[aliromman]

Scoped negative result: every caller made from the exact seven-axis B/C whole calls loses the complete recursive moment in the declared coordinate model, for every 0<C<1. This covers arbitrary numbers of independent main inputs, field mixing, caller graphs, axis reuse, reciprocal orientations and paid extra queries of any rank. It prevents further schedule searches in this model from being mistaken for a route to higher kappa. No new kappa is claimed.

Scope, proof, exact checks, source pins, registered replay. Base: canonical main 6cf7a683f447b9f1e2333791907fd92be5009a63, priority revision 7. Contribution head: f06dabb7efc09edfa5efafeb9ebf60331790cdd7.

The proof replaces the fixed-224-owner serial ceiling of PR #4848. A two-character rank-distance argument gives main capacity K(t)=28+140*7^t+84*8^t per whole call after the exact extra-query moment is subtracted. The actual paid-minus-helper profiles strictly exceed this capacity throughout 0<t<1. At raw saving C=.0036, the deficits exceed 31.58147 per B call and 23.98603 per C call. Discussion #5628 contains the claim and scope update.

Normal and optimized registered replay pass. Checks authenticate seven frozen source files, verify 864 rational pair/orientation/sign cases, enumerate the source cut polynomial, compare 5952 character pairs in twelve finite-field circuits, and check the complete bill with integer-certified power intervals. Four corruption controls reject. Query-only equality and the larger eight-axis capacity are positive scope controls. The all-caller, all-width and all-exponent statements have a written proof; finite tests are supporting evidence. RESULT.json SHA256 is ffd64dc6fcfd498c53cc3ade2ae5a8ff0dcef5e4b5607f88122da60a97774cc4.

python3.12 -B scripts/research_package.py --package research/complementary-caller-capacity-gate

Python 3.12 and the standard library suffice. Committed-byte checks pass. The contract requires one coordinate chart, complex-linear ordinary maps in the even-power Gaussian algebra, f>=3, independent full Gaussian main targets, and fresh separate source helpers. General address maps, value conjugation, shared helper feedback, changed native profiles and nonlinear callers are outside it. The productive eight-axis P104 family is outside it. Full native phase/ownership/compiler audits are inherited and were not rerun. No formal-kernel or independent scientific acceptance is claimed. Expected replay output:

PASS_COMPLEMENTARY_CALLER_CAPACITY_GATE
PASS_REGISTERED_RESEARCH_PACKAGE research/complementary-caller-capacity-gate outcome=negative-result

Hosted status is unconfirmed at publication.

Credit Dugongue for the exact PR #4703 suppliers and PR #5578 / PR #5586 typed interfaces; Cao Yifan/intqwq for the PR #4712 audit; Chris R/Clear1nsight for the serial ceiling; Cinna Davis for the PR #4674 direct-price method; and Ali Romman for the PR #5626 query-rank perspective. Credit DaysSky, zxv, Jacob Alan Sussman and all retained native/controller/compiler authors. The rank-distance and integral identities are classical.

Next: give an exact shared-helper producer or a priced map outside the declared algebra, with an all-input endpoint and full bill. More main owners, role mixing, sector packing or coordinate queries alone do not reopen this model. The selected frontier is unchanged.

Prepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0.