Conditional kappa 0.001467978682990812: paid circuit retirement on the 112-port supplier

[Dugongue]

Result

Conditional kappa = 0.001467978682990812, exactly 366994670747703/250000000000000000.

• +0.046974% versus updated Conditional kappa 0.001467289440740487: rank-sector factory on 112 ports #473's frozen ranksector112 candidate, 0.001467289440740487.
• +0.688155% versus Punctured Hamming ports for conditional κ = 0.001457945761723368 #523's 112-port claim, 0.001457945761723368.
• +4.674157% versus our preceding checked deliverable, 0.001402427047420522.

The complex supplier binds at b = 735068406246315949703/500000000000000000000000. The unchanged cited #493 bit supplier remains c = 391360506745414227149/250000000000000000000000. The new contribution beyond the public combination is modest; most of the larger previous-deliverable comparison comes from incorporating the credited 112-port advance. This is not an unconditional multiplication theorem or a claim to beat proposals under different interfaces.

New concrete mechanism: optimize the circuit together with its physical complement

Maximizing the number of canceled response pivots is not the same as minimizing the complete recurrence moment. Some pivots save a first-frame increment but impose costly donor entrance work. We retire two closed components of the 99-pivot rank-sector provider, rebuild every dirty-response correction, and pay for the resulting wider helpers through an explicit physical allocation.

The retired components are:

E=[6]:   donors 9,11,12,508,509,511; pivots 8,13,14,184,185,510
E=[480]: donors 272,273,298; pivot 299

Every retained pivot relation has zero coefficient on the retired donors. Exact rational reconstruction leaves 92 pivots and all 560 dirty helpers. The local histogram delta is {1:-15,3:+6,5:-4,6:+4}, adding seven units of local rank mass. Seven helper widths grow from eight to nine in each of 72 complete calls. The new owner map pays for all 504 extra residual axes from actual idle remainders; there is no free storage, ignored spectator or split recursive oracle.

We also apply exact backward-observation slicing: 140 additions and 70 scalings have zero suffix response to the target outputs, so they and their 210 inverse-cleanup instructions can be removed. This saves 420 scalar instructions while preserving every arbitrary dirty input and the paid frame profile. It is not counted as a separate exponent gain.

The selected local 112-port profile is

{1:2451,2:182,3:522,4:88,5:238,6:128,7:1,8:1}

with residual widths {7:18,8:154,9:388}. Twenty strictly improving same-call owner exchanges and the provider transfer produce the full global profile

{1:176472,2:13104,3:40938,4:6336,5:20406,6:9216,7:132,8:72,48:230}

Its rank sum is 520704 = 73*7168-2560. Live stock is 7168, physical stock 7738 and deficit 2560. Every one of 40,320 whole-helper uses, 16,128 pending bins and 3,214 actual 73-column orthogonal charts is reconstructed and independently checked. The entire final profile is priced through the existing outer assembly; separate PR gains are never added.

Four proved construction lemmas, all used

1. Closed response-circuit retirement and paid accounting. Exact support closure preserves retained response identities. Retiring donor/pivot sets changes the histogram by sum_h ([f_h]-[f_h-e]) - |D0|[e]; residual width growth equals added local rank mass. This is the selected source transformation.
2. Reversible observable slicing. A background write whose coordinate has zero exact suffix-observation column can be deleted if cleanup is regenerated. Closed background updates and invertible elementary gates prove arbitrary-dirt restoration. This removes the 420 actual scalar instructions.
3. Isolated-register restriction. With no cross-boundary gates, restriction commutes with every retained program prefix, including arbitrary dirty inputs. This supplies the scalar proof for the credited Punctured Hamming ports for conditional κ = 0.001457945761723368 #523 eight-port removal; its physical cover and invoice are still explicitly rebuilt.
4. Colored whole-owner exchange and provider transfer. Within-call permutations preserve the whole-family set and its chronology. Explicit capacity checks and new source-bound charts realize changed widths. Strict remainder majorization proves exchange-only moment improvement for every exponent in (0,1); the provider change is accepted only through its complete final profile.

Full proofs are in proof/, with exact constructors and receipts. These are newly written proofs for this composition, not four claims of global mathematical originality or four independent numerical gains. Response kernels, direct-sum restriction and majorization have credited ancestry. No new Lean certification is claimed.

Direct sources and credits

• Punctured Hamming ports for conditional κ = 0.001457945761723368 #523, head a900f98be8ff2c09d3292b5112d4731dbd0c8438: eight isolated ports, the 112-port local restriction, cover reconstruction and physical-stock reduction. This is the main inherited gain over the previous deliverable.
• Conditional kappa 0.001467289440740487: rank-sector factory on 112 ports #473, updated head c26b3cc74d0203948f973a41d38340116c79dab8: the public ranksector112 combination, owner-map seed and source-bound independent audit adaptations. Our comparison is against this updated candidate, not its older weaker word.
• Conditional kappa 0.001402213284556683: rank-factor coordinate totals merge 56 recursive pairs #522: direct 99-pivot rank-sector source, which combines response-kernel entrances with coordinate-total rank-factorization. Its complete local ancestry is vendored for offline reconstruction.
• κ = 0.001363614743745701: partial-own factory with 84 kernel pivots #507, 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: partial-own factory, exact gauge/kernel constructor, physical wrappers, whole-owner parent and finite 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 integrations.
• Asynchronous whole-owner replicas: kappa 0.001357701757628940 (+1.9236% over #496) #505, Conditional kappa 0.001372554837726243: coordinated gauge collapse with retimed asynchronous whole owners #508, Conditional kappa 0.001391523459591829: partial-own factory, 92 pivots and asynchronous whole owners #514 and Conditional kappa 0.001393662920776407: blockwise pair exposure, 99 pivots and whole-owner allocation #518: asynchronous complete-invocation scheduling, pair-cover and source lineage. 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 without redundantly reconstructing its operator.
• Open asynchronous whole-owner allocator and a delivery-layer map of the complex word #520: explicit allocator/delivery and matching perspective, used as research context. Conditional κ = 0.001369588870945540: retimed word with asynchronous whole owners #506: composition and portability feedback. Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458: spectator/whole-owner 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.
• Carry-graded box convolution removes exponential axis-padding overhead #524: carry-graded box convolution read as a possible future route; its unpaid routing/table/Schur work is not silently imported as a saving. Kernel102 checkpoint: full cold reconstruction and exact fixed-word ceiling #525: kernel102 cold checkpoint read and compared; no numerical gain is attributed to it.

The snapshot is frozen through #525. SOURCES.json pins current heads; vendor/base120/SOURCES.json retains earlier source pins, including OpenAI proof-source explorations. Original attribution and license material are preserved. Later proposals are left for the next sweep.

Reproducibility and exact checks

From research/observable-circuit112, using Python 3.11 or later with assertions enabled:

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

Standard library only, offline. All 27 stages passed on a fresh CRLF copy, with mandatory manifest and expected-result checks:

• 800 arbitrary-input columns in both orientations before restriction, and 92 omitted-correction controls;
• all 784 columns after restriction, exact Gaussian phases, frame transitions and normalized residual wrappers;
• independent physical chronology, all owners/charts/remainders, 19 rejected controller corruptions and a separate raw audit that imports neither the emitter nor the hosting checker;
• the actual scalar/Horner prefix and row invoice: 206 bits required versus 512 charged; physical row coefficient 16467 versus allowance 20161;
• two exact rational moment engines, adjacent-endpoint rejection, six explicit bootstrap steps and all 47 strict outer inequalities.

Canonical template SHA-256:

59138bef1f8e23fb5f1b1692b137dbae801f51667da142973f7ec393f8b4c1dd

The selected owner file is stored in stage order. We fixed an order-sensitive receipt discrepancy by hashing chart streams in actual invocation/helper order; all matrices and the profile already agreed. No mathematical check was weakened. Gzip generation pins level 9, timestamp zero and OS byte 255; text manifests normalize only CRLF/LF. Changed tokens, missing inputs, missing manifest/expected result and optimized Python reject before output creation. The browser-upload batches are reassembled and checked byte-for-byte.

Local execution was Windows Python 3.11; no unexecuted Linux, macOS or Python 3.14 run is claimed. Historical vendor documents describe their ancestor, while the root verifier, manifest and expected result define this derivative.

Preserved research and scope

RESEARCH.md and research-notes/ record the losing S100/112 transfer, the winning 99-to-92 circuit trade, bounded deletion screens, neutral frame-lowering attempts, the stable-carrier quotient lemma and its failed lifetime screen, and the fully charged K5 architecture nomination. A failed bounded search is not an impossibility theorem; no global optimum is claimed.

Inherited all-size compilation, common-label/mutable-basis transport, normalized Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. This is a finite conditional construction with a fully recounted improvement, not an unconditional integer-multiplication theorem. Nothing in the package publishes or modifies GitHub.

[Mister-Meeseeks]

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

Contribution: Paid kernel-circuit retirement with a wider physical complement.

Review and limits: Fewer pivots can improve the final moment when wider residuals are fully hosted. Full dirty compensation and changed ownership are required; bounded losing routes remain research notes.

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: 9b8a8ece611da59ef93a05820da66c5bdb9026c7. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.