κ = 7.69557449978832e-4: three rank-two kernels after frozen PR322

[eumemic]

κ = 7.69557449978832e-4

Three additional rank-two response kernels improve frozen #322 from 30782267613603/40000000000000000 to 769557449978832/10^18. The exact gain is 759638757/10^18. This remains a conditional finite construction, with the bit supplier binding.

The three disjoint four-helper relations use pivots 7000, 7234 and 7349 on #322's final scalar word. They remove 32 compensation ADDs and add 18 setup/restoration ADDs, for 14 fewer ADDs. Their actual local paid-profile change is {1:+12, 2:+9, 3:-12} and their total new entrance rank is six. Explicit width-100 banks with 300 replicas retain all three without adding a rank-balancing kernel or padding.

research/p10-presink-three-quads/ is self-contained. It vendors the immutable #322 package (manifest 32d0bc5569f3bbdcbc488d88f06c688f07b905870db730dd63e1f0920ff627c7) and its exact #320 dependency, then runs the predecessor's full strict verifier before transforming the emitted word. It checks source and dirty restoration, both reflected frame ledgers, complete paid profiles, exact prime/chart coverage, all role/replica/stage bank assignments, both rational moment engines, the full rank-one fallback, all 47 assembly inequalities, and the complete finite invoice.

Validation: two fresh complete immutable replays and a separate C++ audit of the literal word, inverse, dirty restoration, both paid ledgers and tiling. Omitting the new kernel restoration causes nine rows to fail. The final word has 386,904 records and 336,239 ADDs with 8,223 dirty helpers. There are 427,872 banks per stage and 12,334,500 enumerated helper assignments; literal stock is 3,291,360. The literal profile has 75,078,000 paid children, rank mass 328,524,000 and deficit 612,000. The selector charge is 1,951,324,377,000; the counted primitive coefficient is 127,531,482,262,151,501 and the payload bound is 98 bits.

python -m pip install -r research/p10-presink-three-quads/requirements.txt
python -B research/p10-presink-three-quads/verify.py --output /tmp/p10-three-quads-proof --cxx g++ --boost-include /usr/include

The inherited BANK-REVIEW.json diagnostic saved_literal_banks = 23790 uses the original PR315 stock as its reference. The incremental stock saving against #322 at 300 replicas is 90 families (3291450 → 3291360); the exact price and invoice use the absolute stock, not that legacy diagnostic.

A dedicated CI workflow runs this full offline replay. The exact bit root is 770150125081479/10^18; the unchanged complex supplier is 772714351296671/10^18.

The result retains the inherited all-size compiler, weighted-selector, common-chart, restored-row, routing, prime-supply, precision/recovery, complex-symbolic and analytic interfaces. These finite checks do not establish those hypotheses.

Provenance: #322's four frame retimings; Chafik Boukhalfa's #320 transcript stack and kernel transform; DreamingOfClouds' #315 p=10 word and complex supplier; and the earlier source527, transcript, kernel and five-stage contributors. All original Apache-2.0 notices and Anthropic Claude/OpenAI disclosures remain in the vendored snapshots. The new selection, 300-replica admission, packaging and audits were prepared with substantial OpenAI Codex assistance.

This new branch and PR leave #322 and every earlier published head and claim frozen.

[Mister-Meeseeks]

Thank you @eumemic. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Three rank-two kernels after the frozen presink word.

Review and limits: Original CI fails before replay because its dependency path is wrong. PR324 changes only that workflow path; its full replay covers byte-identical scientific sources here.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: e51f5ffee8ab574e5b8249a4612411b2ca5f100d. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.