Independent audit: exhaustive full-query support hypotheses

research/source-query-finite-field-audit/EXTERNAL-SOURCES.json

@@ -0,0 +1,18 @@
+[
+  {
+    "pr": 1877,
+    "commit": "4d9fa6016682c910be06e55b1c974d53052aee76",
+    "path": "research/sourcecode-commutant/README.md",
+    "local": "references/pr1877-README.md",
+    "git_blob": "ceb230b0493d9f6ab143b4b3665f086effe6aef1",
+    "sha256": "3fb74b799b467c7ef80505e5a25ab969b12d9e6b71bdcfab0791fe2b8359a686"
+  },
+  {
+    "pr": 1877,
+    "commit": "4d9fa6016682c910be06e55b1c974d53052aee76",
+    "path": "research/sourcecode-commutant/PROOF.md",
+    "local": "references/pr1877-PROOF.md",
+    "git_blob": "cd1362b7da35337224c9dcd1e5d2cf23a55b7117",
+    "sha256": "476eeab29a1af705ecffd7ba0d36c3ed305db7fdb57df0b861edf05111df6db7"
+  }
+]

research/source-query-finite-field-audit/OVERLAP.json

@@ -0,0 +1,23 @@
+{
+  "fetched_at": "2026-10-14T12:56:55.916545+00:00",
+  "open_prs": 535,
+  "discussion_records": 517,
+  "complete_pagination": true,
+  "scope": "PR bodies and Discussion records; not all code diffs or literature.",
+  "predecessor": {
+    "kind": "pr",
+    "number": 1877,
+    "title": "Source-query encoder support tradeoff and fixed-frame obstruction",
+    "body": "An invertible source encoder that logs the complete eight-coordinate query cannot make both endpoints sparse: its changed source fields and required target corrections together cover all **112 ports**. Each support also has at least eight ports. This is a scoped structural result for PR1862's clean-J interface, **not a new supplier or kappa**.\n\nFor Delta=G-I and H=(I-KR)Delta, the logger condition LG=R gives RDelta=(R-L)G. Its full row rank, together with nonzero K rows, proves the support cover. The statement also allows arbitrary finite address-linear encoders. Three explicit counterexamples show why the hypotheses are needed, and a valid three-port toy attains the cover.\n\nFor PR1862's fixed response Z, LZ=I makes the complete logger unique. It cannot commute with the unchanged line or specified output frames; two exact nonzero minors witness that obstruction for every positive tensor power. Changed/conjugated codes, paid transitions and carrying work through later native operations remain open. Endpoint support is not a universal native-child cost; the 112/120 rowwise figures in the report are conditional comparators only.\n\nValidation at `4d9fa6016682c910be06e55b1c974d53052aee76`:\n\n- [Dedicated Linux CI](https://github.com/chafreaky/integer-mult-bounds/actions/runs/38566908597) passes on Python 3.11 and 3.14.\n- Local Python 3.11.15, 3.14.8 and a read-only source export run without Git/private dependencies; all six committed/local/Linux receipts are byte-identical.\n- Source-derived scalar-prefix replay, 512-character census, two rational minors, four mutation controls and three missing-premise examples pass. No pending PR implementation is imported.\n\nOnly the new package and its dedicated workflow change. No full native supplier, global routing, hosting/precision or multiplication-theorem audit is claimed; other repository workflows are separate.\n\nCredit aliromman's [PR1862](https://github.com/CrocSwap/integer-mult-bounds/pull/1862) for the valid local encoder and stated interface, plus the pinned PR1042/PR1094 archive and retained E8/gauge44/native lineage. New proof and checker prepared for Chafik Boukhalfa with substantial OpenAI Codex assistance; no independent human review or formal proof assistant.\n",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1877",
+    "head": "4d9fa6016682c910be06e55b1c974d53052aee76",
+    "updated_at": "2026-10-14T12:53:23Z",
+    "draft": false,
+    "state": "open"
+  },
+  "prior_batches_checked": [
+    "integer-mult-20-contributions",
+    "integer-mult-20-rounds-20261014"
+  ],
+  "added_value": "Independent endpoint-support theorem audit over exhaustive small finite-field full-query encoders with rank and invertibility premise removal controls; rational sharp toy and source hypotheses separately pinned."
+}

research/source-query-finite-field-audit/README.md

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+# Exhaustive independent audit of full-query endpoint support
+
+This audit independently stress-tests the algebraic support theorem in Chafik Boukhalfa / @chafreaky's PR1877. It adds a complete small finite-field census, independently found missing-premise witnesses and a rational sharp example. It does not re-audit the 112-port physical Fourier-frame obstruction or claim that finite fields certify complex rank.
+
+## Statement being audited
+
+Let L,R be r-by-n matrices, K be n-by-r, and let G be invertible with LG=R. Put Delta=G-I, J=I-KR, H=J Delta. If rank(R-L)=r and every K row is nonzero, the supports of rows of Delta and H cover all n ports. Indeed
+
+    R Delta=(R-L)G
+
+has full row rank. If Delta_i=H_i=0, then K_i R Delta=0, contradicting the nonzero row K_i. Further L Delta=R-L gives rank(Delta)>=r. The separate assertion rank(H)>=r needs J invertible; it does not follow from the support cover alone. Right-multiplication by G^-1 shows that G^-1-I has exactly the same nonzero row support as Delta. These arguments work over any field. They are the credited predecessor proof, independently checked here, not inferred from the census.
+
+## Complete finite domain and new evidence
+
+Over GF(2), enumerate all 168 invertible 3x3 G, every r-by3 L for r=1 and2, and every 3-by-r K with no zero row. Set R=LG, then retain rank(R-L)=r. This exhausts 1008 rank-one and 117936 rank-two full-query cases. All satisfy the cover. For invertible J, the 432 rank-one and 40560 rank-two cases also satisfy both individual rank floors. The exact attainable (source support,target support) pairs are recorded by the verifier; these are finite GF(2) spectra, not the 112-port complex spectrum.
+
+The checker independently searches the complete 3-port rank-one matrix domain for witnesses violating the cover after removing exactly one of G invertibility, full rank of R-L, or nonzero K rows, while retaining invertible J. It requires nonzero query/read matrices and at least one nonzero K row, avoiding empty-query controls. A separate actual witness has full hypotheses for the cover but singular J and H=0, demonstrating why the target rank conclusion needs that additional premise. The predecessor's PROOF.md already states this premise; no error in it is alleged.
+
+A separately multiplied rational sharp example is
+
+    L=[1,0,0], R=[1,1,0], K=[1,1,1]^T,
+    G=[[1,1,0],[0,1,0],[0,0,1]].
+
+Delta has only row0=e1 and H has rows1,2=-e1, so the support sizes 1 and2 attain total 3. RK=2 ensures J invertible over Q. This is not a lift of a finite-field rank claim. It independently tests the original characteristic-zero algebra.
+
+## Reproduce and limitations
+
+    python3.12 scripts/research_package.py --package research/source-query-finite-field-audit
+
+Read-only standard-library Python; explicit checks remain active under -O. The unchanged PR1877 README and PROOF are pinned by SHA256 and Git blob; no predecessor executable is imported. The exact head and complete overlap snapshot are recorded. This contribution is intentionally an independent proof-hypothesis audit. The actual112-port source instance, fixed-frame minors, native access costs, carrying the encoder through later work, hosting, precision, cold replay and all-size theorem remain outside this audit. No new supplier or kappa.
+
+## Source-head refresh
+
+Before publication, PR1877 advanced from the audited head `4d9fa6016682c910be06e55b1c974d53052aee76` to `6d455d2d71eb35ecf8e562711e5f719b994fe3f3`. The first 2386 bytes of PROOF.md, through “The verifier checks all four examples.”, are identical and include the audited algebraic theorem and hypotheses. SOURCE-REFRESH.json records both full-file Git blob and SHA256 hashes plus the identical section hash. The newer actual 112-port 8+104 sharp construction, generalized fixed-read frame obstruction and additional mutation controls belong to the credited predecessor and were inspected for scope, not independently verified here. The original immutable source pins remain the inputs to this audit.
+
+## Open next questions
+
+Can a paid chart transition or changed response space realize a complete useful source encoder? First pin an actual pair of native charts and price transport/restoration. The support theorem alone supplies neither a universal native-cost lower bound nor a construction.
+
+## Credit
+
+Chafik Boukhalfa / @chafreaky, PR1877, supplies the support theorem and source/frame proof; @aliromman /PR1862 the valid source encoder. PR1042/1094, E8/gauge44/native lineage retains its attribution in the pinned predecessor. New exhaustive audit and exact controls prepared for woklerx with substantial OpenAI Codex assistance, Apache-2.0. No independent human or formal proof-assistant review.

research/source-query-finite-field-audit/RESULT.json

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+{"GL3": 168, "exhaustive_rows": [{"endpoint_support_pairs": [[1, 2], [2, 1], [2, 2], [2, 3], [3, 2], [3, 3]], "full_query_cases": 1008, "invertible_J_cases": 432, "query_rank": 1}, {"endpoint_support_pairs": [[2, 2], [2, 3], [3, 2], [3, 3]], "full_query_cases": 117936, "invertible_J_cases": 40560, "query_rank": 2}], "missing_J_control": {"G": [2, 1, 7], "H": [0, 0, 0], "K": [1, 1, 1], "L": [1], "R": [2], "r": 1}, "no_new_kappa": true, "premise_controls": {"full_rank_difference": {"Delta": [0, 0, 0], "G": [1, 2, 4], "H": [0, 0, 0], "K": [1, 1, 1], "L": [3], "R": [3]}, "invertible_G": {"Delta": [1, 0, 0], "G": [0, 2, 4], "H": [1, 0, 0], "K": [1, 1, 1], "L": [7], "R": [6]}, "nonzero_K_rows": {"Delta": [0, 0, 1], "G": [1, 2, 5], "H": [0, 1, 1], "K": [0, 1, 0], "L": [4], "R": [5]}}, "rational_sharp_support": [1, 2], "scope": "GF2 exhaustive stress test plus separately proved field-independent cover; no finite-field inference about physical frames", "status": "PASS_SOURCE_QUERY_FINITE_FIELD_AUDIT"}

research/source-query-finite-field-audit/SOURCE-REFRESH.json

@@ -0,0 +1,54 @@
+{
+  "source_pr": 1877,
+  "audited_head": "4d9fa6016682c910be06e55b1c974d53052aee76",
+  "observed_head": "6d455d2d71eb35ecf8e562711e5f719b994fe3f3",
+  "inspected_at_utc": "2026-10-14T13:26:11.255Z",
+  "evidence": "Git objects fetched from origin pull/1877/head; exact source files read with git show.",
+  "files": [
+    {
+      "path": "research/sourcecode-commutant/README.md",
+      "audited": {
+        "git_blob": "ceb230b0493d9f6ab143b4b3665f086effe6aef1",
+        "sha256": "3fb74b799b467c7ef80505e5a25ab969b12d9e6b71bdcfab0791fe2b8359a686",
+        "bytes": 5602
+      },
+      "observed": {
+        "git_blob": "9d236651529a326861d258c741c485f1b8c06232",
+        "sha256": "afc65ab6a27b93c3a7ad6ade6c8694f7d0f6777fd1cda085cdbc381916671850",
+        "bytes": 6160
+      }
+    },
+    {
+      "path": "research/sourcecode-commutant/PROOF.md",
+      "audited": {
+        "git_blob": "cd1362b7da35337224c9dcd1e5d2cf23a55b7117",
+        "sha256": "476eeab29a1af705ecffd7ba0d36c3ed305db7fdb57df0b861edf05111df6db7",
+        "bytes": 7832,
+        "audited_prefix_sha256": "214d133bf3e6624a45a3c920aab38eb7437b811249e70c4e44aa46d829e251e0",
+        "audited_prefix_bytes": 2386
+      },
+      "observed": {
+        "git_blob": "7c1a95e6fd50634c59051908b1f0d6eadcc48513",
+        "sha256": "e91bc6879224cc06ea463d2a92a57b8d83c3b20d0c7cdf9980a3fd542bf20a5c",
+        "bytes": 9707,
+        "audited_prefix_sha256": "214d133bf3e6624a45a3c920aab38eb7437b811249e70c4e44aa46d829e251e0",
+        "audited_prefix_bytes": 2386
+      }
+    }
+  ],
+  "audited_section": {
+    "path": "research/sourcecode-commutant/PROOF.md",
+    "start": "Beginning of file",
+    "end_inclusive": "The verifier checks all four examples.",
+    "bytes": 2386,
+    "sha256": "214d133bf3e6624a45a3c920aab38eb7437b811249e70c4e44aa46d829e251e0",
+    "unchanged": true
+  },
+  "conclusion": "The algebraic endpoint-support theorem and its hypotheses audited here are unchanged. Retain original exact source pins for reproducibility.",
+  "new_source_extensions_outside_this_audit": [
+    "Actual 112-port sharp 8-source plus 104-target encoder construction",
+    "Fixed eight-port read obstruction generalized beyond the particular logger Z",
+    "Additional source-frame mutation controls"
+  ],
+  "limitations": "This refresh establishes unchanged theorem text, not independent verification of the new source-frame extensions."
+}

research/source-query-finite-field-audit/SOURCES.json

@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
+  "base_commit": "0b1cccf86e2f5132ed286a26ef0a681a495740ea",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "06c96f5579bb67ed1b86d334e78fbed7da6945f1",
+      "sha256": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075"
+    }
+  ]
+}

research/source-query-finite-field-audit/TASK.json

@@ -0,0 +1,68 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-rank-shape-decoder",
+  "priority_revision": 3,
+  "base_commit": "0b1cccf86e2f5132ed286a26ef0a681a495740ea",
+  "original_card": {
+    "id": "complex-rank-shape-decoder",
+    "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?",
+    "starting_points": [
+      "research/complex-local-word-ceiling/README.md",
+      "research/complex-decoder-field-extension-seed44/README.md",
+      "research/complex-frame-pair-decoders/README.md"
+    ],
+    "methods": [
+      "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.",
+      "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration."
+    ],
+    "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/complex-local-word-ceiling/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+      "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+      "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).",
+    "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.",
+    "allowed_variations": [
+      "One masked, overcomplete or block decoder family with exact labels and supports.",
+      "A scoped lower bound on effective rank for one alphabet.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Repacking idle remainders of an unchanged word (covered by the packing ceiling).",
+      "Repeating the eight-term all-pairs search inside its proved scope."
+    ],
+    "overlap_terms": [
+      "rank shape",
+      "block climb",
+      "masked decoder",
+      "overcomplete",
+      "effective rank"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Independent endpoint-support theorem audit over exhaustive small finite-field full-query encoders with rank and invertibility premise removal controls; rational sharp toy and source hypotheses separately pinned.",
+  "scope_change_reason": "Fresh overlap found a directly relevant pending result. Deliberate independently implemented audit adds distinct finite evidence and controls; it does not assert a new physical supplier or repeat the predecessor as an original theorem.",
+  "bottleneck_link": "Strengthens independently reviewable evidence for a named mathematical boundary; no new kappa or complete supplier claimed.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after the declared exact audit domain, premise controls, optimized replay and source validation.",
+  "outcome": "completed",
+  "evidence": "README.md and deterministic verify.py output",
+  "author": "woklerx with substantial OpenAI Codex assistance",
+  "ai_assistance": "OpenAI Codex derived and implemented this independent audit; no independent human review.",
+  "open_questions": [
+    {
+      "question": "Can a paid chart transition or changed response space give a useful complete source encoder?",
+      "why_it_matters": "The endpoint-support theorem is not a universal native-cost bound.",
+      "first_step": "Pin two native charts and price transport and restoration before assembly.",
+      "blocked_by": "No source-bound complete physical transition or precision/hosting invoice is supplied."
+    }
+  ],
+  "claim_url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1163#discussioncomment-18924424",
+  "selection_nonce": "8251907335fc151d2de2de0b56909bd2"
+}

research/source-query-finite-field-audit/VERIFY.json

@@ -0,0 +1,20 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Exact independent mathematical audit, positive fixtures, premise-removal controls, immutable source pins."
+    }
+  ]
+}