Whole-caller capacity and price gate for seven-axis B/C suppliers

[aliromman]

DONE / RELEASED — Bound every coordinate caller of the seven-axis B/C suppliers, exact head f06dabb7efc09edfa5efafeb9ebf60331790cdd7.

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.

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.

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

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. No new search is reserved. Prepared for Ali Romman with substantial OpenAI Codex assistance.

Original claim

CLAIM — whole-caller rank capacity for the actual seven-axis B/C suppliers

I will test a caller-level obstruction for the exact PR4703/4712 B and C profiles. This extends the PR4848 serial ceiling: the proposed scope permits any number of independent main fields, arbitrary scalar/even-power mixing across ports, arbitrary caller graphs, repeated coordinate axes, COPY/retained observations, reciprocal local orientations and fully paid coordinate-Gaussian queries. Source helpers remain independent and separate, with their actual profiles credited once per call.

The discriminating invariant is the odd coefficient rank in each coordinate Gaussian. An A, B or C pair has central odd rank one and noncentral odd rank two. I will bind this to the 112-port source, then test whether the resulting all-axis capacity can pay the exact complete concave bill. The intended boundary is explicit: ordinary maps lie in the scalar algebra of the Gaussian even powers; targets use the same coordinate axes; no free odd input gauges, main/helper mixing or changed source word is granted. I will report any cutoff relation between additional-query and target ranks rather than claim a universal B/C impossibility.

Base canonical main 6cf7a68, priority 7, selected record unchanged. Live overlap refreshed before this claim. Discussion4853 / PR4848 is DONE and covers the narrower fixed-224 serial model. PR5617 concerns P104 stages, not this seven-axis B/C contract. PR5626 supplies the new query-rank perspective; no emitter code will be duplicated. This is a handoff-led formal-interface-lemma override of the picker suggestions.

Credit Dugongue PR4703 and PR5578/5586, Cao Yifan/intqwq PR4712, Chris R/Clear1nsight PR4848, Cinna Davis PR4674 and the controller lineage, Ali Romman PR5626, DaysSky, zxv, Jacob Alan Sussman and all retained native/compiler authors. Prepared for Ali Romman with substantial OpenAI Codex assistance. Claim expires 2026-10-26T04:30:00Z.

[aliromman]

UPDATE — the rank cutoff can be removed. A two-character rank-distance argument bounds the whole main moment by L*(1407^t+28+848^t) plus the exact extra-query moment, for any 0<t<1. It permits arbitrary target ranks and extra-query ranks. The proof uses all sign characters in a fixed even-power sector at each width f>=3. I am verifying the 56 A / 56 exceptional port count, all reciprocal orientations, the integral from random sign cuts to r^t, and the complete source invoices. The ordinary-coordinate and separate-helper premises stay unchanged. No new caller construction, new kappa or claim on changed address maps is implied.

Prepared for Ali Romman with substantial OpenAI Codex assistance.