[aliromman]

This construction raises complete conditional κ to 0.00309980, tested at 0.0030998005. It consumes PR #5580 at 6efa248cf456d6101d757e9d09ba29711d18a13a, whose claim is 0.00308189: the gain is 0.00001791. The newly released parallel PR #5599, head 0644592d421b375c221045954fdf13932575ffa8, claims 0.00309839. This package exceeds it by 0.00000141, with 126 fewer paid calls and 108 fewer productive fields. The helper-splitting mechanism was developed in parallel; its author released the split component for composition and left the paid-boundary changes with this claim. No exclusive method-discovery claim is made. The consumed constructor input remains PR #5580; PR #5599 is retained as an exact comparison input.

Proof, fixed witness and construction, complete receipt, source pins, and validation.

Six helper boundary basis changes remove seven paid transports per local call. Nine coupled handoffs isolate a helper-only input functional and output direction at a common interior chart. Scalar input/cut/output bases split each channel into two independent productive targets. The new word has 744 arbitrary public inputs, including 536 helpers. All 104 main shears and all eight owned COPY paths remain; their complete costs are charged.

Relative to PR #5580, the complete target-minus-paid moment increases by 18 * [7 g(4,5) + 5 g(2,7) + 3 g(1,8) + g(1,4)], where g(a,b) = a^(1-k) + b^(1-k) - (a+b)^(1-k) > 0 for 0 < k < 1. This changes the invoice. The exact raw crossing is (0.00309980120533, 0.00309980120534); the raw gain over PR #5580 is between 0.00001790623666 and 0.00001790623668. The headroom above the claim is between 1.20533e-9 and 1.20534e-9. A rational derivative bound proves the unique fixed-invoice crossing on [0,0.0034]; no broader optimum is claimed.

Relative to the pinned PR #5599 word, the complete signed-moment gain is exactly 18 * g(4,5) > 0. Its raw crossing is (0.00309839352211, 0.00309839352212), so the additional raw gain lies in (0.00000140768321, 0.00000140768323). The verifier authenticates that comparison word, replays its arbitrary inputs, recounts its complete invoice and isolates its crossing. It does not repeat the parallel package's native/compiler verification. The two split sequences are not additive gains.

Complete quantity	PR #5580	This construction
Paid jobs	66852	66726
Productive fields	12814	12976
Paid rank mass	241250	240782
Target rank mass	242010	241542
Rank-mass surplus	760	760

The unchanged p16/a7 caller retains 18 forward local calls, 15 query shears and 3120 whole idle jobs. The price includes every helper normalizer, main adapter, route, COPY/CLEAR path, restoration and scalar operation. The complete nonrecursive allowance is 184647552, below the 1e9 budget. The enlarged target inventory requires logarithm power 1024 instead of 1000; the old value fails the complement-capacity test. The other compiler parameters retain power 1024, cutoff 17, floor 18 and reserve 1e-10.

Python 3.12 and the standard library suffice:

python3.12 -B scripts/research_package.py --package research/p104-coupled-helper-bases

Each registered mode prints:

PASS_P104_COUPLED_HELPER_KAPPA_00309980

The launcher ends with:

PASS_REGISTERED_RESEARCH_PACKAGE research/p104-coupled-helper-bases outcome=completed

Normal and optimized registered replays pass. The checks authenticate the unchanged 33-file PR5545 capsule, regenerate all 15 changes, replay arbitrary inputs after every step, check 565504 dense transpose coefficients and 2926 exact signed native maps, replay the full physical caller, derive the invoice three ways, check two rational moment engines, the compiler and all 54 strict plus four functional outer predicates, and compare the full receipt. Negative controls reject false helper independence, a false cut witness, missing basis work, wrong coefficients/frames/phases, a missing central translation, and the old invoice/compiler/BIT choices. Source corruption is rejected in both modes. A read-only Git-free optimized export with empty PATH passes and preserves every exported byte. Package metadata, exact committed bytes and immediate-base ancestry pass. Full-history ancestry mode is unavailable in this shallow checkout. Hosted CI and independent scientific review are separate from these author checks.

This remains conditional on the five inherited framework assumptions: native all-column realization, owned erasure, uniform compiler closure, precision and fixed-tape execution, and analytic recovery. The free helper endpoint contract is inherited. The construction changes helper boundaries within that contract. The enormous uniform word and a complete rounded multiplier are not materialized. The selected record remains 0.003027288235; this PR does not change it.

Publication head: 6c224aa720203c4f4615e6538d8038a275387db8. The branch starts from canonical main 5e0052ca0aa3036a3afa8b0438927377c8d97d53, priority revision 7. Coordination and scope distinguish this work from the active changed-contact, native-history and global-controller threads. The former private-fanout claim changed scope to the released PR #5599 split component, which is credited above. The fixed-contact floor in PR #5590 fixes a scalar realization; this construction changes scalar bases and the independent target inventory. No other contributor's work is edited or closed.

Credit and consumed sources:

• Ali Romman's PR #5580 supplies the exact input word and contact gain. PR #5544 and PR #5545 supply the complete caller and source closure. The caller, native engines, moment engines and outer ledger are retained; the local checker only changes its explicit public width and removes its unused old constructor. The checker diff and pricing diff make those changes explicit.
• Joel Pulikkan, @GamingPuzzled, supplied the successor method in PR #5472 and the priced handoff in PR #5569. @DreamingOfClouds supplied PR #5561 free endpoints and PR #5553 single-helper handoffs. @thu-nmrc supplied PR #5551 coupled contacts. The shared handoff component uses coupled input and output bases instead of a pure original helper coordinate. The paid-boundary reductions and smaller complete invoice are this package's distinct contribution.
• Gareth Davidson's PR #2305, David Arias's PR #2152, and Cinna Davis's PR #2219 supply composition, coalescing and private reuse. Cinna Davis supplied the controller, Jacob Alan Sussman productive recursion, and zxv and Cao Yifan the interval/compiler/native framework. The retained capsule preserves all earlier geometry, BIT, analytic and license notices.

New construction, proof and verification by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. The same assistant performed discovery and verification; no subagent, independent human or proof-kernel review is claimed.