Conditional kappa 0.001393662920776407: blockwise pair exposure, 99 pivots and whole-owner allocation

[Dugongue]

Result

This constructs and independently replays a new complex supplier giving conditional kappa = 0.001393662920776407, exactly 1393662920776407/1000000000000000000. It improves our preceding checked construction, 0.001391523459591829, by 0.153750%. The complex side binds at b = 697803963898659915203/500000000000000000000000; the unchanged cited PR493 bit supplier has c = 391360506745414227149/250000000000000000000000.

The inherited all-size compiler, common-label/mutable-basis interface, normalized Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. This is not an unconditional multiplication theorem or new Lean certification. Larger submissions with different or disputed interfaces are not treated as comparable verified baselines.

New mechanism

Instead of using a uniform pair choice throughout the local fourteen-block factory, choose pairs blockwise and reconstruct the exact downstream decoder. The selected witness uses option [0,0] everywhere except blocks (0,2,4,6) and (0,3,4,7), where it uses [1,1]. This changes the exposed intermediate rows, rather than merely changing coordinates within an identical response class.

The construction retains the preceding four coordinated rank-two gauge reductions and compatible scalar-body retiming. Exact response reduction now yields 99 cancellations rather than 92. The local paid profile is {1:2530,2:182,3:516,4:88,5:298,6:68,7:1,8:17}; residual widths are {7:18,8:161,9:381}.

Constructive width-dominance transport and pattern exchange then produce a new literal whole-owner allocation. Eight replicas retain the complete-invocation order (7*stage+6*replica, stage, replica). All 40,320 helper uses have explicit legal owners, and every remaining pending factor is paid. The complete global profile is {1:182160,2:13104,3:40196,4:6336,5:25064,6:4896,7:164,8:1224,48:796}. Ambient dimension 73, live stock 7,680, physical stock 8,258 and rank deficit 2,496 are unchanged.

No helper is split across owners, no scalar instruction crosses an unfinished invocation, and headline gains are not added.

Direct credits and context

• κ = 0.001363614743745701: partial-own factory with 84 kernel pivots #507: partial-own factory, old response reference and pinned retiming map.
• Complex supplier b ≈ 1.327·10⁻³ (+4.7%) on whole-residual hosting: shared-donor kernel and entrance gauges with paid residual wrappers (conditional on two lemmas) #484 and Conditional κ = 0.001332077359286333: pooled whole-owner complex supply #496: gauge/kernel construction, paid wrappers, whole-owner parent and invoice ancestry.
• Add combined E8 witness at κ = 0.001307044366925301 #495, Conditional κ = 0.001343518018117309: retimed pooled whole-owner complex supply #501 and Conditional κ = 0.001343518018117309: retimed gauge word with pooled whole owners #502: scalar-body retiming and its integrations.
• Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493: unchanged cited bit supplier; its published histogram is repriced, not its whole operator reverified.
• Conditional kappa 0.001467289440740487: rank-sector factory on 112 ports #473: gauge inspiration and updated scheduling comparison; Asynchronous whole-owner replicas: kappa 0.001357701757628940 (+1.9236% over #496) #505: our earlier asynchronous complete-invocation schedule; Conditional κ = 0.001369588870945540: retimed word with asynchronous whole owners #506: related composition and portability feedback.
• Add categorized experiment log: 100 ideas, 300 trials, and recorded failures #477: experimental records consulted. Conditional kappa 0.001372554837726243: coordinated gauge collapse with retimed asynchronous whole owners #508 and Conditional κ = 0.001388049083313897: fresh partial-own asynchronous whole-owner certificate #512: public asynchronous partial-own comparison points.
• Lemma G of #484: clean proof and Lean 4 formalisation of its core #509: abstract Lemma G proof context. Bit word R480 at nine stages: c = 0.001587447106092548137108 (+1.41% over #493) #510: stronger but nonbinding bit headroom. [Lean] Add checked binary count dispatcher #511 and [Lean] Add sequential completed-bank source bindings #513: formal dispatcher/completed-bank work. These are acknowledged without claiming their formal results were recompiled or add numerical gains here.
• Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458: whole-owner spectator wrappers; Split centres and source-basis reuse for conditional κ = 0.001120864952258278 #433, κ = 1.048005508028206e-3: mutable-basis Hamming packets (≈2^-9.89814; conditional; complex +4.97%) #425 and κ = 8.75481145306751e-4: first E8 bit word (complex-bound; +9.29% over #352) #370: geometry and scalar/phase compilation; Conditional κ = 8.04849251275843·10⁻⁴: post-Design-T kernel, retiming and reorders on #357's reordered base word with all 471 twins (+0.0679 % over #359) #361 and Conditional κ = 7.64230861320245e-4: the paired-cube bit word at cube size p = 10 (h = 20, m = 100), with a new centre-sharing complex supplier (+1.21% over #314) #315: exact moments and outer arithmetic; Conditional kappa 0.001249035299298004: hosting-selected rank147 kernel #434, E8 bit supplier c ≈ 1.044064·10⁻³ in the nine-stage word (+2.2 % bit cap; no new κ, complex-bound) #417, κ = 0.001128832830332521: #417's shared-donor kernel on #433's R758 bit word (+0.71%) #435, κ = 1.136403735815528e-3: R740 shared-donor kernel with 57 primitive frame changes #440, research: response-subspace gauges and two-sided normalization, kappa = 1.013310887459710e-3 #401, κ = 1.017022657082799e-3: 205 shared-donor gauges with 64-replica banks #408 and κ = 1.017798035290733e-3: propagated frames admit 214 entrance gauges #416: response-kernel/gauge ancestry.

SOURCES.json pins direct dependencies and separates ingredients from context. The snapshot is frozen through #513.

Four OpenAI-source research routes

The appendix preserves mathematical rules, source hashes and bounded experiments from four distinct proof families in OpenAI math at adc7f1241b42e322a6451854ab7e4b4c146bf78a:

1. HoneycombChords sparse interpolation/Newton evaluation inspired blockwise exposure choices and exact decoder reconstruction; this contributes to the selected word.
2. MatchingCount unit flow/mincut and perfect matching inspired constructive ownership transport and pattern exchange. The new allocation contributes; the separate cut-guided scheduling experiment did not win.
3. ThinTrees rational Schur history inspired paid internal-register elimination. Four finite screens found no legal cheaper witness.
4. QuantumCircuit pruning inspired the exact sufficient condition (U-I)R=0 on all reachable input columns. Both orientations of the new program have 3,700 positive child sites; no zero-operand candidate survived modular screening.

These are source-inspired adaptations, not four imported Lean theorems or four numerical gains. No global originality claim is inferred from the search. Alternative losing architectures and the sufficient conditions for future use are documented rather than counted as savings.

Reproduce and validation

From research/nodal-pair-async, with Python 3.11 or later and assertions enabled:

python -B verify.py --work /absolute/path/to/a-new-output-directory

Standard library only; no network, optimizer, C++ compiler or Lean required. Fourteen stages rebuild the word, check all 800 arbitrary-dirt columns in both orientations and 99 correction-omission controls, verify exact Gaussian phases and physical wrappers, audit all whole owners and remainders, recount the finite invoice, and execute two rational moment engines and all 47 strict outer constraints. Adjacent-price and invalid assembly controls are rejected.

The actual scalar envelope requires 21 local prefix bits and 206 global bits, below the retained charge of 512. The inherited meaningful owner-alias control remains in place. A full fresh replay passed with every recognized package text file converted to CRLF. Missing inputs, changed tokens and optimized Python are rejected before output creation. No hidden file is required; LF/CRLF normalization does not ignore any other content. No Linux or Python 3.14 execution is claimed from this Windows test.

The package includes the exact expected result, complete assembly receipt, portability receipt, source credits and research appendix. Nothing has been published by the tooling.

[Mister-Meeseeks]

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

Contribution: Blockwise pair exposure and 99 response pivots.

Review and limits: Changes the factory rather than only coordinates within a fixed response class. Complete dirty restoration, physical owner maps and prefix/invoice bounds are recomputed.

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: e0a071dce251eeca96d446f73147048cfebbd5c7. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.