[flyingviper]

This combines the compensated dirty relay in #5605, Pierre-Loic Doulcet's commuting-contact cascade in #5565, and 13 of Ali Romman's 15 independent helper splits from the consumed #5599 version. The complete conditional endpoint is kappa 0.00310184. Its raw crossing is (0.00310184254783, 0.00310184254784); the claim is tested at 0.0031018405.

The consumed #5599 head 0644592d421b375c221045954fdf13932575ffa8 claims 0.00309839, so the historical comparison receipt shows a gain of 0.00000345. During verification, #5599 independently composed with #5565 and advanced to 0.00310045 at 09dd0965711ca7eeb169057a420abab1c9052137. This result is 0.00000139 above that updated claim. Immutable consumed inputs remain explicitly pinned; the selected frontier is unchanged.

The cascade removes the line visits required by original splits 12 and 15. Those splits and their credits are omitted. Every remaining rational prefix/suffix witness is checked again on the evolving combined word; merely adding headline improvements would overcount. The complete bill has 66,690 paid calls, 13,048 productive targets and rank surplus 760. The local word has 748 independent inputs, 540 helpers, eight owned lifetimes, peak one and 25,502 events.

Proof · Construction · Exact split witnesses · Complete receipt · Source pins

Validation passed: independently merged source edits; all 13 exact cut witnesses and all intermediate arbitrary-input rows; dense transpose; 2,920 signed native maps; physical caller; complete paid/target accounting; two interval engines at the tested endpoint; compiler and 58 outer predicates; five semantic rejection controls. Registered normal/optimized replay, exact committed bytes/source history, and a read-only Git-free export pass. Independent agents checked algebraic hazards, geometry, inventory, ordinary costs and source/price edits.

python3.12 -B scripts/research_package.py --package research/p104-relay-split-composition

The five inherited framework assumptions and helper-endpoint contract remain. The enormous uniform word and complete rounded multiplier are not materialized. This is a finite certificate and conditional calculation, without independent human or proof-kernel acceptance or a global optimum claim. The fixed-invoice ceiling and headroom are documented.

Base: canonical main 5e0052ca0aa3036a3afa8b0438927377c8d97d53, priority revision 7. Credit Ali Romman for #5580/#5599 and caller/price machinery; Pierre-Loic Doulcet/hexapode for #5565; flyingviper for #5605; Joel Pulikkan/GamingPuzzled, DreamingOfClouds, thu-nmrc, Gareth Davidson, David Arias, Cinna Davis, Jacob Alan Sussman, zxv, Cao Yifan and all retained geometry/native/BIT/analytic predecessors. The elementary split identity is credited, not claimed as new. New composition prepared for flyingviper with substantial OpenAI Codex assistance and independent agents; Apache-2.0.

Next: independently review the complete composition, seek different legal split cuts after changed contacts, or replace another owned consumer with a fully corrected and priced relay. Positive-frame split successors must not be treated as free zero-frame correction channels.