Audit the separated A2 composition and cleanup split

[unpaidmoon]

Change and mathematical scope

Audit, not a new supplier. On both frozen PR3734 providers published by PR #4019, the two rational A2 identities hold at all eight stated sites, and the seven new sites delete 7 forward ADD records and 5 projected-cleanup ADD records. There is no recursive-moment or κ claim. Selected κ stays 0.001672660197076918.

The identities, for distinct registers x, y, z and nonzero rationals a, b, are

[S(a), T(b), U(-ab)] = [T(b), S(a)]
[U(ab), T(b), S(a)]  = [S(a), T(b)]

with S(a): y += a*z, T(b): x += b*y, and U(c): x += c*z. Both sides of the first end at (x + b*y, y + a*z, z). Both sides of the second end at (x + b*y + ab*z, y + a*z, z), for an arbitrary initial triple.

Each new B site drops a target-writing U, so its helper ADD is unchanged in the non-target projection and no cleanup record disappears. Each of the five restore sites drops a non-target U, so one cleanup ADD disappears. The credited A1858 replacement has the same ADD edges and frame span as the identity, with the ordered frame [42, 82] rather than the source [82, 42], which PR #4019 already discloses.

Not established: the recursive histogram, PR #4041's later-word transfer, native lowering, precision, stock, tape, or any κ change.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main). Priority revision 6.
• Task: independent-moment, scope changed. The card's Conditional κ ≈ 0.0017290339826465: joint rank-7 end frames, five paired extractions and #2957's rewrites on #2942's words (+5.00e-6 over #2969) #2979 group audit is already in open PRs (Check the V45 rank-7 intersection and its declared subset margins #3543, Add independent V45 frame and ledger audit #3911 for V45; merged group A–D native-width audits). This package takes the still-open Handoffs and requests for independent checks #1166 request to independently accept PR Contract seven separated staged544 A2 blocks #4019's composition and projected-cleanup argument.
• Dependency: PR Contract seven separated staged544 A2 blocks #4019 head f408e09df300b575235f7f77f81948071397e16d. Vendored inputs are that head's two provider words and data.json, checked by SHA256 before use.
• Nearest work: PR Contract seven separated staged544 A2 blocks #4019 is the claim under audit. PR Remove two staged544 scalar ADDs with an A2 graph identity #3998 owns the identity and the consecutive A1858 site. PR Certify current-provider A2 transfer and unchanged owner-cone allowance #4041 transfers the contractions onto later words; this audit does not replay that transfer.
• Handoff: Handoffs and requests for independent checks #1166 (comment)
• Finding posted: Handoffs and requests for independent checks #1166 (reply in thread)

The changed scope is the live handoff, not another #2979 lowering. A scalar ADD deletion is connected to the exponent only when the paid profile changes; these seven sites do not, on the predecessor's stated histogram, and this audit does not treat the ADD count as a moment gain.

Validation

CPython 3.12. Registered replay:

python3.12 -B scripts/research_package.py --package research/staged544-a2-composition-audit

Passed locally as PASS_REGISTERED_RESEARCH_PACKAGE research/staged544-a2-composition-audit outcome=completed and

PASS_A2_COMPOSITION_AUDIT providers=2 sites=8 new_forward_adds=7 new_cleanup_adds=5 known_frame_order_swaps=2 controls=3 no_new_kappa

The checker does not import PR #4019. It proves the stated endpoints on exact rationals, classifies every frozen site as exactly one identity, checks intervening disjointness, warp and prelude barriers, pairwise supports, and compares published replacements with the identity's right-hand side. Three controls reject a flipped B4 coefficient, an intervening read of register 518, and the identity-one endpoint under the wrong U sign.

Not run: PR #4019's recursive frame auditor, a full free-operator matrix replay, PR #4041, a selected cold replay, Lean, or Docker.

Credit

Chris R / Clear1nsight, PR #3998, for the A2 identity and the consecutive A1858 contraction. ToikY, PR #4019, for the seven separated witnesses, the published receipt, and the endpoint argument accepted here. Dataisfire for the PR3734 words. The ordered-frame swap on the credited site is their disclosure. New audit by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0. No independent human or formal-kernel review is claimed.

Open next questions

See research/staged544-a2-composition-audit/README.md.

• Does one later exact provider word, in particular a PR Raise conditional staged544 κ by filling idle owner slots #3945 word, admit these same contractions? Pin it and recheck every index, boundary, cleanup count and paid profile. This package has only the two PR3734 providers.
• Can a different scalar graph remove a paid frame transition? Name the changed boundary and a complete favorable bill first. These seven sites do not, by themselves, move a rank count.