[aliromman]

This local construction carries centre information across two replicas of the historical gauge44/t16 interface without adding a native recursive child or a Walsh frame change. Its typed monomial-square theorem gives G_s H_t = 0 at every pair of stages when the stated common global involution and frame hypotheses hold. Thus the resulting residual factors compose by addition, with an explicit inverse.

The proof, fresh independent agent review, cold replay receipt, and source pins define the submitted claim.

The general theorem assumes an admitted raw interface, legal monomial access to Q^2 and Q^-2, matching replica views, and the stated productive-frame intertwiners. It does not require Q^4=I. The concrete instance uses the original complex phases, including their scalar phase. Both paired words accept all 1,408 independent inputs: 448 data fields, 16 arbitrary mode fields, and 944 arbitrary ordinary helpers. The helpers restore in their specified output frames; the mode outputs remain part of the coupled interface.

Per pair, each orientation adds 2,688 physical ADDs and 448 literal translations. The added real scalar allowances are 25,088 forward and 34,048 backward; including the two cores gives 433,924 and 442,884. Both retain 10,112 native events and rank mass 11,044. Translation execution, native children and wrappers, owner access, mode histories, the final decoder, storage, precision, and recursive assembly still need their separate bills. These are local allowances, not a complete supplier cost.

No complete kappa improvement is claimed. Final odd-phase reads and injections, arbitrary-mode restoration through a full controller, and global supplier admission remain unresolved. The branch starts from canonical main b58ad9ef4d4e861b0eaa5dba41742bdc072dca51; that commit selects the conditional PR #4470 joint-helper result. The historical source remains bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Admission to the newer selected construction is not established, and no selected file changes. See the current-source boundary.

The old-owner view annex adds a general coefficient interpretation for the unchanged physical paired word. If the old inherited frame is O and the fresh exterior frame is P, Delta=P^-1 O commutes with the complete local transform under the stated exterior-axis and convolution hypotheses. Thus B_old=D_out^-1 B D_in, with identity on data and ordinary helpers and the appropriate Delta on each promoted mode. Delta may differ between modes and need not be monomial. No Delta conversion is executed. For example, v=-z-Gx becomes h'=-h-Delta^-1 Gx, and y'=y+x+Hv becomes y'=y+x+H Delta h'. The result interprets changing promoted-mode outputs as well as restored ordinary helpers.

The written proof review requires the complete arbitrary-input helper jobs, actual entry/output views, and destination wrappers. Correlated inputs are allowed. Promoted owners must avoid every role in the other core, and shared ordinary owners need the checked complete-job conditions. Owner matching, all phase records, the 37 exchanges, helper windows, every physical view cost, and later productive restoration remain inherited obligations. The fixed original and repaired full words are known to fail: family 13005=1 gives family 112=-1/4 in both mode-sign variants. The retained final status preserves this boundary. The view theorem supplies neither a global repair nor a complete kappa improvement.

There is no separate numerical checker for this general change-of-coordinates theorem. The fresh source audit checks thirteen original files and all four written-review pins; normal and optimized receipts agree. It explicitly records that no mathematical replay occurred. The existing published paired replay validates B. The published-source identity record binds the inherited native review and notices to the accepted f917bc1b4a769a241349eda7c0e22e374548cf58 tree. No old phase/history, matching, global-defect, or restoration suite was rerun for this annex. With Python 3.11+, the standard library, and a new output directory:

python3 -I -B research/original-paired-gap/annexes/productive-owner-view/check_sources.py --out /tmp/productive-owner-view-audit

Expected output:

PASS_PRODUCTIVE_OWNER_VIEW_SOURCE_AUDIT

The annex notice credits the source-domain, coherent-port, and circuit-interface contributions and retains the published historical gauge44/t16 notices byte for byte. Accepted package files and historical source pins stay unchanged. Substantial OpenAI Codex assistance was used; Apache-2.0.

The independent annex review checks the ordered proof and exact source identities. It is a separate agent review, not human peer review.

Reproduce with Python 3.10 or later, the standard library, and Git. The clone must contain the historical source commit and its pinned archive. No network is needed for replay.

python3 -I -O -B research/original-paired-gap/replay.py --repo . --out /tmp/original-paired-gap

Expected output:

PASS_EXACT_ORIGINAL_PAIRED_MAPS
PASS_ORIGINAL_PAIRED_NATIVE_COMPONENTS
PASS_GENERAL_MONOMIAL_SQUARE_IDENTITIES
PASS_PORTABLE_ORIGINAL_PAIRED_GAP

The fresh isolated replay checks all core and paired input columns, frame records, retained native streams, 57,344 line columns, and 1,008 affine routes. Its six mathematical receipts match the retained evidence. A separate implementation also recounts the costs and reproduces six failures on actual Fourier characters, including omitted translations and incorrect update order. The all-depth claim comes from the operator proof. The separate owner patch, every inherited native kernel, the repository-wide suite, and the full selected replay were not rerun. The reviews are by separate AI agents, not humans.

Predecessor credit remains with @icekylinx for the source gauge and pipeline, @FanPUYen for the t16 construction, @jeremykothe2 for the retained PR #799 word, @chafreaky for the PR #741 frames and PR #685 owner construction, and @rohanarun for the native complex recurrence correction. The retained notices give the full lineage. The loader comes from PR #1862 at 7649d9ceecec949541bec4bbde5929344166ba59; route reconstruction adapts PR #1969 at a6e6ad3936f67b8f63b5b68c5e75d540610a65e7.

Recent PR #4694 and PR #4698 study a different retained-centre interface and conditional consumer on a newer source. They are related work, not consumed dependencies or admission evidence for this package. No priority claim is made for elementary block identities. Prepared with substantial OpenAI Codex assistance under the user's direction; Apache-2.0.