Prove an all-length balance law for native source-code controllers

research/native-controller-congruence/ARCHIVE.json

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+{
+  "path": "research/community-frontier1094-audit/selected-replay.tar.gz",
+  "sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6",
+  "members": {
+    "candidate/strict/global/base/providers/gauge44/CANONICAL-WORD.json.gz": {
+      "sha256": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+      "payload_sha256": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c"
+    },
+    "candidate/strict/global/base/providers/gauge44/LOCAL-PROGRAMS.json.gz": {
+      "sha256": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a",
+      "payload_sha256": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3"
+    },
+    "candidate/strict/global/base/split-centres/GLOBAL-TEMPLATE.json.gz": {
+      "sha256": "a179dad87651aba340a5a8ddbcd86a8e757cad87b8a1f8bad48106fbecd38518",
+      "payload_sha256": "8904bbbf46dfbf1c6df0e43479a23913fc59a410e879188112e88f16c850ede8"
+    }
+  }
+}

research/native-controller-congruence/PREDECESSOR.json

@@ -0,0 +1,19 @@
+{
+  "sources": [
+    {
+      "upstream_path": "research/native-source-codes/UNIT-TRANSFER-PROOF.md",
+      "local_path": "references/UNIT-TRANSFER-PROOF.md",
+      "commit": "bb29ea73ad9be9a0c3d53cdcb1d22b2ee9ffe42f",
+      "sha256": "2e83366264c108b2c9f371a13b379093813d99060b88858c640a7c403bbd3c3d",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1862"
+    },
+    {
+      "upstream_path": "research/native-source-codes/NOTICE.md",
+      "local_path": "references/NOTICE.md",
+      "commit": "bb29ea73ad9be9a0c3d53cdcb1d22b2ee9ffe42f",
+      "sha256": "d86f31a4c0bafd4271fe0c0e087a7fc1cd72d5b705e3739c4ba3e9241b7ba3f9",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1862"
+    }
+  ],
+  "executed_predecessor_code": false
+}

research/native-controller-congruence/RESULT.json

@@ -0,0 +1,57 @@
+{
+  "status": "PASS_NATIVE_CONTROLLER_CONGRUENCE",
+  "selected_source_query_sha256": "70055070e6f0465dcb9f99773769809f032043e7a1cba4f0c0fe5e5c365f0213",
+  "ports": 112,
+  "query_rank": 8,
+  "fixed_dimension": 96,
+  "minimal_polynomial_low_to_high": [
+    -1,
+    2,
+    -2,
+    1
+  ],
+  "active_powers_0_to_5": [
+    [
+      1,
+      0
+    ],
+    [
+      0,
+      1
+    ],
+    [
+      -1,
+      1
+    ],
+    [
+      -1,
+      0
+    ],
+    [
+      0,
+      -1
+    ],
+    [
+      1,
+      -1
+    ]
+  ],
+  "recipe": [
+    "F",
+    "B",
+    "F",
+    "B",
+    "F",
+    "B",
+    "F",
+    "B",
+    "F"
+  ],
+  "signed_winding": -1,
+  "required_winding_modulus": 6,
+  "changed_chart_pairs_checked": 4,
+  "changed_chart_defect_compression": "12 I_8",
+  "changed_chart_defect_rank_lower_bound": 8,
+  "selected_frontier_changed": false,
+  "coverage": "Source-column prefix and scalar-controller algebra; no native or all-size cold replay."
+}

research/native-controller-congruence/SOURCES.json

@@ -0,0 +1,36 @@
+{
+  "schema_version": 1,
+  "base_commit": "ecc75c79c22d909fd42aa68437eb77c4c1361835",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "input",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "06c96f5579bb67ed1b86d334e78fbed7da6945f1",
+      "sha256": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075"
+    },
+    {
+      "path": "docs/research/community-batch1099-review.md",
+      "usage": "input",
+      "git_blob": "6cb6ec061a071a06a2d18cd4dc3e9a2b05d28099",
+      "sha256": "7e76d2c38e5fce30587835b7251df1430488ae4dd372611ef69a3f03f476b6cb"
+    },
+    {
+      "path": "research/community-frontier1094-audit/SELECTED-SOURCE.json",
+      "usage": "input",
+      "git_blob": "6a75493790b4eff9c4a98051ef8b01d6aad0d5a8",
+      "sha256": "79b3de5db3dbcb9829789ba58e9e45758926031e2a7d80667a08429d369be53b"
+    },
+    {
+      "path": "research/community-frontier1094-audit/selected-replay.tar.gz",
+      "usage": "input",
+      "git_blob": "c24daf067f9c543421d89ca2eeaa4eb78a57fb6f",
+      "sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6"
+    }
+  ]
+}

research/native-controller-congruence/TASK.json

@@ -0,0 +1,124 @@
+{
+  "schema_version": 1,
+  "task_id": "centre-path-sharing",
+  "priority_revision": 3,
+  "base_commit": "ecc75c79c22d909fd42aa68437eb77c4c1361835",
+  "original_card": {
+    "id": "centre-path-sharing",
+    "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?",
+    "starting_points": [
+      "research/complex-local-word-ceiling/README.md",
+      "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.",
+      "Prove a lower bound on copied information per call for the selected decoder contract."
+    ],
+    "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...).",
+    "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": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).",
+    "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.",
+    "allowed_variations": [
+      "One sharing pattern across a fixed number of calls.",
+      "One reduced copied-total contract for the existing decoder.",
+      "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": [
+      "Removing copies without a replacement contract for the decoder's copied totals."
+    ],
+    "overlap_terms": [
+      "centre path",
+      "copied totals",
+      "private temporary",
+      "shared centre",
+      "batching"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "A determinant conservation law for arbitrary-length controllers of PR1862 identity transfers and whole-bank scalar bridges; independent changing-chart three-call rank obstruction.",
+  "scope_change_reason": "The first suggested coverage-law card overlaps Discussion1587 and PRs1825/1889/1900/1936. The second suggested centre-path card is narrowed to the native source-code controller missing from PR1862, a prerequisite for replacing the paid centre path. This proves an obstruction rather than proposing a centre charge.",
+  "bottleneck_link": "PR1862 is a native candidate for removing the 64-per-call centre path; a full-source-restored controller is still missing. Test the entire inherited scalar-controller class before attempting native admission.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after the exact controller law, source-bound selected-word fixture and independent controls; do not manufacture a kappa or cold-replay claim.",
+  "outcome": "negative-result",
+  "evidence": "README proves the unbounded determinant law and universal three-chart rank bound. RESULT.json binds exact selected source columns, the112-port chart decomposition, nine-stage orientation census and four actual chart-pair compressions. test_verify.py independently checks dense rational interleavings, inverses, legal signs/scales, six-call positive control and failing hypotheses.",
+  "author": "David Arias, with OpenAI Codex assistance",
+  "ai_assistance": "Substantial OpenAI Codex assistance in research, proof, implementation and independent agent checking; no independent human review.",
+  "open_questions": [
+    {
+      "question": "Can a code-balanced even controller make useful native frame progress?",
+      "why_it_matters": "The conservation law is necessary, not sufficient; useful progress could still realize the centre-path candidate.",
+      "first_step": "Construct a zero-winding bank word, then replay its typed native entry and exit frames.",
+      "blocked_by": "True inverse cancellations may undo the required coordinate advance."
+    },
+    {
+      "question": "Can one actual priced chart transition escape the normalized scalar controller algebra?",
+      "why_it_matters": "Physical port-dependent transports are excluded from the determinant theorem and may permit a real implementation.",
+      "first_step": "Derive a selected source transport and check full-source restoration, not only query transport.",
+      "blocked_by": "Nonuniform address maps and frame conversions must be implemented and charged."
+    },
+    {
+      "question": "Can the rank-eight three-chart defect be repaired affordably?",
+      "why_it_matters": "Every three-call exchange with the same R,K retains an observable eight-dimensional error.",
+      "first_step": "Factor D for a chosen pair of admissible charts and locate a legal native correction cut.",
+      "blocked_by": "Rank alone is not an implementation or a recursive child invoice."
+    }
+  ],
+  "selection": {
+    "seed": "5793b6b4f3a4e9b073ecf21eab76559f",
+    "track": "recursive-interfaces",
+    "scope_key": "184695337cedab03152e",
+    "track_override_reason": "User requested a significant structural contribution rather than marginal refinements."
+  },
+  "coordination": "Live read-only overlap checks; no public coordination post because the user-supplied AGENTS instructions restrict those without authorization.",
+  "optimistic_budget": "The existing centre-free relaxation is 2.80x the fixed-word primitive ceiling; this necessary controller test precedes any realized budget. No altered profile is priced or accepted.",
+  "overlap": {
+    "searched_at": "2026-10-14T15:33:43.867059+00:00",
+    "terms": [
+      "code winding",
+      "controller determinant",
+      "native source code",
+      "source-code controller",
+      "M-2I",
+      "three-chart"
+    ],
+    "coverage": {
+      "open_prs": {
+        "fetched_at": "2026-10-14T15:32:26.111961+00:00",
+        "complete_pagination": true,
+        "records": 538
+      },
+      "discussions": {
+        "fetched_at": "2026-10-14T15:33:43.779050+00:00",
+        "complete_pagination": true,
+        "records": 599
+      }
+    },
+    "warnings": [],
+    "limits": "Remote PR scope is open PRs including drafts. Closed work is searched through local READMEs, TASK metadata and ledger only. No code diffs or arbitrary package files are searched. Recheck relevant heads before submission.",
+    "remote_matches_for_final_terms": 0,
+    "closest_predecessors": [
+      {
+        "pr": 1862,
+        "head": "bb29ea73ad9be9a0c3d53cdcb1d22b2ee9ffe42f",
+        "delta": "Adds all-length scalar-controller conservation and arbitrary-chart FBF rank obstruction to valid native local words."
+      },
+      {
+        "pr": 1877,
+        "head": "6d455d2d71eb35ecf8e562711e5f719b994fe3f3",
+        "delta": "Identity-target source codes rather than original clean-J logger support/commutant."
+      }
+    ]
+  },
+  "submission_base": "ae95f60feec79897b153dba6459bb3f9fd4d7b8e"
+}

research/native-controller-congruence/VALIDATION.json

@@ -0,0 +1,55 @@
+{
+  "checked_at_utc": "2026-10-14T15:36:19.115360+00:00",
+  "python": "3.12.14 (main, Aug 25 2026, 13:50:33) [Clang 22.1.3 ]",
+  "platform": "macOS-27.0.1-arm64-arm-64bit",
+  "submission_base": "ae95f60feec79897b153dba6459bb3f9fd4d7b8e",
+  "commands": [
+    {
+      "argv": [
+        "python3.12",
+        "scripts/research_package.py",
+        "--package",
+        "research/native-controller-congruence"
+      ],
+      "exit_code": 0,
+      "stdout": "CHECK Exact source-column prefix, actual source-code split, four changed-chart rank witnesses, nine-call orientation census and recorded receipt.\n{\n  \"status\": \"PASS_NATIVE_CONTROLLER_CONGRUENCE\",\n  \"selected_source_query_sha256\": \"70055070e6f0465dcb9f99773769809f032043e7a1cba4f0c0fe5e5c365f0213\",\n  \"ports\": 112,\n  \"query_rank\": 8,\n  \"fixed_dimension\": 96,\n  \"minimal_polynomial_low_to_high\": [\n    -1,\n    2,\n    -2,\n    1\n  ],\n  \"active_powers_0_to_5\": [\n    [\n      1,\n      0\n    ],\n    [\n      0,\n      1\n    ],\n    [\n      -1,\n      1\n    ],\n    [\n      -1,\n      0\n    ],\n    [\n      0,\n      -1\n    ],\n    [\n      1,\n      -1\n    ]\n  ],\n  \"recipe\": [\n    \"F\",\n    \"B\",\n    \"F\",\n    \"B\",\n    \"F\",\n    \"B\",\n    \"F\",\n    \"B\",\n    \"F\"\n  ],\n  \"signed_winding\": -1,\n  \"required_winding_modulus\": 6,\n  \"changed_chart_pairs_checked\": 4,\n  \"changed_chart_defect_compression\": \"12 I_8\",\n  \"changed_chart_defect_rank_lower_bound\": 8,\n  \"selected_frontier_changed\": false,\n  \"coverage\": \"Source-column prefix and scalar-controller algebra; no native or all-size cold replay.\"\n}\nCHECK Independent dense rational determinant, arbitrary bank mixing/inverse controls, varying-chart defect and six-call positive control.\nPASS_REGISTERED_RESEARCH_PACKAGE research/native-controller-congruence outcome=negative-result\n",
+      "stderr": "............\n----------------------------------------------------------------------\nRan 12 tests in 1.958s\n\nOK\n"
+    },
+    {
+      "argv": [
+        "python3.12",
+        "-I",
+        "-O",
+        "-B",
+        "research/native-controller-congruence/verify.py"
+      ],
+      "exit_code": 0,
+      "stdout": "{\n  \"status\": \"PASS_NATIVE_CONTROLLER_CONGRUENCE\",\n  \"selected_source_query_sha256\": \"70055070e6f0465dcb9f99773769809f032043e7a1cba4f0c0fe5e5c365f0213\",\n  \"ports\": 112,\n  \"query_rank\": 8,\n  \"fixed_dimension\": 96,\n  \"minimal_polynomial_low_to_high\": [\n    -1,\n    2,\n    -2,\n    1\n  ],\n  \"active_powers_0_to_5\": [\n    [\n      1,\n      0\n    ],\n    [\n      0,\n      1\n    ],\n    [\n      -1,\n      1\n    ],\n    [\n      -1,\n      0\n    ],\n    [\n      0,\n      -1\n    ],\n    [\n      1,\n      -1\n    ]\n  ],\n  \"recipe\": [\n    \"F\",\n    \"B\",\n    \"F\",\n    \"B\",\n    \"F\",\n    \"B\",\n    \"F\",\n    \"B\",\n    \"F\"\n  ],\n  \"signed_winding\": -1,\n  \"required_winding_modulus\": 6,\n  \"changed_chart_pairs_checked\": 4,\n  \"changed_chart_defect_compression\": \"12 I_8\",\n  \"changed_chart_defect_rank_lower_bound\": 8,\n  \"selected_frontier_changed\": false,\n  \"coverage\": \"Source-column prefix and scalar-controller algebra; no native or all-size cold replay.\"\n}\n",
+      "stderr": ""
+    },
+    {
+      "argv": [
+        "python3.12",
+        "-B",
+        "-m",
+        "unittest",
+        "discover",
+        "-s",
+        "tests",
+        "-p",
+        "test_research_*.py"
+      ],
+      "exit_code": 0,
+      "stdout": "CHECK Scoped test fixture\nPASS_REGISTERED_RESEARCH_PACKAGE research/fixture outcome=partial\nCHECK Scoped test fixture\n",
+      "stderr": "...........................Traceback (most recent call last):\n  File \"<string>\", line 1, in <module>\nAssertionError: invalid fixture\nTraceback (most recent call last):\n  File \"<string>\", line 1, in <module>\nAssertionError: invalid fixture\n.........sss......\n----------------------------------------------------------------------\nRan 45 tests in 4.608s\n\nOK (skipped=3)\n"
+    }
+  ],
+  "unrun": [
+    "Selected complete make frontier1094-verify",
+    "Native endpoint or compiler replay",
+    "Full multiplication theorem or proof-assistant verification"
+  ],
+  "review": "Two separate agents checked proof scope and actual source extraction; no independent human review.",
+  "interpreter_note": "Commands use the portable python3.12 name for the recorded CPython 3.12.14 bundled runtime.",
+  "expected_negative_test_stderr": "The two invalid-fixture AssertionError tracebacks in the research-workflow suite are expected failure-control subprocesses; the suite exits zero."
+}

research/native-controller-congruence/VERIFY.json

@@ -0,0 +1,35 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "certificates/selected-result.json",
+    "docs/research/community-batch1099-review.md",
+    "research/community-frontier1094-audit/SELECTED-SOURCE.json",
+    "research/community-frontier1094-audit/selected-replay.tar.gz"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Exact source-column prefix, actual source-code split, four changed-chart rank witnesses, nine-call orientation census and recorded receipt."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/test_verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Independent dense rational determinant, arbitrary bank mixing/inverse controls, varying-chart defect and six-call positive control."
+    }
+  ]
+}