Improve conditional κ to 0.00172009662868483 with shared kernels

[Lyy-iiis]

The previous fixed-word packing had only about 1e-9 of room above #2848. This contribution changes the literal local words and constructs a new chronological allocation, completing the conditional finite supplier and modern outer release at

κ = 0.001720096628684832600972 − 10^-46 − 10^-70.

The exact gain over #2848 (c50d12e4720cd1fef2b5a65e337e37de9731879a) is 1438120379902596153 / 10^24 ≈ 1.43812e-6. The exact comparator also exceeds concurrent #2853 (d01045dfb67428679618027dff552f1d032fa999) by about 7.18970e-7.

What changes

Only research/shared-kernel-repacking/ is added. Four staged raw-dirt kernel changes reduce helpers 460/462/478/480 from width 9 to 8. Delaying within-pair mixing and changing the compensation basis gives a paid local delta 12 H1 − 8 H2, including inverse cleanup. A new T37 fill assigns all 135864 helper roles in 333 calls, with every idle child charged. The actual full profile and independent exact moment bracket are included.

Concurrent credit: @philippeVV's #2853 treats the same four A-phase helper quartets, using a different early-read schedule with delta 20 H1 − 12 H2. No priority or exclusive helper-selection claim is made. This contribution adds the cheaper staged word, new actual owners, exact comparisons and independently implemented checks. Source words are Jeremy Kothe's #2833 at e9307b48d7d1b690939935ecef0f8e524e6d92f4; allocation construction credits Marius-Paul Dumitrean's #2843, and the native/outer lineage retains Dugongue, Tekalign and all predecessor notices.

Evidence

• Full portable replay passed, including two fresh changed-provider native chains, unchanged strict admission predicates, physical/prefix/precision invoices and the modern outer release. Release receipt SHA256: c052decb90ceae345b398f111781f567fb787309a528877500cf7fe1cff13b3d.
• Separate exact local, chronological owner, full-pattern primal/dual and integration-derivation checkers. The complete release evidence, source manifests, cache receipt, logs and corruption controls are included.
• The local profile's coverage-law cap is about 0.001758838084; the headline realizes 97.797326789% of it. The tighter changed-inventory fractional cap is 0.001720100805416885927945; the realized gain is 99.71041112% of its available gain over T248 residue exchange: conditional κ ≈ 0.00171865850830493 #2848.
• An initial run exposed a no-op inherited geometry mutant: setting call counts to 333 did not alter the new T37 input. The derived test now subtracts one from each actual count and requires a changed input before the unchanged predicate. All six controls remain required; the full replay then passed. Both failed and corrected evidence are preserved.
• Bounded stdlib replay commands are registered in VERIFY.json. Metadata and direct executions passed locally on Python 3.13.7. Generic CI targets Python 3.12; no hosted CI or fresh Lean result is claimed. Allocation regeneration compares the complete decompressed payload, with alternate-container and changed-payload controls.

Scope and remaining work

This is author-checked conditional finite evidence with separate AI-assisted audits, not maintainer acceptance or an unconditional theorem. Two retained native chains and the 16-stage retained parent proof are explicitly reused by full-tree source hashes; this is not a cold replay of every predecessor. All inherited all-size compiler, source-access, hosting, precision/tape and analytic obligations remain. No selected record, predecessor package or global priority is modified.

Started from current main, refreshed through 130a7ce63a233e6812b7c037993c721fec827014 (priority revision 5), and rechecked updated open PRs and Discussion #2612 before submission. #2855's newer T372 result is weaker; no global novelty claim follows from this bounded overlap coverage.

Canonical coordination: #2612 (comment)

Prepared for Yiyang (@Lyy-iiis), with substantial OpenAI Codex assistance for research, implementation, separate construction/audit agents and publication. Apache-2.0; original notices retained. The README supplies exact replay commands, limitations and scoped next questions.

Post-submission overlap readback also found #2856 (7a43b24c4b6729d171f3a2a11ef3b7dc77aabaa4), a four-owner vacancy relay on #2853 with reported conditional target 0.001719378870495538841812 − 10^-46 − 10^-70. Its reported target is below this contribution. It was not used as a source; the package's exact authenticated comparison gates remain the pinned #2848 and #2853 claims. Its reference to the then-local-only Discussion2612 lead now has the public artifact linked above.

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