[dillona]

The center-free producer in #4929 deletes eight recursive center calls per FULL but changes the main outputs by an owner-mixing code. This package supplies a phase-correct common-query interface and emits the entire exact rational p16 caller using that interface. Across 18 FULLs it removes 144 rank-eight recursive calls, retaining all 15 paid IDLEs and 15 thin queries.

The 3,584 arbitrary main inputs and 7,344 independent helper inputs remain independent. The 16 negative-query banks end at Q^-1 B_i D_i; the 16 positive-query banks end at B_i D_i Q. Every ordered code product B_i is emitted. Positive-bank postdecoding is priced. The negative banks remain coded outputs: this is not yet a Gaussian supplier, a profitable complete multiplication algorithm, or a new κ.

What is new

• 112 phase-correct normalizers and 896 literal monomial wrappers, preserving the full Gaussian including absolute phase. The backward convention requires X-only Q^2 conjugation; the old Y-only convention fails.
• A costed eight-mode owner recoding and complete rational caller recipe. The caller uses 194 code evaluations: 173,824 scalar ADDs, 43,456 monomial field maps, 3,104 CLEARs and eight reusable temporary fields. Optional positive-half postdecoding costs 97 additional evaluations. Inverse recoding has coefficient -1/52; fixed-denominator implementation and precision remain obligations.
• A scoped terminal obstruction: each of the 5,824 nonzero blocks of one Q^-1 C Q has 4^f row support. A fixed finite monomial/scalar word cannot silently erase that one-stage code uniformly in width. This does not exclude cancellation across stages, a paid decoder or another caller.

The all-width arguments, exact emitted recipe, source manifest, independent finite check and open next questions are in research/coded-native-caller/. The noncommuting controller core is inherited, with an independent source-bound replay; it is not claimed as a new theorem.

Evidence

At submission head d969c458c24278e0fd37e5b4c0ff8a53a496b430:

• Registered Python 3.12.15 replay passed; isolated optimized Python 3.14.7 replay passed.
• Exact phase/tableau, wrapper, eight-mode factorization, symbolic transport, all 1,024 noncommuting-controller core entries and emitted boundary checks passed.
• Separate-agent modular propagation over F_65537 checks two deterministic vectors on 112 owners × 512 addresses and rejects the obsolete backward correction. Sampling corroborates the written universal argument; it does not replace it.
• Fresh pinned Construct a center-free native producer with an explicit rank-8 port code (no new κ) #4929 replay passed for all 632 arbitrary source rows in both orientations, 28,045 events each. This is predecessor evidence, not a new producer result.
• Committed-byte/source-history preflight, whitespace checks, official 26-file export and export integrity passed. The exported package passed under Python 3.12 with -I -O -B, network denied and no Git on PATH.
• Selected baseline source bindings passed. No selected cold replay, Lean/kernel verification or full multiplication implementation was run. Hosted CI passed: both the onboarding/selection job and the registered package replay, including the committed-input check (run).

Reproduce from repository root:

python3.12 -B scripts/research_package.py --package research/coded-native-caller
python3.12 -I -O -B research/coded-native-caller/verify.py
python3.12 -B scripts/check_research_commit.py --package research/coded-native-caller --check-source-history

Scope, overlap and next theorem

Canonical investigation #4930. This approximately one-hour session spent more than five minutes comparing high-impact avenues and reserved its final quarter for verification. Scientific inputs remain frozen at canonical 624de9dc66858af0945e5f8a0942488d62280d43 and #4929 head 361f5d4100640177d6a983dd2f336021c75bfd5e. Refreshed canonical cef4b52f2a59009865bf8eabde1be3f159063703 is merged into the branch; priorities and selected κ=0.00302015 remain unchanged. Only this new research package differs from main.

The final full overlap refresh covered 303 open PRs and 4,003 Discussions with complete remote pagination; sparse local-note coverage was incomplete and is recorded in TASK.json. A later live check read #4931 at 90a0124d306ef8802ac2dc3601c6705dca407e45: its one-port physical-prefix offer is distinct from this full coded-producer caller. These checks do not establish universal novelty.

The next decisive question is whether the negative coded jobs admit a recursive interface or affordable decoder. A chronological child substitution must survive the next scalar/warp contact, preserve independent ownership, and pay every query. Fixed-denominator recoding, precision, routing/tape, complete compiler closure and outer recovery remain open. The unchanged-target planning estimate near 0.00765 is motivation only and is not an admissible bound.

Credit

Dugongue / mdumitrean: #4929 center-free producer, code and conditioning, plus the existing noncommuting-controller theorem. Cinna Davis / 1337isnot1337: #4694 cache, #4698 helper basis and #4470 controller. Cao Yifan / intqwq: round-three native word and #4610. Ryanson Jonathan: #4516 controller checks. Retain zxv's native/Clifford/compiler work, Jacob Alan Sussman's mixed-target recursion and all frozen source lineage, licenses and notices. Center deletion itself is predecessor work.

Prepared for Dillon with substantial OpenAI Codex assistance from research and separate review agents. No independent human acceptance claimed. No merge or selected-frontier change is requested by this contribution.