Conditional κ = 7.51472114011902e-4: #307's fresh selections on the weighted gen5b word with #306's reorder stages

[rohanarun]

Conditional κ = 375736057005951/(5·10^17) = 7.51472114011902e-4, +1.32 × 10⁻⁸ over #306 (7.51458925311258e-4), +3.32 × 10⁻⁷ over #305, +3.96 × 10⁻⁷ over #275. The bit side binds below #233's complex supplier.

One self-contained package, research/gen5bw-full-reorder/, with its own workflow; branched from main, no existing file changed.

Full replay: PASS on the committed package: all fourteen stages fresh (virtual, raw, bit with descent and targets, kernel, second descent, restore, sink, reorder, reorder2, scalar, primes, banks, complex, math, finite), package integrity unchanged (171 files), PASS_IMMUTABLE_GEN5_KERNEL_RESTORE_SINK_FIVE_STAGE_BANKED_CONSTRUCTION, κ 375736057005951/500000000000000000, ~7 minutes.

Change

#306's package (eumemic's #305 composition on George Lydakis' weighted gen5b word, plus chafreaky's two reorder stages) with the kernel, second-descent, restoration and sink selections replaced by the ones re-derived on the weighted word in #307, and the two reorder selections re-screened on that word with #306's own discovery/build_reorder_selection.py:

stage	#306	this package
collective kernel entries (450-restart packing)	1,734, rank 2,196, φ −3,860	1,738, rank 2,200, φ −3,880.5
second constructed-frame descent	87 gates	90 gates
early restorations / terminal sinks	440 / 8	440 / 8 (R 15,424)
reorder (screened on this word)	237 moves, φ −495.07	234 moves, φ −493.29
reorder2 (re-screen)	2 moves, φ −1.18	2 moves, φ −1.18
κ	7.51458925311258e-4	7.51472114011902e-4

Transforms, checkers, pins plumbing, bank tiling, the weighted virtual word and producer are byte-identical to #306; the six selection files, expected/kernel-pins.json and MANIFEST.json (171 files) are the changed inputs, every changed count a recomputed pin (913 charts, literal stock 1,229,655, 721,438 weighted ADDs). The gain over #306 is #307's packing search and descent on the actual kernel word, carried through the reorder stages (the weighted word's kernel census is identical to gen5b's).

Verify

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

python3 -B research/gen5bw-full-reorder/verify.py --output /tmp/gen5bw-full-reorder-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 (14 fresh stages, 14 omitted-stage controls).

Scope and credits

Exactly #275/#305/#306's hypotheses and conditional interfaces; no Lean build. chafreaky (#306/#299: the reorder stage and its screen; #296 gen5b; #295 stages; kernel discovery), eumemic (#305 composition, #268), George Lydakis (#275 weighted matching), DreamingOfClouds, Dugongue, utcorvusvolat-dotcom, hcg890, Jacob Sussman, Evan McKinney and the retained lineage; the second descent and restart packing are from #291/#300/#307. 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: Composition of fresh weighted selections with reorder stages.

Review and limits: One source-bound stage stack; no arithmetic summing of independent claimed gains. Retain every stage and omission control.

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: 02d769b6a4dc1ac351bab06f4e9afd74d9c3995e. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.