Conditional κ = 7.51154847341386e-4: 1,738 kernel entries, 90-gate second descent, restorations and sinks re-derived fresh on #275's weighted gen5b word

[rohanarun]

Conditional κ = 375577423670693/(5·10^17) = 7.51154847341386e-4, +1.43 × 10⁻⁸ (+0.0019 %) over #305 (7.51140529238897e-4), +0.0105 % over #275 (7.51075693834608e-4). The bit side binds below #233's complex supplier.

One self-contained package, research/gen5bw-full/ (#305's package with its selections re-derived), with its own workflow; branched from main, no existing file changed.

Full replay: PASS on the committed package: all twelve stages fresh (virtual, raw, bit with descent and targets, kernel, second descent, restore, sink, scalar, primes, banks, complex, math, finite), package integrity unchanged (167 files), PASS_IMMUTABLE_GEN5_KERNEL_RESTORE_SINK_FIVE_STAGE_BANKED_CONSTRUCTION, κ 375577423670693/500000000000000000, ~7 minutes. Note: #306 (chafreaky, reorder stage on #305) is above this PR; the composition of that stage with these fresh selections follows as a separate PR.

Change

#305 translated #300's 1,734 kernel entries and 87 second-descent gates onto George Lydakis' weighted gen5b word by logical helper roles. Here every selection is re-derived on the weighted word itself by the same discovery scripts (discovery/coll/load.py → families.py → pack_restarts.py → build_selection.py; descent4g; build_restore_selection.py; build_sink_selection.py), with a longer randomized packing search:

stage	#305 (translated from #300)	this package (fresh on the weighted word)
collective kernel entries (450 restarts, seed 21)	1,734, rank 2,196, φ −3,860	1,738 (920 pairs, 427 triples, 391 quadruples), rank 2,200, φ −3,880.5
second constructed-frame descent	87 gates	90 gates (delta {1: +39, 2: +153, 3: −81, 4: −51, 5: +27, 7: −48, 9: +24, 12: −24, 14: +24, 18: −39, 19: +39})
early restorations	440	440
terminal sinks	8 (R 15,424)	8 (R 15,424)

The twin/collective census of the weighted word is identical to gen5b's (952 pairs, 2,104 triples, 3,807 quadruples; plain greedy φ −3,799, 1,720 entries), so the gain is the packing search plus the descent run on the actual kernel word. Transforms, checkers, pins plumbing, bank tiling, #275's weighted virtual word and producer are unchanged from #305; expected/kernel-pins.json and MANIFEST.json regenerated (167 files). Every changed count is a recomputed pin; none dropped.

Verify

python3 -m pip install -r research/gen5bw-full/requirements.txt

python3 -B research/gen5bw-full/verify.py --output /tmp/gen5bw-full-verification

Python 3.11+, SymPy 1.14.0, new output directory outside the package; about 7 minutes; prints PASS_IMMUTABLE_GEN5_KERNEL_RESTORE_SINK_FIVE_STAGE_BANKED_CONSTRUCTION with the pinned κ.

Scope and credits

Exactly #275/#305's hypotheses and conditional interfaces; no Lean build. George Lydakis (#275: weighted gen5b matching and package), eumemic (#305: the composition this re-derives), chafreaky (#296 gen5b, #295/#299 stages, kernel discovery), DreamingOfClouds, Dugongue, utcorvusvolat-dotcom, hcg890, Jacob Sussman, Evan McKinney and the retained lineage; the second descent and restart packing are from #291/#300. Prepared by Rohan Arun with Anthropic Claude assistance; Apache-2.0; lineage in NOTICE.md.

🤖 Generated with Claude Code

[Mister-Meeseeks]

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

Contribution: Fresh kernel packing and second descent on weighted gen5b.

Review and limits: Independent parallel selection improvement, with all downstream restorations and sinks re-derived. Credit the weighted word and earlier kernel mechanisms separately.

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: b4f85afd6a54a2d593519c59690586a34fac2dfc. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.