[aliromman]

Result

Conditional κ increases from 0.003288299 (#6529) to 0.00329394: an incremental gain of 0.000005641, or 0.17155%. This excludes all inherited gains. It is below the requested 1% target.

The caller now returns one completed Gaussian at an intermediate cut and gives the remaining suffix a fresh, independent input. On each of 104 ports, one rank-17 target becomes independent rank-1 and rank-16 targets. The productive change is exactly 104(H1 + H16 − H17); all 67,096 paid Gaussian jobs remain. This changes the fixed-target premise of the earlier packing ceiling.

Complete invoice	#6529	This PR
Independent caller fields per port	34	35
Productive fields, including native helpers	13,652	13,756
Paid Gaussian jobs	67,096	67,096
Full native calls / thin queries	18 / 17	18 / 17
Caller events	570	609

Proof and implementation

At event 328 of the #6398 root, explicit dual pairs isolate a central involution S = λq⁻¹, where λ = (1+i)/2 + (1−i)q²/2. Two literal ordinary basis changes separate that completed output from the suffix. The input basis mixes only three equal complete targets, so the suffix has an independent rank-16 block. A new input can enter it without copying or reusing the returned input.

Start with PROOF.md, the literal construction, and WITNESS.json. RESEARCH.md records the discovery, the improved ordinary basis word, the fixed-invoice ceiling, and open questions. Every new basis gate, route, normalizer and public field is charged; the complete ordinary-work bound is 254,699,248, below the inherited 10⁹ allowance.

Verification

• Two complete caller engines check all 1,225 coefficients over the unspecialized central ring. Exact dual-pair and basis checks, plus invalid variants, cover the retirement step.
• Full source regeneration checks all 799 native columns, 2,939 native maps, 208 main adapters and 7,488 physical contacts, with absolute phases. No cached receipt replaces these checks.
• Two rational price engines certify the tested saving 0.003293945, the strict raw crossing bracket (0.00329394637095319036829691, 0.00329394637095319036829692), the compiler, and all 54 strict plus four functional outer predicates.
• CPython 3.12 normal and optimized registered replays pass. Committed bytes/modes, all 39 retained source files, official export integrity and input coverage pass. Both read-only, Git-free, empty-PATH export replays pass. VALIDATION.md states the coverage and limits. Hosted planning and both registered replays passed at head 775722aa94a5e85b05d1d704d7dca10cbf016f0c in run 41578844006. Completed logs confirm both result markers and unchanged committed inputs.

python3.12 -B scripts/research_package.py --package research/gaussian-root-retirement

Scope and credit

This is an author-checked conditional construction. The source stack includes pending PRs; its admission and independent scientific review remain open. The five inherited assumptions (native_all_columns, owned_erasure, compiler, precision_tape, analytic_recovery) remain. No materialized rounded multiplier, runtime gain, full-history preflight in this shallow checkout, or selected-frontier change is claimed. The raw ceiling applies only to this fixed invoice.

Credit the independent-handoff method in #5599 and #5602/#5611/#5615; the #6348/#6398 root; the #6529 native source, including Rohan Arun's #6399/#6417 and Erwan L.'s #6453; and the #6524 replay interfaces. Exact source bytes, hashes, Git blobs and original notices are retained. NOTICE credits Cinna Davis, Jacob Alan Sussman, DreamingOfClouds, David Arias and the other native, compiler, interval and helper contributors. New construction, proof and package: Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0.

Canonical investigation. Canonical main 7c49fe32, priority revision 8 and live overlap were refreshed. This scope changes the caller boundary and leaves the native word fixed. It is separate from the active fixed-native monotone-contact and overwrite-query work. Maintainer edits are disabled; no merge or frontier update is requested.