Add scoped R439 quartet frame-cut 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-quartet-frame-cut-homelab02/README.md

@@ -0,0 +1,90 @@
+# One frame-available cut in the PR941 R439 four-helper word
+
+**Scoped chronological/frame audit; no supplier, paid-profile, or κ claim.**
+This note checks one implication for the winning quartet in
+`research/r439-helper-quartets-seed07`: after its dependent helper preparation,
+are the four current helper values still present at frame 0 when the compiled
+middle injection begins?
+
+## Exact scope and result
+
+The pinned predecessor uses quartet indices `[114,126]`, helper labels
+`[269,88,288,153]`, and preparation word
+`a ^= b; c ^= d; b ^= c`. With `v=111`, those are register IDs
+`[491,310,510,375]`. In the constructed D section:
+
+- the three quartet gates are D indices **114–116**;
+- all 200 helper preparations and 306 target preparations finish before the
+  compiled middle injection, which starts at D index **506**;
+- none of the four selected helpers is written again between the last quartet
+  preparation and that cut;
+- each selected helper is read by the 111 middle-injection gates (respectively
+  9, 11, 8, and 15 times); and
+- all D gates use frame 0. The four helpers and the targets start at frame 0,
+  so the selected operands are at frame 0 throughout this prefix and at the
+  injection cut.
+
+On arbitrary four-register input `(a,b,c,d)`, the prefix states are
+`(a+b,b,c,d)`, `(a+b,b,c+d,d)`, then `(a+b,b+c+d,c+d,d)`. Its exact row masks
+are `[3,14,12,8]`, matching the pinned certificate. The literal reverse word
+restores the four initial values after the injection and target cleanup.
+
+The frame check is necessary but does not make the word order optional. A
+control that swaps `c ^= d` and `b ^= c` remains frame-0 legal, but changes the
+matrix to `[3,6,12,8]`. Holding the compiled injection fixed, the dirty input
+with only helper 153 set changes the target output. In the 111-bit target
+basis, the expected output is `0x4001480001100e2040150e2110`; the reordered
+output is `0x4041402001008a6004150c2118`; their XOR is supported at target
+indices `[3,17,34,38,46,50,55,60,77,83,94]`.
+
+This establishes one cut-local fact for this finite word: the altered helper
+values are chronologically retained and frame-available at the middle
+injection, while the dependent preparation order is semantically material.
+It does **not** discharge the complete replacement for H2/K. The predecessor's
+syntactic `H2_D_frame0_targets_from_helpers` and `K_equals_D` flags remain
+false. This audit does not re-run the 661-column whole-word verifier, recompute
+the paid profile, or assess hosting, supplier adoption, the selected result,
+or the multiplication theorem.
+
+## Reproduction
+
+From the repository root, with Python 3.12 or later and the pinned inputs
+present:
+
+```sh
+python3 -I -B research/r439-quartet-frame-cut-homelab02/verify.py
+python3 scripts/research_package.py --package research/r439-quartet-frame-cut-homelab02 --check-only
+```
+
+The first command checks the 46 declared input pins (including the
+predecessor's 43-file source closure), rebuilds only the named candidate (not
+its GL(4,2) search), verifies the preparation/cleanup cut and D frames, checks
+the exact four-register matrix, and checks the 16 local dirty-input cases plus
+the reordered control. Expected output is:
+
+```text
+PASS_R439_QUARTET_FRAME_CUT prep=114:117 injection=506 helpers_frame0=true helper_reads=9,11,8,15 local_inputs=16 reorder_failures=8 reorder_witness=153 delta_support=3,17,34,38,46,50,55,60,77,83,94 no_supplier_claim
+```
+
+## Source and credit
+
+The task runs on base `20ecf2891d80b5acf18d980b2164fb44ea7faa90`, priority
+revision 6. The quartet construction is Sagar Thakrar's merged
+[PR #1045](https://github.com/CrocSwap/integer-mult-bounds/pull/1045), current
+head `b4610c1c0ba67111c156bc56e9f16a4aab0fe613`, with package source base
+`2921874911956718fcaaaf9396fe8267b3cfa9f0`. It uses the PR941 matching and
+PR915 target basis, with the earlier PR915/926/941 and PR555/589 lineage
+credited in that package. The exact files and hashes checked here are
+in [SOURCES.json](SOURCES.json); the task card, selected record, and catalogue
+are pinned as provenance by [TASK.json](TASK.json).
+
+Prepared by Codex agent `homelab-02` with substantial OpenAI Codex assistance.
+New work is under the repository's Apache-2.0 license. The predecessor's
+attribution and source licenses are retained.
+
+## Open next questions
+
+No further quartet or supplier-admission question is opened by this one-cut
+audit. A broader replacement contract would need its own complete boundary,
+paid-profile, and consumer ledger under the family expansion gate; this result
+alone supplies no reason to start another construction round.