Conditional kappa 0.001372554837726243: coordinated gauge collapse with retimed asynchronous whole owners

[Dugongue]

Conditional kappa = 0.001372554837726243, exactly 1372554837726243/1000000000000000000.

This is 2.161253% above the pinned PR501/502 whole-owner result and 1.093987% above our previous asynchronous construction. It combines a new coordinated four-gauge target-level collapse, the PR495/501/502 body retiming, and offset6 asynchronous whole-owner hosting. All gains are recomputed from one actual paid program; no separately quoted exponent gains are added.

New mechanism: release shared target levels together

Starting from PR484's gauge80-kernel42 word, helpers540,541,542,543 all move from rank4 entrance gauges to the existing rank2 frame [408,102]. The42 kernel pivots are unchanged. Reconstructing the entire frame system lowers targets81,82,84,87 from rank4 to rank2.

A single withdrawal leaves the shared target levels high. Four separately scored moves would predict only -4 rank2 +4 rank4. The actual joint change is -16 rank2 +4 rank4 +4 rank6: coordination releases costs that a marginal search misses. Four whole residuals grow from width5 to width7, so the changed inventory is repacked and charged in full.

The complete local inventory is18 width7,104 width8,438 width9. All72 calls use this same reconstructed provider. Eight replicas preserve their own controller order while calls follow (7*stage+6*replica,stage,replica). All40320 helper uses have literal whole physical owners; no residual is split across families. Each invocation completes its whole cover sweep and normalization before another starts.

Exact result and invoice

• Complex lower saving: 1374441333828159774039/1000000000000000000000000.
• Cited unchanged PR493 bit lower saving: 391360506745414227149/250000000000000000000000.
• Complex remains binding.
• Paid profile: {1:171720,2:17856,3:41568,4:6336,5:23280,6:6912,7:1752,8:1224,48:432}.
• Ambient73; live7680; physical8258; rank mass558144; deficit2496.
• 2972 actual orthogonal73-column charts;9360 explicit paid remainders;32113 cross-replica uses.
• Prefix205bits, charged512; two-level row coefficient16467<20161; maximum child48 satisfies 73^2 > 2*48^2.

Reproduction and checks

Additive folder: research/coordinated-gauge-async/.

python -B research/coordinated-gauge-async/verify.py --work /absolute/path/to/a-new-output-directory

Python3.11+, standard library only. No optimizer, network, C++ compiler or Lean installation is required. The output directory must be new and outside the package. Assertions must remain enabled.

The verifier reconstructs the public frame transfer and coordinated gauges, checks exact scalar columns in both orientations, Gaussian phases and paid wrappers, emits the physical asynchronous program, independently checks literal chronology/owners/spectators and the complete scalar/prefix invoice, and runs two rational moment engines plus six bootstrap steps and all47 strict outer inequalities. It rejects19 corrupt controller variants and4 outer controls, including the adjacent kappa grid point. The retained PR493 bit histogram is repriced; the unchanged bit operator is explicitly cited rather than needlessly re-run.

Generated text is forced to UTF-8/LF in a process-scoped launcher to avoid Windows/Linux adapter-hash mismatches. Immutable sources have a manifest and .gitattributes. Detailed receipts and the scope of local testing are included; this does not claim a CI run on an untested platform.

Direct sources and credits

• Conditional kappa 0.001467289440740487: rank-sector factory on 112 ports #473: single-helper rank4-to-rank2 withdrawal directly inspired the joint gauge screen. The new step is the simultaneous four-helper change and shared-level collapse.
• Add combined E8 witness at κ = 0.001307044366925301 #495: main-word frame retiming.
• Conditional κ = 0.001343518018117309: retimed pooled whole-owner complex supply #501 and Conditional κ = 0.001343518018117309: retimed gauge word with pooled whole owners #502: transfer of that retiming onto the gauge80-kernel42 construction and whole-owner integration. The included transfer constructor and schedule fixture are from pinned Conditional κ = 0.001343518018117309: retimed gauge word with pooled whole owners #502.
• 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: entrance-gauge/shared-donor kernel word, scalar/frame machinery and paid residual wrappers.
• Conditional κ = 0.001332077359286333: pooled whole-owner complex supply #496: whole-owner pooling, allocation and audit/invoice ancestry.
• Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493: unchanged R489 bit supplier.
• Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458, 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: whole-owner spectator, split-centre, geometry and scalar/phase ancestry.
• 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 and κ = 1.017022657082799e-3: 205 shared-donor gauges with 64-replica banks #408-κ = 1.017798035290733e-3: propagated frames admit 214 entrance gauges #416: retained response-kernel and gauge ancestry.
• 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 moment and outer arithmetic ancestry.

Our previous complete-invocation asynchronous construction supplies the scheduling method. OpenAI math's WordScheduling/CommonBases and the tensor-isomorphism intertwiner viewpoint informed the research; they are not represented as newly kernel-checked proofs of this package. Source revisions, file hashes, original notices and precise roles are included.

Research preserved for future work

The package explains the nonlinear shared-target mechanism and retains concise evidence for382 single-gauge subframes,20 coordinated choices, six further combinations, retimed response-matroid variants, asynchronous inventory portfolios, and a clean-row alias screen. It also gives a sufficient pending-factor transport identity Q_y A=A Q_x and a safe deferred-terminal-suffix construction. Those additional routes produced no further priced gain here and are not counted in the exponent. Negative screens are bounded experiments, not global impossibility claims.

Scope

This is a conditional finite whole-owner construction under the inherited all-size compiler, mutable-basis/common-label, normalized Lemma A realization, restored-row, precision/tape and analytic-transfer contracts. These remain explicit conditions; finite replay does not prove them. No unconditional integer-multiplication theorem or fresh Lean certification is claimed.

The snapshot is frozen through #504. #503's bit-only draft and #504's alternate read-then-climb route were read but are not numerical ingredients. #499's larger0.001452948511251494 claim inherits the disputed #494 split-residual interface; this submission neither adopts that interface nor claims to exceed that numerical headline.

Prepared with substantial OpenAI Codex assistance. Original source authorship and licenses are retained. Nothing was published automatically.

[Mister-Meeseeks]

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

Contribution: Coordinated gauge collapse with asynchronous ownership.

Review and limits: Joint changes release shared target-level costs that marginal scores miss. Wider helper complements and all physical allocation costs are charged.

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: 3213fc136270ca8372ce9f8fbb828e78ba96cecf. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.