[aliromman]

This construction certifies conditional κ = 0.00308189, up from 0.00308181 in PR #5569. The raw crossing increases by 7.645343e-8 to 7.645345e-8, from (0.00308181851522, 0.00308181851523) to (0.00308189496866, 0.00308189496867). It changes the complete paid profile and leaves the selected record unchanged.

Proof · Complete receipt · Source pins · Four-site construction.

The edit moves ADD 451 += 228 from a three-dimensional chart to a four-dimensional chart. At each of 18 forward calls, two rank-three paid transports become one rank-two and one rank-four transport. Strict concavity proves the signed-moment gain. All 735 public endpoints, 527 helper targets, 21,686 ordered scalar/owned operations and eight owned lifetimes stay fixed. The complete bill retains 66,852 paid jobs, 12,814 productive fields and rank surplus 760. It includes all helpers, normalizers, adapters, queries, idles, routes and owned costs. The reported native growth bound now derives the actual paid-rank sum 6,013; the source's old literal 5,894 was stale. That report correction does not cause the κ gain.

The claim is tested at 0.0030818905. The exact derivative is negative throughout [0,0.0034], so the new crossing is the raw funding ceiling for this fixed invoice under the retained BIT cap. Raw headroom above the claim is 4.96866e-9 to 4.96867e-9. This is not a global P104 optimum.

Verification uses Python 3.12 and the standard library; no solver is required:

python3.12 -B scripts/research_package.py --package research/p104-event-contact-step

Expected markers are PASS_P104_EVENT_CONTACT_KAPPA_00308189 in both modes and PASS_REGISTERED_RESEARCH_PACKAGE. Warning-strict registered normal and optimized replays passed on CPython 3.12.13. A separate isolated, optimized Git-free export replay passed with read-only files, empty PATH and unchanged source hashes. Committed-byte and source-pin checks passed. Full-history preflight was not run because the checkout is shallow; immediate-base ancestry was checked. The checks cover exact arbitrary-input endpoints, 552,049 dense transpose coefficients, 2,921 signed native maps, the full physical caller, two rational moment engines, compiler conditions and all 54 strict plus four functional outer predicates. Four invalid contact words and the unchanged-word control reject; the retained phase, BIT and cutoff controls also reject. Validation details.

The same five framework assumptions remain, together with the source helper-endpoint contract. This edit changes none of those endpoints. The enormous uniform word and complete rounded multiplier are not materialized. Independent scientific review and hosted CI remain pending. The larger p19 headline in PR #5440 retains an unresolved chain-to-native compiler and physical attachment; this contribution improves the complete P104 paid-caller line and does not claim to exceed that extra-premise numerical model.

Base is canonical main 5e0052ca0aa3036a3afa8b0438927377c8d97d53. The consumed PR5569 word is pinned to af9f091ac6f30c6eaacb9c27777bfbe2d0e5ffdf. The unchanged executable source closure is PR #5545 at 18968423711fd902aaee1099979497d55603e1dc. Canonical coordination records overlap and the released handoff; current main was refreshed before submission.

Credit: @GamingPuzzled (Joel Pulikkan) supplied PR #5569's priced handoff; @DreamingOfClouds supplied PR #5561, PR #5568 and its released event-placement lead; @thu-nmrc supplied PR #5551. Ali Romman's PR #5544 and PR #5545 supply the complete caller and source closure. The local-word source notices credit Gareth Davidson, David Arias and Cinna Davis. The pricing source notices credit Cinna Davis's controller, Jacob Alan Sussman's productive recursion, and zxv and Cao Yifan's interval/compiler work. Earlier geometry/BIT/analytic attribution remains in the authenticated closure. New work is by Ali Romman with substantial OpenAI Codex assistance; the same assistant performed the construction and checks. Apache-2.0. No independent review is claimed.