Research: exact raw agreement set for compact dirty-control selected-bit updates (no new kappa)

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Adversarial mathematical audit with an independent finite checker; no new kappa. The selected record, production predicates, upstream/ and all frozen pins are unchanged.

• Track: adversarial-audit. Card: supplier-boundary-audit (scope key 66632af6c86d34fb0fdc, chooser OS nonce 9e531d2bfd9e08f12db2843ca19eac2c, priority revision 3), scope refined to one named current condition (task card in research/compact-agreement-set-seed29/TASK.json).
• Base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea, head 5577d53f on research/agent-29-compact-repair-9e531d2b.
• Package: research/compact-agreement-set-seed29/.
• Contributor: Aaron Wang, with help from opencode.

What this adds

For the compact dirty-control selected-bit operation of notes/compact-control-movement.tex ("Guards and deterministic repair"), the exact raw agreement-and-restoration set AG — states where the complete routine already equals the ideal selected-bit XOR map and restores every dirty temporary — is computed on complete bounded domains and compared with the three published sufficient guards:

Guard	Source
G0 original temporary+target guard (plus u nonsaturation for the later source)	the source note
G1 expanded source-control predicate (last u digit free)	research/compact-carry-repair-audit
H two-pass guard (1)	#1247 (Hanson Sun), independently re-derived in research/compact-late-guard-audit-seed73

1. Independent sufficiency check: all three guards hold. Zero violations across 47 cells / 24,074,240 complete-fiber states (n in {2,3}, K in {3,4,5,6}, G in {1,2}, both source orders). Both published failure fixtures reproduce exactly under the independent interpreter: (x,y,t,u,b)=(16,4224,0,1,2) returns y=4752 against ideal y=4240 with temporaries restored, and (2,124,1,0,7) returns the correct y=126 while corrupting the temporary 1 -> 5.
2. The exact agreement set strictly exceeds every guard, everywhere. |AG|/total = 11880712/24074240 = 49.35% overall, against guard maxima of 14.06% (G0), 7.03% (G1) and 44.83% (H); e.g. at n=2,K=5,G=1 (later source): AG 39.55% vs G0 1.562%, G1 3.125%, H 18.750%. Smallest necessity witnesses are recorded per cell (ag_outside_all, ag_outside_all_active in RESULT.json), e.g. [y,t,u,c]=[0,1,0,1] at n=2,K=3,G=1: the saturated temporary digit is never loaded, so the feared carry cannot fire. The guards are safe repair envelopes, not the agreement set — quantifying the gap the seed73 README leaves open ("not the global exact agreement set").
3. The seed73/PR 1247 closed form (2) is independently verified: H's exact density matches the enumerated counts at all 21 later-source cells (exact integer agreement required). Inclusions G0 => G1 => H hold on every cell, and G0/G1's target condition 2B <= g < 2^(K-1)-2B is empty for K <= G+3 — those guards only engage at K >= G+4.
4. Controls: both fixtures above (fidelity); a sign-flipped unloading must be caught by the restoration check inside the guarded domain (witness [4240,0,0,1]); low-rho target bits and arbitrary dirty back-field values must not change results (256 states x 4 dirty values); pinned source hashes verified; receipt replay compares with RESULT.json and writes no artifacts.

Relation to concurrent work

Open #1603 (research/compact-late-carry-guard, claim/handoff in #1588) is independent concurrent work on the same family: a stronger sufficient guard admitting inactive saturated digits (exactly the class of the smallest AG \ guard witnesses above), with maximality proved only for n=1, and a handoff requesting the n>1 enumeration. This package supplies that enumeration layer at n=2,3 and additionally includes agreement states with internal u-load carries and cancellations between individually inexact subcalls, which that PR states remain outside its guard. Its guard is not present in this base and was not transcribed or tested here.

Reproduce

From the repository root, Python 3.10+, standard library only:

python3 -B research/compact-agreement-set-seed29/verify.py

Expected: PASS_COMPACT_AGREEMENT_SET: 24074240 states; 11880712 raw agreements; 47 cells; 2 fixtures; 2 controls. Registered replay (Python 3.12) passes: python3.12 scripts/research_package.py --package research/compact-agreement-set-seed29 -> PASS_REGISTERED_RESEARCH_PACKAGE research/compact-agreement-set-seed29 outcome=completed; metadata/pins: ... --check-only -> PASS_PACKAGE_METADATA_AND_PINS.

Limitations and obligations not checked

• The exceptional repair itself (scan, radix sort under TS^-1, record keys), its cost charges and the complete-range invariant after row splitting (docs/audit.md lines 114-116) remain open; this audits the raw map before any repair.
• No production predicate change, no supplier adoption, no kappa/packing-cap claim; a < D/E and whole-construction budgets do not apply to an audit.
• Finite domains only (n<=3, K<=6, G<=2); no proof-assistant formalization; transcription fidelity rests on the source note, the two reproduced fixtures and the pinned hashes. Unchecked: PR 1603's guard, the n=1 maximality claim, hosting/precision/tape/restoration obligations outside this named condition, and any full cold replay.

Credit

Predecessors: notes/compact-control-movement.tex (Douglas Colkitt / OpenAI source semantics); #1247 (Hanson Sun) for the two-pass guard H and its density, independently re-derived with fixture 2 in research/compact-late-guard-audit-seed73; research/compact-carry-repair-audit for G1 and fixture 1, following #1475 (Sagar Thakrar) and PR 1219's one-pass fact; scripts/audit_compact_controls.py as the pinned source-bound checker of record (no code shared); #1603 for the concurrent stronger guard and its n>1 handoff. Overlap receipt (complete pagination, 482 open PRs / 458 discussion records at 10:53-10:55 UTC) is recorded in TASK.json.

[Mister-Meeseeks]

Batch review at 5577d53f4bc093b5e9e960387ffc5d5bea55ee6f.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent whole-slot raw-map census of24074240 states in47cells reproduces11880712 agreements, sufficient guard inclusions and density formula. Reviewer supplement distinguishes actual sign reversal from submitted omitted-unload control; both reject. Repair/tape costs, all-size extension and production-predicate adoption remain open.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.