Conditional kappa 6.831904550365e-4: coordinated frame optimization and completed entrance banks

[Dugongue]

Add research/coordinated-crossover-pr200, a finite supplier certificate and conditional assembly claiming

kappa = 1366380910073 / 2000000000000000
      = 0.0006831904550365.

This is approximately 0.0189% above the newly displayed PR205 claim of 0.000683061299399923. PR205 also supplies a completed-bank construction on PR200; no exclusive originality is asserted for bank packing. The earlier comparison with PR204 was approximately +0.8675% and is now historical. It combines a new, explicitly paid bit supplier with the retained source-assisted complex supplier; component improvements are not added.

The bit construction starts from PR200, pinned at a1175449f34d39ff933d9d8ab23ced1f32b290ec. Coordinated changes to 302 operation frames reduce the actual internal child histogram while keeping the source and target interfaces fixed. Completed entrance banks then replace the real rank-4 and rank-24 dirty residual completions with explicit coordinate partitions of width 72. Nine physical replicas make every bank full. Internal alias recipients, source births and deleted terminals are excluded from fresh bank allocation. Arbitrary incoming dirty contents and spectator fields are restored.

The resulting integer-normalized bit profile has width 72, stock 56,402, rank mass 4,055,136, deficit 5,808 and largest child 22. Its certified paid coarse saving is 136731504666219/200000000000000000. The complex side uses PR202, pinned at 8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d, with saving 700918443859411/10^18.

Exactly three stopped-leaf bootstrap levels are used, following PR185 and PR197. Each level calls only its predecessor for ordinary leaves and routing. The unattained limiting saving is not substituted. The final paired assembly uses eta = beta = 10^-24 and preserves the original strict scalar, router, row and recovery constraints.

Validation and scope

The included verifier checks the actual finite frame/source/gauge chronology, the original and terminal-modified binary and defining integer columns, explicit bank assignments and inverses, frame prime witnesses, adverse controls, rational supplier moments, the finite ordinary-leaf recurrence and all 47 strict assembly inequalities. The next final 10^-18 grid point fails for these fixed suppliers and parameters; this does not assert global optimality.

The claimed consequence is conditional T(n) = O(n (log n)^(1-kappa)) under the retained all-size interfaces. General Clifford/tensor realization, uniform weighted local-ring compilation, completed restored-row and fixed-tape leaf guarantees, paid routing/layout, prime supply, precision/recovery and analytic transfer remain disclosed conditions. A finite column replay and positive moment do not independently establish these conditions. This submission makes no new Lean-certification or practical-speedup claim.

Offline replay from the repository root uses Python 3.11+ with the pinned NumPy/SciPy requirements:

python -B research/coordinated-crossover-pr200/verify.py

An optional --temp-root chooses scratch storage. The replay never fetches sources. The bank chart/router bound K = 21,900,544,398 remains paid through the ordinary routing toll and its strict exponent gap.

Other routes tested

Shared-total/rank-two compensation saves 230 scalar additions but fails 260 actual target-cap membership checks. The integral 165-to-55 residual factor is exact, but its real paired-address features require ranks 19/20 and its outputs rank 20 against side caps of rank 18. Source-assisted rewrites also fail to improve this bit word: the full port lacks required donor stock at an actual vertex, the A0-only rewrite adds 440 rows, and the G12-only rewrite leaves the paid profile unchanged. None of these gains is credited.

Sources

The package retains the pinned upstream sources and their license/attribution notices. It builds on the public PR200 physical bit construction, PR202 source-assisted complex construction, completed-bank work and finite-bootstrap argument. No files or claims were published by the local research process; this is a manually uploaded research addition.

[Mister-Meeseeks]

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

Contribution: Coordinated frame optimization, bank charts and native replay.

Review and limits: Prior exact-head full native offline archive replay. Source notices retain the underlying bit, complex and assembly contributors.

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: cd14825023b75af4f5919a30e5e6d548b6ade5bc. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.