Conditional kappa 0.001467289440740487: rank-sector factory on 112 ports

[rohanarun]

Conditional κ = 0.001467289440740487, exactly 1467289440740487/10^18; complex b = 0.001469445542668988969610. 0.6408797% above #523 at pinned head a900f98be8ff2c09d3292b5112d4731dbd0c8438. The complex side binds; unchanged #493 bit supplier remains nonbinding.

research/ranksector112-async/ composes #522's rank-sector99 factory with #523's removal of eight isolated coordinate ports. Every helper is reassigned to a whole physical owner using width dominance, and offsets are compacted within the existing idle families. All40,320 roles have explicit owners; no helper is split and no unfinished invocation is interleaved. Live families7,168; physical7,738; deficit2,560.

The early draft's full finite composition checks have passed. Independent full source522 and source523 Python3.14 replays passed. The changed112-port local word passes exact restriction/transport, both-orientation arbitrary-dirt scalar/frame replay, Gaussian phases and paid wrappers. Fresh global restriction, controller/owner/chart audits, independent raw reconstruction, finite invoice, two exact moment engines, six bootstrap levels,47 strict inequalities and four outer controls pass. The new scalar prefix is25bits locally and210globally;512charged. Receipts and immutable source packages are included.

Verification scope: source522's complex supplier freshly reconstructed; bit493's unchanged operator cited and histogram repriced. The portable composition wrapper is being checked after early publication; no cold wrapper or GitHub CI pass is claimed. All-size compiler, common-label/mutable-basis realization, normalized Lemma A, restored-row, precision/tape and analytic-transfer assumptions remain. No unconditional theorem, fresh Lean proof, global optimum or practical speedup claim.

Run python -B research/ranksector112-async/verify.py --work /absolute/new/output. Default freshly rebuilds source522; explicit --reuse-source522 accepts only published byte-pinned completed outputs, then freshly reruns changed-local and global checks. Standard library, Python3.11+, assertions enabled.

Credits: Dugongue #522/#518/#514 rank-sector factory, pair choices, kernel and retiming; icekylinx #523 port restriction and112-port audits; eumemic #507/#493; #484/#496/#505 and all retained source authors. New composition and owner transport by Rohan Arun with OpenAI Codex assistance. The initial old514-specific fixture failure is preserved in the research findings; it was replaced by source-bound compensation and bank-route recounts without removing the physical checks.

Historical packages and results follow.

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Conditional κ = 0.001388082565814657, exactly 1388082565814657/10^18, 0.0024121986% above our preceding verified result. Complex b = 0.001390012017262092088600. The bit supplier remains nonbinding.

research/complex-partial-coordinated-async/ applies #508's coordinated helper540..543 gauge collapse to #507's partial-own factory/kernel84, then repacks our nonuniform asynchronous order. All40,320 helpers have literal whole owners,800 distinct owners per invocation,7,680 live /8,258 physical families. The first aggregate allocation failed stronger pattern/call constraints; the joint model and explicit matching succeed. Discovery failures remain in #477.

The early draft's pending finite checks have passed. Fresh changed-word scalar/frame/Gaussian/wrapper/labels, guarded helper-instance and whole-program checks and mutation controls pass. Fresh emission and independent global audit pass2,963 actual charts and19 rejected mutations. Prefix205bits,512charged,row16467<20161. Both exact moment engines, six bootstrap steps,47 strict inequalities and four outer controls pass.

Verification scope: unchanged partial-own factory/provider explicitly reused from completed byte-pinned verification; changed-gauge local physics and global composition are fresh. The unchanged #493 bit operator is cited and its profile repriced. The packaged wrapper also passed with explicit byte-pinned factory/admission and changed-local reuse, fresh word reconstruction and fresh asynchronous replay. No cold packaged or CI pass is claimed. All inherited all-size compiler, mutable-basis/common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer assumptions remain.

Portable command: python -B research/complex-partial-coordinated-async/verify.py /absolute/new/output --boost-include /path/to/boost/headers. Requires the retained sibling complex-partial-own-async source. Explicit factory/admission and optional changed-local reuse paths check published byte pins; reconstruction and asynchronous stages remain fresh. Frozen exact inputs and completed receipts are included.

Credit Dugongue #508/#505, eumemic #507, #501/502/#496/#484 and all retained source authors. New composition by Rohan Arun with OpenAI Codex assistance. Historical packages and results follow.

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Conditional κ = 0.001388049083313897, exactly 1388049083313897/10^18, 1.211951295% above our preceding verified finite result. Complex b = 0.001389978441615608493590. The bit supplier remains nonbinding.

The new research/complex-partial-own-async/ combines #507's partial-own factory/kernel84 with our nonuniform asynchronous order. Its changed widths are explicitly repacked, with40,320 whole helper roles,800 distinct owners per complete invocation,7,680 live /8,258 physical families and no cross-family split.

The early draft's pending finite checks have now passed. New factory/kernel/retiming reconstruction, scalar/frame and pipeline controls, Gaussian phases, wrappers, local replay and14 Lemma G necessity controls passed. Independent partial-basis algebra and retiming reviews passed, along with fresh guarded helper-instance and whole-program simulations. The changed asynchronous controller passes3525 actual-chart checks and19 rejected mutations. Exact finite invoice:205prefix bits,512charged,row16467<20161. Two exact moment engines, six bootstrap steps,47strict inequalities and four outer controls pass.

Verification scope: unchanged complex provider explicitly reused from a completed byte-pinned replay; the changed local construction and physical checks are fresh. PR493's unchanged bit operator is cited, its profile repriced. The portable wrapper also passed with explicit byte-pinned completed-local/guarded reuse and fresh asynchronous replay; no cold full-package or CI pass is claimed. Receipts, exact inputs and complete immutable source are included.

Fresh command: python -B research/complex-partial-own-async/verify.py /absolute/new/output --boost-include /path/to/boost/headers. Explicit --reuse-local plus --reuse-admission validates every published input byte and completed receipt, then freshly reruns the new async composition. The arithmetic-only entrypoint is clearly separate.

Inherited all-size compiler, mutable-basis/common-label, Lemma A spectator realization, restored-row, precision/tape and analytic-transfer assumptions remain. This is not an unconditional theorem or new Lean proof. Credits: eumemic #507, Dugongue #505, PR501/502, PR496, DreamingOfClouds #484, PR493 and all retained source authors; new schedule allocation and composition by Rohan Arun with OpenAI Codex assistance. Failed/no-gain research and the scoped inventory obstruction remain in #477.

Historical results remain preserved below.

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Conditional κ = 0.001371428043382419, exactly 1371428043382419/10^18: 0.1342864619% above our preceding result and 1.0109941802% above #505 at head 4ee769c8e28837482272b5f4742497da8e2fc9d4. Complex saving b = 0.001373311441205186394130; the unchanged cited #493 bit supplier is nonbinding.

The latest package, research/complex-async-order24/, uses the already verified retimed local word with a new nonuniform order of 72 complete replica invocations. Every replica retains its complete local, bridge, idle and terminal order. A rebuilt physical map hosts 40,320 whole helpers, with 800 distinct owners per invocation, on 7,680 live / 8,258 physical families. No cross-family residual split is used. The profile is {1:171720,2:19008,3:41568,4:6048,5:22992,6:6624,7:2040,8:1224,48:432}.

Completed before this draft update: fresh emission; independent controller and bridge-sensitive owner-window audit with 3,564 actual orthogonal charts and 19 rejected mutations; exact finite invoice; both exact moment engines; six bootstrap steps; 47 strict outer inequalities and four rejection controls. Prefix 205 bits, charged 512; row coefficient 16,467 < 20,161. The initial aggregate matching attempt failed and was repaired using explicit per-pattern/call capacities before constructing and auditing the literal owners. Full discovery history, failures and no-gain screens remain in #477.

The local retimed word reuses its completed, byte-pinned scalar, Gaussian, common-label and guarded physical verification. The unchanged #493 bit operator is cited and its profile repriced, not freshly reconstructed. The packaged wrapper passed after early publication, with published byte-pinned completed-local reuse and fresh replay of every asynchronous stage. No cold full-package or CI pass is claimed.

Run python -B research/complex-async-order24/verify.py /absolute/new/output. Default rebuilds the source-pinned provider/local dependency through the sibling verifier. Explicit --reuse-local checks the completed local receipt and every published input pin, then freshly verifies this new composition. The frozen integer order and literal owner map are the verification inputs; no floating timestamps or optimizer are trusted during verification.

Inherited all-size compiler, mutable-basis/common-label, #484 Lemma A spectator realization, restored-row, precision/tape and analytic-transfer conditions remain. #505's sufficient complete-call scheduling lemma is retained. This is a conditional finite witness, not an unconditional multiplication theorem, a new Lean proof or a global optimum. Larger disputed split-residual claims use a different interface.

Credits: #505 (Dugongue) for asynchronous scheduling and retained emission/audit/invoice/assembly machinery; #501/#502 retiming; #496 pooling; #484 gauges/kernel and normalized spectators; #493 bit supplier and all earlier notices. Nonuniform schedule search, strengthened flow repair, literal matching and source-bound replay by Rohan Arun with OpenAI Codex assistance.

Historical results and their packages are preserved below.

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Conditional κ = 0.001369588870945540, exactly 68479443547277/50000000000000000: 0.8755319973% above #505 at head 4ee769c8e28837482272b5f4742497da8e2fc9d4. The complex saving is b = 0.001371467217183061206788; the unchanged cited #493 bit supplier remains nonbinding.

research/complex-async-retimed/ combines #501/#502's retimed local word with #505's frozen asynchronous whole-owner schedule. Entrance widths are unchanged. The verifier rebuilds the paid profile from emitted local programs and explicit residual footprints, then independently checks all owner intervals, replica-local events and actual charts. This uses whole helpers, with no cross-family residual split.

The construction has 72 complete local invocations, 40,320 helper roles, 800 distinct owners per invocation, 7,680 live families and 8,258 physical families. All 3,194 actual orthogonal charts pass; 19 deliberately broken controllers are rejected. The prefix recount includes 72 individual bridges and 72 complete local sweeps: 205 bits required, 512 charged. Row coefficient 16,467 < 20,161. Both exact moment engines, six bootstrap steps, 47 strict outer constraints and four outer rejection controls pass.

Verification scope at draft submission: the exact retimed local word already passed fresh scalar restoration, Gaussian phases, wrappers, common labels and guarded physical checks in the sibling package. The asynchronous emitter, independent controller audit, finite invoice and exact assembly passed freshly for this composition. The packaged verifier also passed after the early code publication, using byte-pinned completed local outputs and freshly rerunning every asynchronous stage. No cold full-package or CI pass is claimed. PR493's bit operator is source-pinned and cited; its profile is repriced, but its operator is not freshly reconstructed.

Run python -B research/complex-async-retimed/verify.py /absolute/new/output. Default rebuilds the source-pinned provider/local dependency through the sibling verifier. Explicit --reuse-local accepts only byte-pinned completed local outputs and freshly runs the asynchronous stages, recording the reuse scope. All source pins, exact inputs, inherited notices and validation receipts are included.

All inherited all-size compiler, mutable-basis/common-label, #484 Lemma A spectator realization, restored-row, precision/tape and analytic-transfer contracts remain assumptions. #505's sufficient asynchronous scheduling lemma is retained. This is a conditional finite witness, not an unconditional multiplication theorem or new Lean proof. It does not claim to surpass the larger disputed split-residual constructions.

Credits: #505 (Dugongue) for the asynchronous schedule, assignment and audit machinery; #501/#502 for retiming; #496 for pooling; #484 for gauge/kernel and normalized spectator machinery; #493 for the bit supplier, with earlier credits and notices retained. Composition and source-bound replay by Rohan Arun with OpenAI Codex assistance. Failed searches remain in #477.

The following results are historical and preserved with their receipts.

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Conditional κ = 0.001343523016252057, a 0.0003720184% improvement over #501/#502 from a stage-dependent gauge choice. #505 subsequently reported a higher asynchronous result; this is not a claim to surpass #505.

The new research/complex-stage4-gauge-mix/ uses the retimed baseline at eight stages and reduces helper540's entrance from rank4 to rank2 only at the middle stage. A homogeneous use of this change loses. The stage-specific allocation fits all40320 whole helper roles on existing data families with no banks.

Completed after the early draft: fresh checks of both local words (exact scalar restoration, emitted orientations,2952 Gaussian transitions per word, wrappers, common labels, guarded exhaustive operator identities and806basis+8dense physical tests); independent5007chart/72invocation owner audit with10negative controls; conservative finite union invoice; global142bit prefix below192; both exact moment engines; six bootstrap steps and47strict outer inequalities plus four controls. The complete conditional complex endpoint is1345330498741582613827/10^24.

Verification scope: the PR484 provider was reused from a completed, byte-pinned replay. Both local words were freshly checked; the packaged entrypoint was then verified with those pinned completed outputs and freshly reran the mixed controller and invoice. PR493's unchanged bit saving is source-pinned and cited, not freshly replayed. No cold standalone or CI pass is claimed yet. Receipts, exact inputs, source hashes and an offline verifier are included.

All inherited all-size compiler, mutable-basis/common-label, Lemma A spectator realization, restored-row, precision/tape and analytic-transfer conditions remain. No cross-family split or unconditional theorem claim. Credits and notices cover PR501/502 retiming, PR496 pooling, PR484 gauges/kernel and PR493 bit supplier.

Historical R715 packages and receipts remain unchanged below.

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Conditional kappa 0.001297486611380425, exactly 51899464455217/40000000000000000: 0.06745494% above our previous0.001296611982495107. The bit supplier binds. This compares the complete whole-family contract; it does not exceed PR480's larger disputed cross-family headline.

The new research/r715-basis-exchange84/ package exchanges pivot and donor roles in the response kernel, updates every affected response equation, and promotes entrances while preserving nested donor chains. It keeps110 pivots but raises total entrance rank129→139, with102 distinct donors,130 correction rows and19 coordinate residual isometries. It retains PR483's14 target factors and22 paired source-injection cancellations. Exact rational packing scales the assignment to84 replicas: all660660 helper occurrences stay whole on individual physical families across924 complete invocations.

At draft submission, fresh source reconstruction and all955 arbitrary-dirty columns,110 correction-omission controls,22 single-injection controls,native signed/formal checks,labels/mixing/Gram checks,physical emission and independent ownership audit,fresh invoice,both rational moments and47outer inequalities passed. Initial assembly explicitly reused the unchanged completed complex supplier after binding87 implementation hashes and17 output hashes to its completed receipt. Fresh full Python3.14 passed, rebuilding both suppliers. Complete Python3.11 passed with explicit completed-complex reuse, checking its receipt,87 implementation hashes and17 output hashes. Receipts/logs are in research/r715-basis-exchange84-validation/. No GitHub CI pass is claimed.

Bit lower 649586135003318032049/500000000000000000000000; complex lower 1305231506267591/1000000000000000000. Run python -B research/r715-basis-exchange84/verify.py /absolute/new/output. Default reconstructs both suppliers; explicit --complex-output accepts only the pinned completed provider and emits a distinct reuse receipt. Python3.11+,SymPy,C++17 and Boost are required. Python3.11/3.14 CI includes the new package. The verifier reconstructs the final witness directly and runs no optimizer; it does not claim to replay every search decision.

Credits: PR483 (Dugongue) supplies the nested110-pivot seed,response-packet method and target factors, building on our warm PR473 kernel and PR478. PR485's basis-selection work motivated the role-exchange search; its112-pivot seed was tested but is not the winning seed. New basis exchanges,nested promotions,source reconstruction and84-replica rational packing by Rohan Arun with OpenAI Codex assistance. All upstream notices remain intact. Earlier complete28/64/84 packages and their receipts remain unchanged.

All inherited all-size compiler/supplier,correlated-dirty complete-call hosting,same-owner spectator,mutable-label,precision and analytic interfaces remain conditional. This is not an unconditional multiplication theorem or a global optimum. Failed and non-improving searches continue in PR477.

Subsequent frontier note: PR493 now reports a stronger489-helper bit construction and kappa0.001303530097714685 with the same cited complex supplier. This PR does not claim to exceed that newer result; it records the independently replayed R715 improvement and its reusable basis-exchange mechanism.