Research audit: independent check of PR1005/1018 mutable-leaver cells (no new kappa)

research/leaver-cell-audit-seed65/README.md

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+# Independent audit of the mutable-leaver all-K cells (PR1005) and the seven-slot word (PR1018)
+
+**Status: adversarial audit / independent verification. No new kappa. No counterexample found; one
+documentation discrepancy.** The selected result and `upstream/` are unchanged.
+
+Track 60–74 (adversarial audit), OS-random assignment seed **65** (`secrets.randbelow(100)`).
+Base `2921874911956718fcaaaf9396fe8267b3cfa9f0`. Audited heads: PR1005
+`779e80aef469bc3a28b19f1adde199871a9a22e3` and PR1018 `eac7547cb191f875d5f5ea5f9bbb1d2b8c51c4ef`.
+PR1022, PR1028, PR1031 and PR1042 pin the same seven-slot local word (`c2b29430…`), so the
+local-word results below also apply to them. Their owner maps and global replays are not covered.
+
+## Why this object
+
+PR1004/1005 introduce "mutable-leaver" cells. A coded 21-gate circuit uses face-event operands that
+have no later reads as mutable scratch, and the "inherited cleanup" restores them at FULL. The k8
+cells are the local word for six open κ claims (PR1005, PR1018, PR1022, PR1028, PR1031, PR1042). Their
+recorded reviews come from the authors' own reviewer agents. Checking the premise independently is
+the cheapest way to support or block that whole lineage.
+
+## Statements checked
+
+The verifier is standard-library only and imports nothing from the audited packages. Their words are
+read as data (inputs pinned in `SOURCES.json`).
+
+1. **Exact local map (all three words).** Every one of the 224 data columns, replayed forward through
+   precondition, A, cut, B, tail and cleanup, gives `x -> x` and `y_t -> y_t + x_t`. For each of the 480
+   helper columns, the inverse of the post-precondition program returns the unit vector plus a residue
+   supported on targets only. This is exactly the condition for the pre-main compensation `y -= a·h`
+   to exist, and it is a different formulation from the authors' constructive one. The residue
+   vanishes for every entering helper.
+2. **Frames.** An independent replay of monotone climbs over A, the centre paths, B, the early-cleanup
+   tail and the terminal ends reproduces each word's recorded paid profile. The FULL cleanup touches
+   only registers that end at FULL.
+3. **Leaver premise.** All 8 coded cells are found literally, each exactly once, contiguous and in the
+   published gate order, by unifying the `scaled` gate lists of `CODED-CELLS-k8.json`. The target sets
+   come from `TRI-LEAVER-k8.json`; the coded target index is the TRI read index + 8, checked for all
+   cells. The 24 mutated leavers (12 data registers, 12 helpers) satisfy all of the following:
+   * none is a centre, entering helper or low-ended helper;
+   * none is touched again in A, cut, B or the early-cleanup tail after its cell;
+   * each is written in the FULL cleanup;
+   * each holds a value different from its input at the end of B, so the restoration is real FULL
+     work.
+4. **No new class of source mutation.** Each of the 12 data-register leavers receives exactly one
+   B-section write in both the no-triangle base word (`3e99ba77…`) and the cell word, and their
+   A-section writes are identical. The cells re-pair or re-scale these pre-existing face-event writes
+   (8 of 12 differ) and remove the packet-copy helpers. They add no mutation event to any data
+   register. The dependence on mutable sources is therefore the one the gauge44 lineage already
+   inherits.
+5. **Profile deltas.** The raw-stage paid profiles, recounted with the replay of item 2, are additive
+   per cell:
+
+   | word | R | raw paid profile |
+   |---|---:|---|
+   | no-triangle | 504 | `{1:1880, 2:832, 3:312, 4:168, 5:168, 6:56, 8:8}` |
+   | k5 cells | 489 | `{1:1910, 2:772, 3:327, 4:168, 5:168, 6:41, 8:8}` |
+   | k8 cells | 480 | `{1:1928, 2:736, 3:336, 4:168, 5:168, 6:32, 8:8}` |
+
+   `k5 − notri = 5u` and `k8 − k5 = 3u`, where **u = +6H1 −12H2 +3H3 −3H6** (rank mass −27, three
+   helpers removed per cell). The seven-slot word differs from the final k8 word by exactly
+   `7×{3:+2, 4:−4, 5:+2}`, which matches PR987's per-slot claim.
+
+## Finding: per-cell profile claim not reproduced
+
+The PR1004/PR1005 descriptions state: "Each cell changes the raw paid profile by exactly
+−30H1+6H2+6H3." That claim is rank-mass-neutral. Against the no-triangle comparator, the measured
+per-cell change is `+6H1 −12H2 +3H3 −3H6`. No rebuilt stage (raw, regroup, hpe, cold44) shows the
+stated vector. The packages do not state the claim's comparator, and no code asserts it.
+
+**This does not affect κ.** κ is priced from the final word's full profile through the reviewed
+global replay. It is a description that reviewers should not rely on. The authors should state the
+comparator or correct the sentence.
+
+## Negative controls
+
+Each mutant must be rejected by the check it targets. All 14 are rejected (7 on the final k8 word, 7
+on the seven-slot word):
+
+| control | rejected by |
+|---|---|
+| N1 drop a leaver write | endpoint |
+| N2 drop the FULL-cleanup restoration of a leaver | endpoint |
+| N3 neutral `h += ½x; h −= ½x` on a leaver at FULL after its cell | **premise only** |
+| N4 wrong cell coefficient | endpoint |
+| N5 leaver write moved after its first dependent read | endpoint |
+| N6 entering-helper dirt into a cell target | endpoint (entering response) |
+| N7 leaver gate below its current frame | frames |
+
+N3 passes both the exact endpoint and the frame replay with an unchanged paid profile. The stated
+premise is therefore a design property that the exact map and frame checks do not enforce on their
+own. This audit checks it separately.
+
+## Reproduce
+
+```sh
+python3 -I -B research/leaver-cell-audit-seed65/verify.py
+```
+
+Expected (about 5 s), with the result byte-compared to `RESULT.json`:
+
+```text
+PASS_INDEPENDENT_MUTABLE_LEAVER_AUDIT cells=8 leavers=24 columns=704 controls=14 per_cell_raw={1: 6, 2: -12, 3: 3, 6: -3} claimed_match=False
+```
+
+To rebuild the inputs, follow the README clean-clone commands of PR1005 (`reproduce.py --until word`,
+`reproduce_notri.py --word-only`, `reproduce_leaver.py --id k8|k5 --word-only`,
+`reproduce_leaver_chain.py --id k8`) and PR1018's `verify_slots.py --baseline <chain>`. The PR635
+supplier is pinned at `a6895a69…`. `SOURCES.json` names each output file and its content hash. Every
+hash equals the pin the PRs publish. In this run all 21 PR1005 chain steps (`STEPS.json`) exited 0, and PR1018 printed
+`PASS_SLOTS_ON_CHECKED_K8_BASELINE 0.00167166528321877`.
+
+## Scope and open obligations
+
+This audit checks the local scalar/frame words only. It does not check the owner maps (K8c8, the T16
+packings), hosting, the finite invoice, the moment and outer pricing, or any κ value. Nor does it check
+the inherited mutable-source/common-label realization, Lemma A/G content, all-size compilation,
+precision/tape or the analytic interfaces. Item 4 shows that the cells require nothing beyond the
+inherited interface; it does not prove that interface. Finite replays are not a formal proof.
+
+## Credit and disclosure
+
+The construction and the audited packages are Jeremy Kothe's PR1004/PR1005/PR1018 (LeaverSAT, the
+reviewer agents and G44Pack3 as named there). They build on rohanarun's PR987 slot search, NewBArch's
+PR869 triangle-hybrid delivery, icekylinx's PR645 gauge44 construction and its `audit_local.py`, and
+chafreaky's PR685/741 lineage. Two input files (`CODED-CELLS-k8.json`, `TRI-LEAVER-k8.json`) are
+copied unchanged from PR1005 under the repository's Apache-2.0 license. The other inputs are outputs
+of the authors' drivers.
+
+Prepared by Sagar Thakrar with substantial assistance from Anthropic Claude (Claude Code).