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T94 retained-tail allocation on PR2802: conditional kappa 0.001717795160032012107407 #2824

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Mister-Meeseeks merged 3 commits into from
Oct 16, 2026
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T94 retained-tail allocation on PR2802: conditional kappa 0.001717795160032012107407 #2824

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29 changes: 29 additions & 0 deletions research/replica-tail-gain/CLAIM.json
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{
"calls": 846,
"comparison_head": "17b2ee6ef3cf1468e78a6267f0ecbc9a0e6f60dd",
"comparison_kappa": "17177949841186346638269999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
"comparison_pr": 2802,
"complex_lower": "1717795160032012107407/1000000000000000000000000",
"complex_upper": "107362197502000756713/62500000000000000000000",
"gain": "8795668872179/50000000000000000000000",
"helpers_per_call": 408,
"kappa": "17177951600320121074069999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
"kappa_decimal": "0.0017177951600320121074069999999999999999999998999999999999999999999999",
"live": 84224,
"physical": 84714,
"profile": {
"1": 2037168,
"2": 548208,
"3": 235104,
"32": 1,
"4": 108288,
"48": 33736,
"5": 34544,
"8": 6768
},
"rank_mass": 6118272,
"replicas": 94,
"roles": 345168,
"scope": "Complete conditional finite supplier and modern outer release. Inherited all-size compiler/source-access/hosting/precision/tape/recovery/ordinary-recursion/bit-supplier/analytic-transfer contracts remain. Mathlib proves the stated universal paid-cost inequalities, not the complete multiplication theorem.",
"status": "COMPLETE_FINITE_RELEASE_PASSED_CONDITIONAL_KAPPA"
}
39 changes: 39 additions & 0 deletions research/replica-tail-gain/FRONTIER.md
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# Frontier comparison and certificate scope

The actual T94 allocation composed with PR2802's retired7 native words passes independent whole-owner and exact rational moment checks. **The complete changed native/global/outer release passes** (`PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE`, with `PASS_RELEASE`). The Mathlib proof supplies paid-profile identities and retained-tail dilution inequalities; finite moment admission alone is not a new all-size multiplication theorem.

The two current native providers were authenticated to fresh five-stage runs. Two retained native chains and parent evidence were reused with checked source/artifact hashes; all changed T94 ownership, global controller/phase, finite invoice, outer and strict release checks ran freshly. The original full-result SHA256 is `14d5153f623b0d32c0fa05e90bfcd758489bfed3f7e94393f2e32e6b0dfc5c64`; its release-receipt SHA256 is `48539b00227ca792b06199e937b12f5c6b79385ce7e4d78743060503c22ba369`. These are source-bound release checks, not an independent proof of the inherited all-size interfaces.

## Current comparison

Repository: [CrocSwap/integer-mult-bounds](https://github.com/CrocSwap/integer-mult-bounds). Ordinary public repository HTML at 2026-10-15T23:14:43UTC identifies main `544a7e82810e30cab61c297cb2e2ea86127fe944`. Its pinned README and selected-result bytes match the earlier snapshot. The maintainer-reviewed selected conditional point remains `836330098538459/500000000000000000 = 0.001672660197076918`; stronger pending claims remain distinct from that selected record.

The highest complete-supplier claim found in the reviewed current sources is [PR2802](https://github.com/CrocSwap/integer-mult-bounds/pull/2802), current HTML head `17b2ee6ef3cf1468e78a6267f0ecbc9a0e6f60dd`. Its exact rational is
`0.001717794984118634663827 - 10^-46 - 10^-70`.
The construction commit is `043467ad07c512a8a1717a03cf940be35936b240`; the later head adds cold evidence. Native words, provider inventory, profile, claim, verifier and derivative overlay were checked byte-identical between those commits. The 124-file current subtree is preserved under `vendor/frontier` with original licenses/notices, SHA256 and Git-blob checks. The exact full comparison is `references/PR2802-CLAIM.json`, SHA256 `a2fcbc8a3ad3095ecbd310a26c02e9d11c28e4d105669a08bbdfb39d7704db51`.

[PR2767](https://github.com/CrocSwap/integer-mult-bounds/pull/2767), head `e8b771ba132fe632796b28c1742a8d096c04519f`, previously claimed approximately `0.001717256973467002308270944796906915`. [PR2766](https://github.com/CrocSwap/integer-mult-bounds/pull/2766), head `e6df920cd0110e4b629e2ad84eddcb539001e174`, has the same mathematical profile/root with a slightly shorter certified rational. Both heads were freshly corroborated by public HTML. The full PR2767 rational remains historical comparison data; improving its rounding is not the current frontier test.

## Attribution and actual change

**PR2802 is Marius-Paul Dumitrean's work**, prepared with substantial Anthropic Claude/Claude Code assistance, as its retained NOTICE states. It moves the hostees of B-warps 30/31 from lenders 401/403 onto retired lenders 564/565, enabling aliases 667<-401 and669<-403, on top of aliases 606<-550,635<-551,637<-552,638<-553,639<-562. Those native improvements, refits and source restoration are inherited here.

Further credit belongs to Tekalign/PR2751's joint twelve-source recovery, PR2766's certified frame refit, PR2733's earlier frame-route work, Philippe Van Velzen/PR2679's pre-life hosting and retired-lender alias mechanism, Mason Hale/PR2696's assignment, zxv/PR2530's source-partner loans, Jeremy Kothe/PR2588's helper-label exchange, and Cinna Davis/PR2226's anticipatory borrowing. The independent frame and chronology methods keep their retained credits. PR2767's alternative route reaches the same predecessor profile and supplies no extra stackable gain. PR2411 links Dan Brown and Kenny Daniel's complete asymptotic FinTM2 multiplication proof; no first-proof claim is made here.

This package changes the **literal paid owner geometry to 94 replicas** and composes it with the inherited native words. Each removed helper has width 5. Deleting its actual roles, renumbering survivors and compacting pending-bin prefixes preserves the checked windows and distinct physical families. The complete profile is
`{1:2037168,2:548208,3:235104,4:108288,5:34544,8:6768,32:1,48:33736}`.
It has 846 calls, 408 helpers per call, 345168 literal owner roles, live stock 84224, charged physical stock 84714 including 72 private buffers, rank mass 6118272 and deficit 30080. Actual word frames, scalar endpoints, cleanup, chronology, capacities and masks were independently checked, including seven semantic corruption controls.

The independent directed rational bracket is
`[1717795160032012107407/10^24,1717795160032012107408/10^24]`.
The proposed outer target is its lower endpoint minus `10^-46 + 10^-70`. Its **exact arithmetic gain over the full published PR2802 rational** is
`8795668872179/50000000000000000000000 = 1.7591337744358e-10`.
Moment controls reject the unchanged predecessor at the improved target, reversed brackets, an inadmissible upper endpoint, changed normalization and an unpaid child. The complete changed native/global/outer release also passes at this exact rational. The resulting multiplication implication retains the inherited all-size and analytic assumptions.

Vendored historical replay evidence and reconstruction overlays are intentional pinned upstream inputs. Their original success records and execution-path strings are historical provenance, not fresh T94 evidence or this package's host paths. Fresh receipts use logical/relative labels. No historical full release is credited as a new-candidate pass.

## Coverage limits

The initial review fetched all 723 then-open PR bodies and 296 Discussion bodies. Of 1140 listed comments/replies, 631 unique flat records were obtained before API 403/429; comment coverage remains incomplete. The normal post-reset quota check at 23:02:45UTC still reported zero and a past reset. Further REST requests stopped. `git ls-remote` failed `SEC_E_NO_CREDENTIALS`; no configuration or credential changes were made.

A separate ordinary-public-HTML refresh fetched and parsed 100 current PR primary bodies and 100 head fields at 23:15:22-23:15:41UTC, using the first 100 unique entries across five updated-open-PR pages. `references/RECENT-PRS.json` and `references/PINS.json` bind channels, dates, heads and source hashes. No higher complete-supplier claim was found in this bounded sample. Larger PR2802/2766 numbers are packing relaxations. PR2464's 0.001730427469823602 figure is a hypothetical shared ledger: its actual body says unchanged hosting pays both wrappers, the moment stays unchanged and no supplier is admitted. Recent QQ16, P104 and BIT component proofs retain supplier/physical/transfer obligations or disclaim new kappa; these costs are not silently treated as free. This review establishes neither universal novelty nor coverage of unpublished work.
201 changes: 201 additions & 0 deletions research/replica-tail-gain/LICENSE
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