Conditional kappa 6.838643131376e-4: composed cascade frames, global cuts and four finite bootstraps

[Dugongue]

Change

Add research/coordinated-crossover-pr200-v2, claiming

kappa = 427415195711 / 625000000000000
      = 0.000683864313137600.

This improves the pinned PR211 claim of 0.000683847872495777. It composes PR211's cascade witness with 220 additional geometrically distinct operation-frame changes from global concavity cuts, completed entrance banks, the retained source-assisted complex supplier and four finite ordinary-leaf bootstrap levels. Component savings are not added.

The complete override list has 6,258 entries. Canonical comparison finds 2,268 genuinely different subspaces relative to PR200's raw op_frame list; basis representations alone are not counted. Every inherited cascade override and every additional override is admitted. Scalar operations, source/target contracts, aliases, partner deliveries, terminal inventory and bank endpoints remain fixed.

The integer-normalized bit profile remains width 72, stock 56,402, rank 4,055,136, deficit 5,808 and largest child 22. Its exact child histogram changes. The retained complex saving is 700918443859411/10^18. The bit supplier binds.

Validation

Three native C++20 checkers build and run offline from included archives:

• complete physical/target chronology, 149,024 required-value checks and 4,346 uniform retained-prime frame certificates;
• all 20,634 source/target/dirty columns over F2 and the defining integers, both orientations, literal restoration and adverse controls;
• rational moment bounds, four finite stopped-leaf bootstrap levels, concrete bridge guards and all 47 strict assembly inequalities.

The next 10^-18 kappa grid point is rejected for these fixed suppliers and parameters. A separate native arithmetic replay agrees. Payload SHA-256 hashes are checked before and after. No Python, network or account access is needed.

Windows replay:

powershell -ExecutionPolicy Bypass -File research/coordinated-crossover-pr200-v2/verify.ps1

C++20 g++ must be on PATH, or pass -Compiler <g++-path>. A POSIX verify.sh is included; the clean packaged replay was tested on Windows.

Scope

The consequence is conditional T(n)=O(n (log n)^(1-kappa)) under retained all-size compiler, weighted/restored selector, routing/layout, fixed-tape leaf, prime, precision/recovery and analytic transfer conditions. This finite certificate does not independently prove those interfaces. It makes no unconditional complexity, practical speedup, global optimality or Lean/kernel claim.

The package preserves the 264 omitted-label research: exact full-decoder checks, cap partitions, 132 source partners, a 139-role repair and a fully paid conservative host. Cheap optimized reuse still needs complete arbitrary-dirty compensation; the paid fallback does not improve the bound. No prospective hybrid gain enters this certificate.

Sources and credits

Pinned primary heads: PR200 a117544; PR202 8d8d67b; PR211 c63e50a; PR210 5de2b89. Original licenses and contributor notices are retained. Cascade construction, earlier completed banks and finite-bootstrap arguments are credited rather than claimed as new. This contribution is the composed cut schedule, independent native admission/column replay and exact finite assembly.

Prepared with OpenAI Codex assistance. This directory was prepared locally for manual upload; nothing was published.

[Mister-Meeseeks]

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

Contribution: Cascade frames, global cuts and completed entrance banks.

Review and limits: Prior exact-head full native replay after placing unchanged, hash-verified archive parts in the baseline directory expected by the wrapper. Original archive-placement defect remains disclosed.

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: 34abdc58ed77329c8bf9af5634531fc41939ba3c. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.