κ = 8.04879370798932e-4: #362 with κ-exact min-cost carrier matching in the base producer (+3.0e-8)

[rohanarun]

Conditional κ = 201219842699733/(2.5·10¹⁷) ≈ 8.04879370798932e-4, +3.01e-8 over #361/#362 (8.04849251275843e-4, tied).

Stacked on #362, which is our composition of #357 (reordered-design PLAIN12 base) with #359's post-Design-T stages. The complex supplier is unchanged: Sussman's E8 unit. The bit side binds.

Change. In the base word's producer, Hopcroft–Karp carrier matching is replaced by the min-cost full matching with the κ-exact first-order weights J(r) = r ln(100/r), from our radical-campaign "I-matching" result (producer/matchlib.py). It is still a maximum matching, and R is unchanged.

Everything downstream is re-derived on the new word:

• Conditional κ = 7.76518649004426·10⁻⁴: the full transcript stage stack on #325's p10b word, priced against #327's p = 10 complex supplier (+0.888% over #325) #329 stages: 480 descent / 120 target / 240 restore / 10 sink;
• Design T + 470 twins;
• Conditional κ = 8.04303459176812·10⁻⁴: kernel, retiming and reorders re-derived on #354's Design T word (+0.0776 % over #358) #359's kernel: 335 entries, φ −403.88;
• retiming: 93 gates;
• reorders: 130 + 2.

On the staged word alone, before the post stages, κ is 8.0368457e-4 against 8.0365454e-4 with HK.

Every stage passes stagelib.full_check. The bit coarse saving comes from both engines, and #315's outer assembly gives 47 strict constraints, all positive.

Draft: the full verify.sh replay is running, and I'll post the PASS line here.

🤖 Generated with Claude Code

https://claude.ai/code/session_01TGoMCHAqctZe4wtb4qr7vv

[rohanarun]

Full replay: bash research/w3-design-t-staged-p10b-reorder-mc/verify.sh /tmp/out → PASS conditional kappa = 201219842699733/250000000000000000 = 0.000804879370798932 (manifest; staged/parity input hashes; Design T + 470 twins rebuild = shipped word; kernel/retime/reorder/reorder2 each with stagelib.full_check and frozen output hash; #346 control on #325 parity; #266 cohort legality + five-stage columns; nondegeneracy; bank tiling; E8 complex b; outer assembly, 47 strict constraints).

[Mister-Meeseeks]

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

Contribution: Moment-weighted carrier matching in the base producer.

Review and limits: Its own workflow tests a predecessor. PR367's exact-source full A/B benchmark supplies separate replay evidence for the 64-file PR364 package; producer-search reruns and downstream native obligations remain scoped.

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: f8c6a47abfec24b87cb1eb0a138dd73dfce2abe4. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.