Independent verification: code-disjoint pricing of all 16 pending kappa claims; every one has deficit W - 64N (no new kappa)

[thakrarsagar]

Status: independent verification. No new κ; the selected result is unchanged.

Track 75–84 (independent verification), assignment seed 83 (OS CSPRNG via Python secrets). Analysis base 29218749; the branch is cut from abdc6a70, where the selected record is unchanged.

What this adds

This checks every open PR claiming a conditional κ at or above the selected record: 16 claims, snapshot at 17:34 UTC, each pinned to its head. Until now these claims had been priced only by the retained engines inside their own packages. #1049 audits the leaver local words and explicitly excludes pricing.

This package re-derives each claim's pricing chain from its committed record with code-disjoint arithmetic. It does not import or read moment.py, base_two_moment.py or outer.py:

• the deficit, and the coverage form D = W − 64N (see Research note: restoration deferral is mass-neutral in the hosted T37 recurrence (no new kappa) #1012);
• the halving guard;
• certification of the recorded complex endpoint: moment below one at b and above one at b + 10⁻²⁴, with a prime-chain atanh logarithm, a Taylor exponential with Lagrange remainder, and 2⁻³²⁰ outward rounding. This extends Independent verification: code-disjoint T37 moment endpoints and kappa reduction (no new kappa) #1051.
• κ through the selected outer reduction with PR589's unchanged bit endpoint, compared with the record and the title.

PR	Head	Author	W	N	Deficit	D = W − 64N	Endpoint certified	κ recomputed	= record and title
#962	50c6ae8151	GamingPuzzled	33,152	333	11,840	yes	yes	0.001661960547713947	yes
#987	0beb9476d1	rohanarun	33,152	333	11,840	yes	yes	0.001662039077758742	yes
#1004	1974578f82	jeremykothe2	7,168	72	2,560	yes	yes	0.001664233607446043	yes
#1005	779e80aef4	jeremykothe2	7,168	72	2,560	yes	yes	0.001671387264390146	yes
#1018	eac7547cb1	jeremykothe2	7,168	72	2,560	yes	yes	0.00167166528321877	yes
#1019	eff6576441	1337isnot1337	33,152¹	333	11,840	yes	yes	0.001661960547713947858091	yes
#1022	58618bcbfe	jeremykothe2	14,336	144	5,120	yes	yes	0.001672081255752945	yes
#1028	be4bd89cb4	jeremykothe2	14,336	144	5,120	yes	yes	0.001672166670891177	yes
#1030	d71857cd0a	AlexS-scale	7,168¹	72	2,560	yes	yes	0.00166202617947539	yes
#1031	e900534f0b	jeremykothe2	14,336	144	5,120	yes	yes	0.001672167430672016	yes
#1042	7e8ef087c0	jeremykothe2	14,336	144	5,120	yes	yes	0.001672188119205421	yes
#1050	c87242f846	jeremykothe2	14,336	144	5,120	yes	yes	0.001672241870811633	yes
#1053	6f92ce8884	jeremykothe2	14,336	144	5,120	yes	yes	0.001672245809535804	yes
#1055	a8ea308976	jeremykothe2	14,336	144	5,120	yes	yes	0.001672251604432734	yes
#1061	223f581afb	jeremykothe2	14,336	144	5,120	yes	yes	0.00167259071506618	yes
#1065	387d935e35	jeremykothe2	14,336	144	5,120	yes	yes	0.001672644568760139	yes

¹ Neither #1019 nor #1030 records W or N in its JSON. They are priced with the selected T37 values and with (7,168, 72) respectively; those rows check the arithmetic under that stated assumption only.

Findings

• All 16 endpoints certify, and every recomputed κ equals both the committed record and the title. The complex side binds everywhere.
• Every claim has deficit exactly W − 64N (320 per replica). The recent gains, up to +0.64% (Conditional κ = 0.001672644568760139: improved T16 owner packing on the seven-slot k8 word #1065), come entirely from the shape of the child-rank profile. That is the mass-neutral consolidation mechanism priced in Research note: restoration deferral is mass-neutral in the hosted T37 recurrence (no new kappa) #1012.
• Reviewer trap. Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005's head also carries Conditional κ = 0.001664233607446043: mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1004's stacked package gauge44-leaver/, whose RESULT and README say 0.001664233607446043. Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005's own claim lives in gauge44-leaver8/ and is consistent there. GitHub's 100-file listing for Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005 hides gauge44-leaver8/.

Reproduce

make pending-claims-pricing-verify     # offline, about 2 s: table regenerated and compared, 6 negative controls, 3 tests
python3 -B research/pending-claims-independent-pricing/rebind.py   # optional, network: refetch heads, check blob ids and values

Expected: PASS_PENDING_CLAIMS_PRICING_REPLAY and PASS_PENDING_CLAIMS_REBOUND. SNAPSHOT.json holds every value with git blob provenance. Nothing from the PRs is executed.

Controls on the top claim: an extra rank-one child; one replica's stock removed; endpoint + 10⁻²⁴; κ + 10⁻¹⁸; a weaker bit side, which changes the binding side and κ; a truncated exponential, which fails closed.

Scope

This covers arithmetic from the committed profile to κ, plus the deficit identity. It does not verify:

• that the claimed words, owners or hosting realize these profiles;
• the local words (see Research audit: independent check of PR1005/1018 mutable-leaver cells (no new kappa) #1049), invoices or owner audits;
• any inherited assumption.

A passing row is consistency evidence, not acceptance. Claims opened after 17:34 UTC are not covered.

Credit

• The constructions and claims belong to their authors: Jeremy Kothe (twelve claims), rohanarun (Conditional κ = 0.001662039077758742 — U10 (two new triangle-hybrid slots) on PR942's T37 owners #987), GamingPuzzled (Conditional κ = 0.001661960547713947: T37 owner map on PR890's U8 word (independent cross-check of #942) #962), 1337isnot1337 (Conditional κ = 0.001661960547713947858091 by exact T37 grid refinement #1019) and AlexS-scale (Conditional κ = 0.00166202617947539: U8 with two rank-seven helper ends #1030), together with the lineages credited in their packages.
• The retained engines' authors, for the reduction replicated here.

Prepared by Sagar Thakrar with substantial AI assistance from Claude (Anthropic) via Claude Code. New material is Apache-2.0.