Add R439 shear rebase profile audit

.github/workflows/community-batch952.yml

@@ -33,12 +33,29 @@ jobs:
         run: |
           sudo apt-get update
           sudo apt-get install -y --no-install-recommends g++ libboost-dev
+      - name: Checkout the historical verifier's pinned source snapshot
+        uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          repository: CrocSwap/integer-mult-bounds
+          ref: 47481c89fd30a43f8f882eb4b391e89c29273fd0
+          path: central-factor-historical-source
+          persist-credentials: false
+          sparse-checkout: |
+            certificates
+            docs/research
+            notes
+            scripts
+            tests
+            upstream
       - name: Scoped bounds and historical verifier
         run: |
           python -B research/owner-profile-uniform/reproduce.py
           python -B research/p112-single-lift/verify.py
           python -B research/p112-single-lift/independent_check.py
           python -B research/r439-copy-path-sharing-barrier/verify.py
+          mkdir -p central-factor-historical-source/research
+          cp -a research/central-factor-packed central-factor-historical-source/research/
+          cd central-factor-historical-source
           python -B research/central-factor-packed/verify.py
           python -B research/central-factor-packed/test_packed.py
           python -O -B research/central-factor-packed/test_packed.py

research/r439-shear-rebase-236-profile/README.md

@@ -0,0 +1,116 @@
+# Rebase the PR1047 helper shear onto the 236-star R439 word
+
+**Scoped profile obstruction; no κ claim.** The exact PR1047 shear is legal on
+the seed-01 degree-two candidate, but on that changed middle matrix it saves 3
+ADDs, not the 14 ADDs it saved on its original PR967 parent. The chronological
+frame paths and paid child histogram are identical before and after the rebase.
+
+## Question and result
+
+Does PR1047's helper transvection `(destination, source) = (242, 19)` change the
+paid child histogram when applied to the 11,500-ADD, 236-helper-edge candidate
+from `research/r439-bsection-stars-seed01`?
+
+The source-pinned rebase changes 13 of the 111 middle target rows. In the
+candidate's exact matrix, column 19 has weight 16, column 242 has weight 13,
+and their overlap has size 9. The transformed column 19 has weight
+`16 + 13 - 2*9 = 11`; after charging the preparation and restoration gates,
+the net saving is `16 - 11 - 2 = 3` ADDs.
+
+| Exact bill | Before rebase | After rebase |
+|---|---:|---:|
+| Complete native ADDs | 11,500 | 11,497 |
+| D ADDs | 5,548 | 5,545 |
+| Forward positive bound F | 25,717 | 25,717 |
+| Reverse positive bound B | 5,911,840 | 5,913,026 |
+| Local / nine-stage guard bits | 95 / 182 | 95 / 182 |
+
+The paid histogram is unchanged:
+
+```text
+{1:1323, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:19}
+```
+
+Its rank mass remains 5,129, including the same nine rank-seven COPY records.
+The exact profile calculation counts each register's consecutive frame-rank
+increments and the paid COPY ranks. The edit adds no frame movement and does not
+change any COPY/ERASE record. It inserts both shear gates in frame zero, so the
+register frame paths and copy ranks stay fixed. Under this scoped paid contract,
+the scalar reduction cannot change the moment because its rank histogram is
+invariant. The reverse positive bound increases by 1,186; this is not an
+additional saving.
+
+## Exact chronology and identity
+
+The candidate's D section has five pieces: 236 helper-preparation gates, 306
+single-source target gates, 111 middle target rows, 306 more single-source
+target gates, and the 236 helper gates in reverse order. All are at frame zero.
+The rebase inserts `x464 ^= x241` immediately before the 111-row middle block,
+updates that block, then inserts the same gate immediately after it. Here
+`x464` is helper 242 and `x241` is helper 19.
+
+Let `T = I + e_242 e_19^T`. The first new gate changes the helper vector from
+`h` to `T h`. The middle matrix becomes `M' = M T` by toggling column 19 in each
+row that contains column 242. Since `T^2 = I`,
+
+```text
+M' T h = M T T h = M h.
+```
+
+The second gate restores the helper vector. This identity holds for every
+initial helper state; the verifier also checks the full forward and reverse
+dirty-input boundaries. The three negative controls reject omission of the
+preparation gate, restoration gate, or middle-column correction.
+
+This proves only the stated rebase on this fixed seed-01 candidate. It does not
+show that all R439 scalar edits are profile-neutral or that no other legal
+frame-changing proposal exists.
+
+## Reproduction
+
+From the repository root:
+
+```sh
+python3 -B research/r439-shear-rebase-236-profile/verify.py
+```
+
+Expected final line:
+
+```text
+PASS_R439_SHEAR_REBASE_236_PROFILE ADDs=11500->11497 D=5548->5545 changed_rows=13 histogram=unchanged rank_mass=5129 F=25717 B=5911840->5913026 guards=95/182 controls=3 no_new_kappa
+```
+
+The verifier checks live-input hashes, the five-part chronological D layout,
+the exact support-delta identity, the full dirty boundary in both directions,
+all register frame paths, the paid histogram, the literal bill, the precision
+guards, and the three rejection controls. It reuses the pinned seed-01 checker
+for the inherited R439 word convention and the pinned owner checker for the
+paid-rank accounting. Local verification passed on CPython 3.14.8. The
+registered CPython 3.12 replay was not run because `python3.12` is unavailable
+in this environment.
+
+## Open next questions
+
+The first-step positive control is the complete pass of
+`research/r439-bsection-stars-seed01/verify.py`. That package's 236-star word is
+the exact input here. The scalar proposal is PR1047's post-helper shear, from
+`research/r439-post-helper-shear-seed03`; its README explicitly leaves
+composition with other sprint results open. The scalar reduction here is a
+different, re-based application of that operation, not PR1047's original
+14-ADD result. Credit PR1047's author and its PR967 / PR915 / PR589 lineage,
+and the seed-01 package's authors and PR1015 / PR923 / PR967 lineage. The
+source pins and exact predecessor files are listed in `SOURCES.json`.
+
+Can a distinct legal frame-moving version of this same
+column change alter the paid profile without adding enough COPY/ERASE or
+restoration cost to erase the gain? A first step is to exhibit one exact
+candidate frame move for the 111-row middle block and prove its dirty endpoint;
+only then should its full child histogram be priced. The current PR1047
+chronology has only frame-zero gates, so it supplies no such move.
+
+## Credit
+
+Prepared by OpenAI Codex (laptop-16) with substantial AI assistance. No
+independent human or formal proof-kernel review is claimed. Apache-2.0; no
+selected-frontier, supplier-adoption, hosted-runtime, or multiplication-theorem
+claim is made.

research/r439-shear-rebase-236-profile/RESULT.json

@@ -0,0 +1,75 @@
+{
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "bill_after": {
+    "B": 5913026,
+    "D_adds": 5545,
+    "F": 25717,
+    "local_bits": 95,
+    "native_ADDs": 11497,
+    "nine_stage_bits": 182
+  },
+  "bill_before": {
+    "B": 5911840,
+    "D_adds": 5548,
+    "F": 25717,
+    "local_bits": 95,
+    "native_ADDs": 11500,
+    "nine_stage_bits": 182
+  },
+  "chronology": {
+    "D_prefix_records_before_middle": 542,
+    "changed_middle_rows": 13,
+    "frame": 0,
+    "middle_target_rows": 111,
+    "register_destination": 464,
+    "register_source": 241,
+    "shear_gates": 2
+  },
+  "controls_rejected": [
+    "missing preparation",
+    "missing restoration",
+    "missing column correction"
+  ],
+  "copy_ranks": [
+    7,
+    7,
+    7,
+    7,
+    7,
+    7,
+    7,
+    7,
+    7
+  ],
+  "frame_paths_equal": true,
+  "input": "PR seed-01 degree-two candidate; 236 helper edges",
+  "paid_histogram_after": {
+    "1": 1323,
+    "2": 1342,
+    "3": 79,
+    "4": 44,
+    "5": 102,
+    "6": 11,
+    "7": 19
+  },
+  "paid_histogram_before": {
+    "1": 1323,
+    "2": 1342,
+    "3": 79,
+    "4": 44,
+    "5": 102,
+    "6": 11,
+    "7": 19
+  },
+  "paid_rank_mass": 5129,
+  "proposal": "PR1047 helper shear (destination 242, source 19)",
+  "scope": "one exact PR1047 shear rebased onto the 236-edge seed-01 candidate; no new kappa",
+  "status": "PASS_R439_SHEAR_REBASE_236_PROFILE",
+  "support_delta": {
+    "destination_column": 13,
+    "net_ADD_saving": 3,
+    "overlap": 9,
+    "source_column_after": 11,
+    "source_column_before": 16
+  }
+}

research/r439-shear-rebase-236-profile/SOURCES.json

@@ -0,0 +1,66 @@
+{
+  "schema_version": 1,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "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/e8-bit-p111-tuned/code/xcheck_p.py",
+      "usage": "input",
+      "git_blob": "184f5dcf94a486cc7db91ca4db5865916bf26009",
+      "sha256": "af3decc877e27c00001cf56f50c6c09566e8e101297ab34c7860aed96a06d80e"
+    },
+    {
+      "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+      "usage": "input",
+      "git_blob": "e293ddc557742637f9f679f083a1a282d87b1b13",
+      "sha256": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4"
+    },
+    {
+      "path": "research/r439-bsection-stars-seed01/candidate.json.gz",
+      "usage": "input",
+      "git_blob": "9a17b4920334878d6c949191f6931bd97126fe3c",
+      "sha256": "b452d2c2b0b2a546d1105b1da9769aa78e5c54d6f00e97b30c77e3f54ce445ee"
+    },
+    {
+      "path": "research/r439-bsection-stars-seed01/candidate_search.json",
+      "usage": "input",
+      "git_blob": "97f5d9f0d3a153feb2b38a39daf826d959364e8f",
+      "sha256": "488741d5ad803372b622495972d754ab2998a8afb0b84ef755edc337b20d0af0"
+    },
+    {
+      "path": "research/r439-bsection-stars-seed01/verify.py",
+      "usage": "input",
+      "git_blob": "be296a579cef6722786d589652f73662a92252fb",
+      "sha256": "eb387243b9071a0309e04248bc088fe6f33067e39f87d9fcd1785866020b97ee"
+    },
+    {
+      "path": "research/r439-post-helper-shear-seed03/README.md",
+      "usage": "input",
+      "git_blob": "fe1f4644264a5e1cddb11506054b2091192398a3",
+      "sha256": "361a177a7e8eab4c5310aa5258824e1c1097e2b0f6f555a30707d15be2635b36"
+    },
+    {
+      "path": "research/r439-post-helper-shear-seed03/SOURCES.json",
+      "usage": "input",
+      "git_blob": "869711b4dc7c05149db7d8381c943b86b1fce540",
+      "sha256": "d2a46e90f179b4de5487d3acf56afe4cd14599964250770b83ffbe43fdb30004"
+    },
+    {
+      "path": "research/r439-post-helper-shear-seed03/independent.py",
+      "usage": "input",
+      "git_blob": "10ae0333f17bce14fb496250688d85623ab09f3a",
+      "sha256": "509f44d07090595b3d714dd185b53cfd86203497560cfe636b50e0fbf2cb8089"
+    }
+  ]
+}

research/r439-shear-rebase-236-profile/TASK.json

@@ -0,0 +1,60 @@
+{
+  "schema_version": 1,
+  "task_id": "scalar-to-moment",
+  "priority_revision": 6,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "original_card": {
+    "id": "scalar-to-moment",
+    "question": "Can one known scalar simplification be converted into an actual paid-profile improvement?",
+    "starting_points": [
+      "research/r439-bsection-stars-seed01/README.md",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Derive the changed legal frame itinerary and exact child histogram.",
+      "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract."
+    ],
+    "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/r439-bsection-stars-seed01/verify.py"
+      ],
+      "expected": "PASS_R439_BSECTION_STARS",
+      "inspect": "Observe that the positive control improves scalar counts while retaining the paid histogram.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Choose one simplification and derive the complete changed frame itinerary, or prove why it cannot change the histogram.",
+    "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.",
+    "allowed_variations": [
+      "One existing scalar simplification and one proposed frame-path change."
+    ],
+    "scope_change_triggers": [
+      "Submitting only another scalar count as completion of a paid-profile task."
+    ],
+    "overlap_terms": [
+      "scalar simplification",
+      "paid profile",
+      "R439"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Rebase PR1047's exact helper shear (242,19) onto the seed-01 236-helper-edge candidate and determine whether its chronological frame itinerary changes the paid child histogram.",
+  "scope_change_reason": "The four seed-01 words' unchanged histogram is already covered by open PR3588. This audit narrows to the explicitly uncomposed PR1047 shear on the later 236-edge candidate, a distinct composition left open in both predecessor packages.",
+  "bottleneck_link": "A scalar reduction reaches the exponent only through a changed paid moment; this rebase preserves the exact paid histogram, so it supplies no moment improvement.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after the exact source-pinned rebase preserves the dirty endpoint and its frame paths, the owner histogram and full scalar/positive-bound bills are recomputed, and the three missing-operation controls fail. Do not search other shear pairs or frame paths in this session.",
+  "outcome": "negative-result",
+  "evidence": "The 236-edge candidate accepts PR1047's (242,19) shear by a T^2=I conjugation. Thirteen middle rows change; exact support weights give a 3-ADD saving (11,500 to 11,497), not the original 14. The frame paths, nine rank-seven COPY records and histogram {1:1323,2:1342,3:79,4:44,5:102,6:11,7:19} remain unchanged. F stays 25,717; B rises 5,911,840 to 5,913,026; 95/182-bit guards still pass. No kappa follows.",
+  "author": "OpenAI Codex (laptop-16)",
+  "ai_assistance": "Substantial OpenAI Codex assistance for research, derivation, implementation, verification and writing; no independent human review.",
+  "open_questions": [
+    {
+      "question": "Can a legal frame-moving version of the same helper column change alter the paid histogram without its frame moves and restoration cost erasing the scalar gain?",
+      "why_it_matters": "The present rebase leaves the paid moment unchanged, so any exponent effect requires a distinct legal frame itinerary.",
+      "first_step": "Exhibit one concrete frame move for a middle-row source, then prove the full dirty endpoint before pricing its paid child histogram.",
+      "blocked_by": "PR1047's exact preparation and restoration both occur at frame zero; no alternate legal itinerary is identified by this bounded audit."
+    }
+  ]
+}

research/r439-shear-rebase-236-profile/VERIFY.json

@@ -0,0 +1,27 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/e8-bit-p111-tuned/code/xcheck_p.py",
+    "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "research/r439-bsection-stars-seed01/candidate.json.gz",
+    "research/r439-bsection-stars-seed01/candidate_search.json",
+    "research/r439-bsection-stars-seed01/verify.py",
+    "research/r439-post-helper-shear-seed03/README.md",
+    "research/r439-post-helper-shear-seed03/SOURCES.json",
+    "research/r439-post-helper-shear-seed03/independent.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Source pins, exact T^2=I shear on the 236-edge word, all 661 full dirty columns in both directions, exact frame-path and paid-histogram invariance, literal scalar/bounds, precision guards, and three negative controls."
+    }
+  ]
+}