Punctured star bit unit: bit c = 0.00165947204563779652541 (+4.54% over #510)

[DreamingOfClouds]

This adds one self-contained package, research/e8-punctured111-star/: an E8 bit word with 111 live ports (9 of #493's 120 labelled lines punctured) whose nine decoder totals are rank-7 pseudo-target helpers (decoder constant 63, not 72), R = 489 helpers, and the parameterisation of #493's hosted-audit chain that prices it.

quantity	value
bit c, eleven stages, eight pooled replicas, every residual whole and hosted (10^-24 grid; #472's pipeline as #493 runs it)	165947204563779652541/10^23 = 0.00165947204563779652541
live bit c: #510's R480 word at nine stages (the bit supplier of #535)	0.001587447106092548137108 -> +4.54%
#503's R480 word, same pipeline (reproduced)	0.001574753352953808650916 -> +5.38%
independent pricing harness, same word	equal to all 24 digits and the same profile
c under a stricter hosting (one helper per family copy per stage)	>= 0.001651282591289915996071 (at most 0.49% lower)
κ with #535's complex b (1589991533606044174031/10^24)	0.001587467473762886 = 793733736881443/5*10^17, complex-bound, +0.16% over #535 (0.001584931111785787)

For context. #543 (eumemic, 420 helpers, unpunctured, nine-stage) reaches c = 1.653827e-3; this word's c is 0.34% higher.

On κ. #535's complex b is 4.37% below this unit's c, so κ is complex-bound and moves by only +0.16% over #535. The same outer code reproduces #535's published κ (0.001584931111785787) from #510's bit c and the same b (step 9, control). The bit word raises the cap: any future complex b up to about 1.659e-3 would now be bit-slack. Nothing here claims more than that.

What it is

• PR Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493's quad skeleton restricted to 111 live lines (P = [39, 52, 57, 71, 76, 78, 103, 109, 114], one punctured line in each of nine 4-frames; lines 0..7 stay live). Each punctured line leaves a rank-7 total, a helper that reads exactly what the removed target would read; the nine totals cannot sit on dead registers (rank 7). verify.py rebuilds the word byte for byte from Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493's frozen plan.
• Rank-mass identity M*live - mass = T(10v - 11 cst) (telescoping, any v): 3336 for v = 111, cst = 63 (3264 at v = 120, cst = 72).
• Payload 91 bits < 104; 636 frames, all Gram > 0 (prime 2 only); exact F2 on all 711 columns.

The parameterisation

code/adapt.py writes adapted copies of nine of #493's files by 55 exact string edits (each anchor counted); the parent tree is untouched, nothing is read from the environment. One configuration (code/punct_cfg.py): v, R and the live labels come from the word, the copy-rank sum (63) is replayed from the word, derived again from the records by audit.py and the two must agree. The cited complex b enters assemble.py as a bare rational; the bit v is not tied to any complex port count (mutant M6 sets v := 112 and is refused).

Checks (verify.py, --light skips #493's own verify.sh)

Independent checker for v <= 120 plus an E8-membership check, interface.py, the word-level mutants, the official legality / five- and eleven-stage column checkers (24/24 omitted-bridge controls), exact Gram, #442 hosting rediscovery, #472 emit and independent audit (22 template mutations), the 47-inequality outer assembly with controls, and the pricing harness.

• Regression: Bit word R480: totals on dead registers, c = 0.001574753352953808650916 (+0.595% over #493) #503's R480 word through the stock chain and the adapted chain: GLOBAL.json, GLOBAL-TEMPLATE.json.gz, AUDIT.json, RESULT.json byte-identical; c, profile, emitted-program sha256 and the three κ equal Bit word R480: totals on dead registers, c = 0.001574753352953808650916 (+0.595% over #493) #503's EXPECTED.
• 8 mutation controls, all rejected: a dropped gate and a wrong frame (relaxed checker), a payload overflow (legal and F2-correct; refused only by columns_h), a hosted-cell collision, a helper hosted on the family the call acts on, a cheaper profile claim, v tied to 112, the stock Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493 emitter.

Scope and caveats

• Hosting stacks helpers on one family. The hosting is the pooled whole-residual programme of Conditional κ ≈ 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434) #442 / Conditional κ = 0.001292099559442278: R715 shared kernel, target mixing and whole hosting #472 / Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493 (hosting_core.solve): in 82 of 88 calls several helpers of one invocation share a family (at most 7) at disjoint cells, so Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458's literal one-owner-per-family rule is not met. This is inherited: Bit word R480: totals on dead registers, c = 0.001574753352953808650916 (+0.595% over #493) #503's accepted emitted program does the same in 80 of 88 calls (reproduced). Mutant M4a tests cell collisions, not Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458. Under the stricter "one helper per family copy per stage" rule c >= 0.001651283 (at most 0.49% lower) and κ is unchanged.
• The word is checked as a bitE8/1 word with 111 labels in the 120-line E8 system; everything Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493 and Conditional κ = 0.001292099559442278: R715 shared kernel, target mixing and whole hosting #472 assume (all-size compiler, common-label/mutable-basis interface, whole-call hosting) is assumed unchanged. No unconditional claim.
• Eleven stages only: the nine-stage hosting wall is R <= 4v = 444. Of 414 sampled punctures, 304 reach R = 489 and 110 need 1-3 Q-node junk wires; the shipped word has the highest c found. No claim that 489 is a floor for other skeletons.

Credit

#493 (eumemic) for the skeleton, the word family and the chain; #523 (icekylinx) for the puncture pattern on the complex side; #503 (DreamingOfClouds) for the dead-total variant and the adapt.py pattern; #472 (chafreaky), #442 (DaysSky), #445, #386, #370 (Dylan Crow), #381, #315 for the pipeline and checkers; #510 for the live bit c; #535 (icekylinx) for the cited complex b. An independent audit supplied the stricter-hosting repricing.

Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.

🤖 Generated with Claude Code

[Mister-Meeseeks]

Thank you @DreamingOfClouds. This contribution at 376426f3b2b26ab430d10baf16bbd9ff42990a7c is incorporated in the reviewed family through #588, published in 9594b61.

Puncture removes nine ports and retains nine rank-seven totals. Finite word and decoder receive actual column/frame audits. Pooled cell hosting is NOT the one-helper-per-family hypothesis of PR458. Stricter price458 is a numerical auxiliary proposal, not a completed emitted witness.

Preserved implementation and research:

• research/e8-punctured111-star

The family review and individual disposition record the scope, evidence and attribution. Parallel and intermediate contributions remain credited even where a later composition has a stronger bound. The published multiplication bound remains conditional on the documented compiler, realization, hosting and analytic assumptions; these finite checks are not a full Lean multiplication proof.