      "pr": 4636,
+      "head": "b0a325a3e312b7c5ebceb420de4b8cb13181f43e",
+      "scope": "Broader negative audit, rational mismatch, endpoint failures, mutations and full scans. README and both short verifiers inspected."
+    },
+    {
+      "pr": 4642,
+      "head": "d8c59e36a8efb301f0298871218cfe00f4e043f7",
+      "scope": "Complex re-padding ledger and price; body and file inventory inspected."
+    }
+  ],
+  "publication_scope": "636-frame monotone contraction obstruction, global padded-hyperplane dimension obstruction, and failed endpoint-preserving expansion. No new kappa. No global novelty claim outside the recorded coverage."
+}

research/pr4633-contract-audit/README.md

@@ -0,0 +1,195 @@
+# Endpoint-preserving repair bounds for PR4633
+
+**The submitted quotient screens do not establish a new κ.** This audit reviews
+PR4633 at `b390d64abfcdba1a3816b86fc763cbc95d43c12c` and keeps every submitted
+package unchanged. The GitHub headline describes kernel 150 and BIT 0.012401086416;
+the checked commit actually ships kernel span{150,102,255} and BIT screen
+0.032249423394893. Both variants are checked here, along with the stacked complex
+kernel-153 artifact. This is a finite audit, not a full multiplication theorem.
+
+The publication package is based on canonical main and vendors six exact inputs
+from the reviewed PR under `vendor/`; `VENDORED.json` records their original
+paths, commit, Git blobs and SHA256 hashes. The vendored Python files are
+unchanged. The audit binds the copied builder's `SOURCE` path to the original
+PR589 source directory before calling it. `SOURCES.json` pins the remaining
+inputs from main. Every audit input is available in the publication checkout.
+
+## Overlap and the contribution here
+
+The publication overlap check found [PR4636](https://github.com/CrocSwap/integer-mult-bounds/pull/4636)
+at `b0a325a3e312b7c5ebceb420de4b8cb13181f43e`, which already supplies a broader
+negative audit: rational-field counterexamples, endpoint failures, verifier
+false positives and full scan discrepancies. Those objections are prior
+concurrent findings; the endpoint and field checks below provide reproducible
+context for this package's repair tests.
+
+This package contributes the exact **636-frame contraction obstruction**, the
+**general hyperplane-dimension obstruction for global full-image padding**, and
+the **endpoint-preserving expansion candidate and its failed price**. PR4636's
+README and both short verifiers were inspected at that head; no equivalent
+repair-bound certificate was found in that scope.
+[PR4642](https://github.com/CrocSwap/integer-mult-bounds/pull/4642), at
+`d8c59e36a8efb301f0298871218cfe00f4e043f7`, independently audits complex re-padding
+and its invoice. Its ledger corrections are separate from the repair bounds
+here. `OVERLAP.json` records the bounded search coverage and exact related heads.
+
+## What reproduces
+
+The submitted BIT and complex verifiers reproduce their committed RESULT.json
+files exactly. Their metadata/source-pin checks also pass. Logical maps, owned
+cleanup and replay against the artifacts' own endpoints are consistent. Those
+checks do not verify that the resulting physical local calls are the operators
+used by the controller. `PASS` below means the audit detects that mismatch.
+
+The controller's `replay_events` multiplies both fields of every LOCAL call by
+the same stage symbol. Its `inventories` then credits all main outputs using
+block 7 (BIT) or block 8 (complex), retaining a rank-one central factor. The
+actual source contracts have X entrance P, X final full ambient, Y entrance
+zero, Y final H, with P a line complementary to H. The original sources pass
+these checks on every port. Checking these dimensions and complements allows
+chart changes; it does not require equality of source frame labels.
+
+## Finding 1: neither quotient satisfies its priced main-port contract
+
+| word | main widths | ports meeting the invoiced contract |
+| --- | --- | ---: |
+| rational BIT source | {7:222} | 111/111 |
+| BIT kernel 150 | {6:107,7:105,8:10} | 0/111 |
+| BIT kernel span{150,102,255} | {4:103,7:70,8:49} | 0/111 |
+| complex source | {8:224} | 112/112 |
+| complex kernel 153 | {7:168,8:56} | 0/112 |
+
+For complex kernel 153, 56 ports have widths (7,7) and a surviving central
+complement; the other 56 have widths (7,8) and X entrance contained in Y final.
+Neither type is the block-8 call priced by the invoice.
+
+There is a general obstruction for the BIT builder's global full-image padding.
+Let h be the original ambient dimension and K a nonzero k-dimensional kernel.
+For a source hyperplane H, dim(phi(H)) is h-k or h-k-1. In the former case the
+image is the full quotient and the builder re-pads it to dimension h. In the
+latter case it remains dimension h-k-1 <= h-2. Thus **no Y terminal can have the
+required dimension h-1**, for any nonzero kernel in this construction. This
+rules out repairing the existing priced BIT contract by searching more kernels.
+It does not rule out a new controller with different operator contracts.
+
+The correct BIT rank-mass decomposition is:
+
+| word | paid mass | main mass | helper mass | owned COPY mass |
+| --- | ---: | ---: | ---: | ---: |
+| source | 5129 | 1554 | 3512 | 63 |
+| kernel 150 | 5023 | 1457 | 3512 | 54 |
+| submitted three-dimensional kernel | 4842 | 1294 | 3512 | 36 |
+
+Paid mass equals main + helper + COPY mass. Relative to the source, the
+one-dimensional saving is **97 removed main ranks + 9 COPY ranks**, totaling
+106. The submitted saving is **260 main + 27 COPY**, totaling 287. The increase
+in the unchanged invoice's surplus is 18 times these totals. This slightly
+corrects the earlier review's attribution of all 106 ranks to mains; the
+contract objection still applies. No corrected complete invoice is asserted.
+
+## Finding 2: BIT's GF(2) conversion changes the source geometry
+
+The BIT source stores rational E8 frames. Its `frame_projectors` constructs
+exact rational orthogonal projectors from B using B^t (B B^t)^-1 B. The quotient
+builder instead reduces A's coefficients modulo 2 and takes a GF(2) nullspace.
+These operations do not preserve the required incidence/orthogonality data.
+
+An explicit witness is port 8:
+
+```
+u = (0,1,1,0,1,0,0,1)
+H = {x : u dot x = 0}
+u dot u = 4 over Q, but 0 modulo 2.
+```
+
+The rational entrance line is complementary to its terminal H. Its reduced
+binary line is inside the reduced H. Even before applying any quotient, this
+conversion leaves only 8 of 111 complementary pairs; the 111 distinct rational
+entrance lines reduce to 22 binary lines. Matching every frame dimension and
+recovering the old bill are insufficient calibration: those tests miss this
+change in incidence. The source itself is not accused of this error.
+
+## Repair attempts and what they establish
+
+1. **Restore the source geometry through a monotone contraction.** For each
+   rational source frame S, compute the span of all source entrance lines
+   contained in S. This span equals S for **all 636 frames**, checked with exact
+   rational elimination and A/B kernel-image consistency. If a framewise map F
+   is monotone, fixes those entrance lines, and satisfies F(S) contained in S,
+   then S is contained in F(S), hence F(S)=S. This entire contraction repair
+   class therefore returns the original profile and screen 0.003464248972024.
+   The lemma does not cover arbitrary resynthesis or role-dependent retiming.
+2. **Expand frames while preserving all endpoints.** Replace S by the
+   intersection of all source Y hyperplanes containing S (full ambient if
+   there are none). This is a monotone expansion; all 661 start/final endpoints
+   remain exactly fixed. It changes 36 frames and replays both logical
+   directions. Its paid mass rises to 5138, surplus falls to 591, and the same
+   screen drops to approximately 0.002750034070107. It is rejected as a repair
+   before native lowering; native realizability is not claimed.
+
+These checks supply no profitable repair of PR4633. A valid replacement would
+need a different physical construction/controller and a fresh complete invoice.
+
+## Finding 3: the outer admission is also missing
+
+The two-constraint roots are supplier screens. They do not supply the ordinary
+BIT conversion and full outer chain. The pinned query-thinned verifier separately
+uses before/after cover savings, an old atom, an admitted BIT saving, and all
+strict outer predicates. The submitted packages do not replace that chain or
+replay it at a larger value. Increasing declared constants would require proof
+of their hypotheses, including a supplier implementing the actual LOCAL operator.
+The large outer value in the GitHub title/body is therefore unsupported as well.
+
+## Reproduce
+
+From the repository root, with CPython 3.12 and only its standard library:
+
+```sh
+python3 -I -B research/pr4633-contract-audit/verify.py
+python3 -B scripts/research_package.py --package research/pr4633-contract-audit
+```
+
+The first command authenticates 19 inputs, checks the original source as a
+positive control, recomputes both BIT logical replays and their contracts,
+checks the stacked complex source/quotient geometry, proves the bounded
+contraction obstruction, prices the expansion, and rejects five mutations:
+wrong MOVE rank, dependent basis, changed source entrance, omitted source ADD,
+and spoofed width metadata. The expected marker is
+`PASS_PR4633_CONTRACT_AUDIT_NO_NEW_KAPPA`.
+
+`RESULT.json` is the deterministic audit receipt. Float roots are labelled as
+screens; only ranks, counts, incidences and source pins are exact claims.
+The full submitted complex logical replay was independently rerun during the
+review; this audit's registered command reconstructs its source and checks its
+endpoint geometry, without repeating its full physical lowering.
+
+## Open next questions
+
+- Can an alternative local word preserve the invoiced operator while reducing
+  the paid moment? Start with the original rational BIT frames or original
+  complex endpoints and check them independently before pricing. The present
+  global quotient with full-image padding cannot do this.
+- Can a different controller use the quotient operators? Derive each actual
+  main operator, its central factor and stage ranks, then factor the controller
+  and reprice all outputs and idles. The existing block-7/block-8 invoice cannot
+  be reused. This is a new construction, not a literal-constant repair.
+- Any eventual supplier improvement still needs ordinary BIT conversion and
+  the complete outer admission with strict predicates and sound source pins.
+
+## Credit
+
+DaysSky supplied both quotient packages (#4633 and #4629), built on
+DreamingOfClouds's PR589 BIT word and the retained eumemic lineage, and Cinna
+Davis's PR4470 complex construction on the credited zxv supplier work. The
+endpoint concern was raised by pinterbanget (#4604), the quotient-kernel census
+by Nick Petalas (#4627), and the per-port controller-contract audit by Rohan
+Arun in his PR4633 comment. This audit independently checks those concerns,
+adds the rational/GF(2) witness, covers the actual three-dimensional artifact,
+corrects the COPY/main rank attribution, and bounds two repair routes. The
+broader independent audit in #4636 already establishes the rational-field,
+endpoint and verifier objections; this package's publication focuses on the
+complementary repair bounds described above.
+
+Prepared for Cinna Davis with substantial OpenAI Codex assistance. Apache-2.0.
+This package changes no selected-result record and claims no new κ. Its local
+checks and publication status are separate from maintainer acceptance.

research/pr4633-contract-audit/RESULT.json

@@ -0,0 +1,110 @@
+{
+  "authenticated_inputs": 19,
+  "bit_field_mismatch_witness": {
+    "port": 8,
+    "source_dot_mod_2": 0,
+    "source_dot_over_Q": 4
+  },
+  "bit_gf2_reduction_before_quotient": {
+    "accepted": 8,
+    "intersection_dimensions": {
+      "0": 8,
+      "1": 103
+    },
+    "main_widths": {
+      "7": 222
+    },
+    "rejected": 103
+  },
+  "bit_quotients": {
+    "headline_kernel_150": {
+      "accepted": 0,
+      "copy_mass": 54,
+      "helper_mass": 3512,
+      "intersection_dimensions": {
+        "0": 10,
+        "1": 101
+      },
+      "kernel": [
+        150
+      ],
+      "logical_replay": true,
+      "main_mass": 1457,
+      "main_widths": {
+        "6": 107,
+        "7": 105,
+        "8": 10
+      },
+      "mispriced_float_screen": 0.01240108641606724,
+      "mispriced_surplus": 2661,
+      "paid_mass": 5023,
+      "rejected": 111
+    },
+    "submitted_kernel_150_102_255": {
+      "accepted": 0,
+      "copy_mass": 36,
+      "helper_mass": 3512,
+      "intersection_dimensions": {
+        "0": 41,
+        "1": 70
+      },
+      "kernel": [
+        150,
+        102,
+        255
+      ],
+      "logical_replay": true,
+      "main_mass": 1294,
+      "main_widths": {
+        "4": 103,
+        "7": 70,
+        "8": 49
+      },
+      "mispriced_float_screen": 0.03224942339489283,
+      "mispriced_surplus": 5919,
+      "paid_mass": 4842,
+      "rejected": 111
+    }
+  },
+  "bit_rational_frames_forced_by_fixed_lines": 636,
+  "bit_source_ports_accepted": 111,
+  "complex_quotient": {
+    "accepted": 0,
+    "intersection_dimensions": {
+      "0": 56,
+      "1": 56
+    },
+    "main_widths": {
+      "7": 168,
+      "8": 56
+    },
+    "rejected": 112
+  },
+  "complex_source": {
+    "accepted": 112,
+    "intersection_dimensions": {
+      "0": 112
+    },
+    "main_widths": {
+      "8": 224
+    },
+    "rejected": 0
+  },
+  "expansion_repair_screen_only": {
+    "changed_frames": 36,
+    "float_screen": 0.0027500340701070436,
+    "native_lowering_checked": false,
+    "paid_mass": 5138,
+    "surplus": 591
+  },
+  "negative_controls": {
+    "changed_source_entrance": true,
+    "dependent_frame_basis": true,
+    "omitted_source_add": true,
+    "spoofed_main_width_metadata": true,
+    "wrong_move_rank": true
+  },
+  "reviewed_head": "b390d64abfcdba1a3816b86fc763cbc95d43c12c",
+  "scope": "Finite endpoint and geometry audit; no new kappa, native realization or outer admission.",
+  "status": "PASS_PR4633_CONTRACT_AUDIT_NO_NEW_KAPPA"
+}