[1337isnot1337]

The coded p2 caller is missing autonomous main Gaussian outputs. This change sends a saved FULL output through two already-paid queries, recovering the previously absent first-input coefficient D1 Q^-1. The complete output still depends on other independent inputs, with second-input coefficient Q^-1 C1 Q (I-Q) D1. Its exact complex rank tends to three quarters of the affected owner-bank dimension.

This is a component construction and a bounded synthesis checkpoint, with no new kappa or complete caller. It changes the fixed-input premise of the passive saved-query result while retaining both FULLs, the paid IDLE, all three query banks, every independent input and all 816 helper jobs. The proof gives the complete four-input row, all-width coupling rank and additional ordinary-operation/storage ledger. The inherited native ABI and phase/helper-autonomy contracts remain premises.

The exact formal search covers 8,281 policies: reduced code words through length seven, six nonzero dyadic coefficients and the stated finite left code/Pauli decoder set. All retain only one of the four required jobs. Failure in this universal algebra is not a physical impossibility certificate; additional physical source relations and other feedback/control grammars are outside the experiment. A separate 49-policy pilot directly checks 196 constructive or separating-functional certificates.

Validation at contribution head 73b5f0d8c0a6410c3ab4bf45643c54f8802b84e3:

• CPython 3.12.15 registered replay passed: full normal 8,281-policy/rank regeneration, followed by optimized component and certified-pilot replay. Exact row formulas, nonzero coupling, rank counts through width 64, source hashes and corruption controls pass.
• Committed-byte preflight and official 14-file export/integrity check pass. Optimized read-only Git-free export replay passes with PATH=/nonexistent and unchanged exported bytes.
• Source-history preflight is unavailable because this clone is shallow. Source blobs and their current pinned bytes are checked; full-history ancestry validation is not claimed.
• Canonical main was refreshed to unchanged ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c. Priorities and selected kappa 0.00302015 remain unchanged. Submission overlap covered 334 open PRs, 4,438 Discussion records and all 6,996 tracked local notes. This does not cover arbitrary diffs or unpublished work.
• Hosted checks are pending. No native-word, compiler, precision/tape, BIT, outer, full multiplier, human-review or proof-kernel acceptance is claimed.

Reproduce:

python3.12 -B scripts/research_package.py --package research/coded-active-feedback

PR5200, head 40bb94aebbf591a99e2f48533f16efe8914fb1e2, concerns two FULLs with restored dirty workspace and excludes additional paid operations/owned COPY/CLEAR resources. This experiment retains three paid query banks and owned captures, and produces no autonomous new job; it is not a counterexample to that result.

Canonical investigation: #4930 (comment) and the linked scope refinement. The next construction must remove the explicit whole-input coupling and provide a favorable complete bill; another selected-column identity is insufficient.

Credit Dugongue/mdumitrean #4948/#4935/#4929, Dillon #4933, the passive saved-query authors and Chris R/Clear1nsight, Cao Yifan #4610, Cinna Davis #4694/#4698/#4470, Rohan Arun #1931, Ali Romman #1862, zxv, Jacob Alan Sussman and the retained native/Clifford/compiler/precision contributors. New work by Cinna Davis with substantial OpenAI Codex assistance; no subagents. Apache-2.0.