Conditional κ = 7.46709720962478·10⁻⁴: gen5b — exactly optimal local design and a debt-10 all-but-one module on #285's word, #287's stages re-derived, #233's complex supplier (+0.348% over #287)

[chafreaky]

Conditional κ = 7.46709720962478·10⁻⁴: gen5b — an exactly optimal local design and a debt-10 all-but-one module on #285's word, with #287's stages re-derived and #233's complex supplier (+0.348% over #287)

One self-contained package, research/five-stage-gen5b-banks/, with its own workflow. No existing file is changed.

κ = 373354860481239/(5·10¹⁷) = 7.46709720962478·10⁻⁴, +0.348% over #287 and +0.525% over #285; bit coarse 7.47268·10⁻⁴, complex coarse 7.54736·10⁻⁴ (the bit side binds). This is a change of the bit word itself, before any entrance lever: it stands above #295's composed 7.45514·10⁻⁴ on its own, and the kernel, restoration and sink stages of #290/#295 can be re-derived on it.

The word

#285's generator is run byte for byte with #285's compile-cost-annealed pair module and two new module data files:

• Local design. An exact model of the generator's per-cube arc rule (discovery/local_model.py reproduces the compiler's 29 additions / 13 arcs / debt 16 on all 220 cubes) and a CP-SAT search over all 15¹² recipe-tree choices (discovery/cpsat_local.py) prove debt 16 optimal in this class — Conditional κ = 7.22869827347495e-4: a new paired-cube bit word (arc-aware local circuit, centre-sharing pair module) in the five-stage completed banks #276/Conditional κ = 7.42785663120535e-4: gen5 — compile-cost-annealed pair and all-but-one modules on #276's gen4 bit word, five-stage completed banks #285's design is optimal — and find an alternative optimum (28 additions, 12 arcs) that admits 1,726 compensated reuse pairs instead of 1,406.
• All-but-one module. The module's arc rule is combinatorial (verified frame-exactly on all 132 instances by module_model.py) and outputs can never be donors, so debt 10 is a floor; a symmetric CP-SAT model (cpsat_abo_sym.py) attains it with 35 additions and 25 arcs, against Conditional κ = 7.42785663120535e-4: gen5 — compile-cost-annealed pair and all-but-one modules on #276's gen4 bit word, five-stage completed banks #285's annealed debt 11. Conditional κ = 7.42785663120535e-4: gen5 — compile-cost-annealed pair and all-but-one modules on #276's gen4 bit word, five-stage completed banks #285 observed that a cyclic-interval debt-10 module costs the word 4.5%; this one lowers the word's descent cost 910,000.8 → 907,245.3 (−0.30%) with Conditional κ = 7.42785663120535e-4: gen5 — compile-cost-annealed pair and all-but-one modules on #276's gen4 bit word, five-stage completed banks #285's local design and to 905,892.5 (−0.45%) with the alternative one.

one invocation, m = 120	gen5 (#285)	gen5b
virtual auxiliary roles	17,292	17,160
compensated reuse pairs	1,406	1,726
independent dirty registers R	15,886	15,434
independent entrances (ranks)	2,554	2,234 (20 × 2,182, 21 × 34, 18 × 16, 17 × 2)
literal stock (60 replicas)	1,247,070	1,236,750
κ with #287's descent + target squares	7.44120696397042·10⁻⁴ (#287)	7.46709720962478·10⁻⁴

#287 ships frozen selections only; discovery/descent_search.py and target_search.py implement its stated rules (greedy concave descent of Σ r·ln(120/r) to frames on the operands' chains; squares with the literal F₂ response dependency, cut at the first target MOVE, close at the common next-need frame). On #285's word they reproduce #287's 904 gates and 220 squares exactly; on gen5b they find 904 and 220, committed as the package's selections. The complex supplier is #233's word (gcert/1 certificate of #256, Lean-checked in jacobalansussman/wht-power-saving-lean#2): with #193's supplier the bit side would sit only 0.025% below the cap.

Checks

The new word passes both retained checkers (PR168-v4, 5 mutation controls rejected; PR200 word classes, formal identity, 4 adverse controls rejected), and regenerate.py reproduces the five pinned bit files byte for byte. verify.py runs all nine stages fresh — virtual, raw, bit (descent and targets), scalar, primes, banks, complex, math, finite — with nine omitted-stage negative controls. Every #287 literal the new word changes is recomputed and re-pinned (word sizes, entrance histogram, path census 17,194, parity counts, scalar events and hash, bank patterns: (3⁴⁰) 531 → 51 and (24⁵) 159,984 → 158,400 per stage, 4,630,200 assignments, 250 charts, selector calls 736,388,225,400, κ); no check is dropped.

Verify

python -m pip install -r research/five-stage-gen5b-banks/requirements.txt    # sympy 1.14.0
python3 -B research/five-stage-gen5b-banks/verify.py --output /tmp/gen5b-verification       # about 4 minutes; not under -I
python3 -B research/five-stage-gen5b-banks/gen5bit/producer/regenerate.py --work /tmp/gen5b-regeneration

Scope and limits

• Conditional finite construction under the retained public all-size hypotheses (no Lean certificate for the bit side). Conditional κ = 7.42785663120535e-4: gen5 — compile-cost-annealed pair and all-but-one modules on #276's gen4 bit word, five-stage completed banks #285 and Conditional κ = 7.44136146100942e-4: two concave-descent retimings (904 + 111 gates) and 220 target-prefix squares on #285's gen5 five-stage banks #287 are open; their generator, pair module and stage code are reused unchanged.
• The pair module (debt 164 in Conditional κ = 7.42785663120535e-4: gen5 — compile-cost-annealed pair and all-but-one modules on #276's gen4 bit word, five-stage completed banks #285) was not improved here (2.7·10⁶ annealing steps at debt 184 on gen4 found nothing; trivial bound 56). The alternative local design raises the weighted payload ADDs (753,472 vs 566,912), which only enters the finite bill; all its checks pass.
• Not composed here: the kernel (Conditional κ = 7.44714499357628·10⁻⁴: 450 collective response-kernel entries on #285's gen5 word, after #287's descent and target squares (+0.080% over #287) #290), restoration and sink (Conditional κ = 7.45513573133379·10⁻⁴: early restorations and terminal sinks on the gen5 kernel word, with #233's complex word as supplier (+0.107% over #290) #295) stages; their re-derivation on gen5b is in progress.

Credits

Prepared by Chafik Boukhalfa with substantial Anthropic Claude assistance. Apache-2.0; lineage in NOTICE.md. The generator and gen4/gen5 word design (including the pair module and the compile-cost method) are DreamingOfClouds' (#276, #285); the descent and target-square stages are rohanarun's (#287; target-prefix mechanism eumemic's #268); the five-stage package is eumemic's source527 lineage on hcg890's #234 layout and Jacob Sussman's construction; the complex word is ours (#233/#256) on ikeboy's #193 and icekylinx's #144. This package contributes the exact compile models and CP-SAT optimality results, the alternative local design, the debt-10 module, the gen5b word, the re-implemented searches and the re-pinned checks.

[Mister-Meeseeks]

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

Contribution: Exactly optimal local debt design in its stated recipe class and gen5b construction.

Review and limits: Source-bound full Linux pipeline and producer regeneration. The local optimum is scoped to that decoder/debt class; it is not a global primitive optimum or a bound on other topologies.

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: b15a33ce4f0e31379be685139f78b9c1e7ffa77b. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.