[aliromman]

This conditional construction improves complete κ to 0.00304057, from the selected 0.003027288235 in PR #5413. The gain is 0.000013281765 (about 0.439%). It changes the recursive cost profile, rather than taking more digits of the old crossing.

The completed P104 word from PR #2305 has 527 independent helper outputs. This contribution binds their actual native Gaussian ranks to the current mixed-target recursion and supplies a literal p16/a7 caller. All 18 full sites execute the published forward word. Ordinary signed exchanges and central-square translations supply its sixteen backward interfaces, without transposing its COPY or CLEAR instructions.

Review the proof and full cost boundary, complete certificate, literal caller, and source pins.

Complete calculation	Result
Paid calls / productive fields	69,930 / 12,814
Thin paid calls / whole idle jobs	1,560 / 3,120
Rank-mass surplus	760
Raw crossing enclosure	(0.00304057807630, 0.00304057807631)
Tested saving / claimed κ	0.003040575 / 0.00304057

All source correction, private COPY paths, helper restoration, main targets, thin queries and whole idle jobs are included. The local word, private reuse and old owner-window result remain credited prior work. The new consumer uses productive helper targets; it does not claim that the old owner invoice was wrong. The selected frontier is unchanged.

Evidence. Two exact interpreters check all 552,049 public/owned coefficients with different arithmetic and chronology. The native check covers 2,981 distinct paid/helper maps, 208 main adapters, 7,488 caller boundary contacts and every helper/main/idle target. Two rational interval engines agree. Cutoff 17 and floor 18 fund all completion tails; the former cutoff 20 fails. The finite compiler threshold is N = 2^64215200000000. All 54 strict outer predicates and four functional predicates pass with retained ordinary BIT saving 0.0034. The complete ordinary-work bound includes every new route and wrapper.

Validation performed. Python 3.12.14 normal and optimized full replays passed. A read-only, Git-free export passed the optimized replay with all bytes and modes unchanged, and a corrupted-source export failed at authentication. Package metadata, immutable source hashes, committed-byte preflight, export inventory and current-base ancestry passed. The optional full-history preflight mode could not run in this shallow checkout; every declared source pin resolves to the immediate base and was byte-checked. The registered commands are:

python3 -B scripts/research_package.py --package research/p104-productive-controller --check-only
python3 -B scripts/research_package.py --package research/p104-productive-controller

Expected scientific marker: PASS_P104_PRODUCTIVE_COMPLETE_KAPPA_00304057. The two scientific commands declared by that hook were also run directly. Controls reject missing COPY, wrong frame/phase, omitted central translation, unearned helper credit, old cutoff and insufficient BIT stock.

Scope. The result retains five framework assumptions: native all-column implementation, owned erasure, uniform compiler, precision/tape and analytic recovery. The package proves the new ideal uniform frame identities, supplies finite growth bounds and checks the full conditional arithmetic. The enormous uniform word and full rounded integer multiplier are not materialized. No proof-kernel theorem, independent human acceptance or optimality is claimed.

Base: 32890bc5de034ab8fc93ac88ead7279a6a416d04, priority revision 7. Contribution: e2a6cce2f9db5a2c5f9714f4b9e5292dd3a10581. The canonical claim records the changed premise. The final refresh covered 402 open PRs and 4,828 Discussion records; canonical main was unchanged. The source's released handoff leaves global binding open. This contribution does not take the active or published literal-slot repairs, original split-contact charts, global border grading, Global120 or p19 work.

Credit. Gareth Davidson @bitplane supplied the exact composition in PR #2305, head 335e78619a17b7c418e11306f86a72fd366de35b. David Arias @DavidAriasC supplied the coalesced word in PR #2152, head 05f7aad0f08992ee48ec2dd93e896d9a4567847d. Cinna Davis @1337isnot1337 supplied private reuse in PR #2219, head 3f913bc17276b68f0c9008a1202b6ce588e77ff6, and the controller lineage. Ali Romman's PR #5398 supplies the conjugation identity, used here in the inverse direction. Jacob Alan Sussman's mixed-target recursion is credited in the retained interval/source note; zxv and Cao Yifan supply the retained compiler/pricing lineage. The source archive and native notices retain the earlier P104, geometry, scalar and native contributors.

New caller, productive binding, independent replay and complete cost: Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0.