[aliromman]

This PR adds a local construction and original-owner binding for one clean core in the original complex frames, at every positive tensor width. The physical prefix and suffix restore all 480 arbitrary helper contents, prevent helper inputs from entering data outputs, and preserve the eight selected complete F9 jobs. They add no field, native child, address map, or phase map.

The proof, fresh replay receipt, independent publication review, and source pins give the evidence. There is no improvement to the complete kappa calculation. The actual routed data controller must still satisfy E=W^-1 at the original terminal.

With K=R^T/4, the data maps are F(x,y)=(x,y+D_plus x) and B(x,y)=(x-D_minus y,y), where:

D_plus  = I-KR+KRQ
D_minus = I-KR+KRQ^-1

These kernels are distinct on the actual native operator at every positive width. The proof keeps operator order and uses no even-width, characteristic-phase, paired-replica, or finite-order premise. Content restoration preserves each helper's declared physical output frame; it does not make its physical job the identity.

The complete body substitution holds on arbitrary correlated physical inputs. The owner check binds all 144 original invocations and 69,120 helper slots, including 1,152 selected width-nine jobs. It preserves the original owner and phase schedule. This establishes helper progress and the local data interface; it does not close the changed global data word.

Each orientation adds 1,792 complex ADDs and eight complex negations. The added real primitive bounds are 17,040 forward and 22,416 backward. Including the raw core gives 221,458 and 226,834. Both retain 5,056 native events, including adapters, with paid profile {1:2412,2:418,3:432,4:142,5:82} and rank mass 5,522. These are component counts. Supplier parser lowering, complete routing and control costs, recursive costs, finite precision, and integer recovery remain open.

Run from the repository root with Python 3.11 or later, its standard library, at least 3 GiB free disk, and a new output directory:

python3 -I -B research/original-clean-source-interface/replay.py --out /tmp/original-clean-source-replay

Expected final output:

PASS_ORIGINAL_CLEAN_SOURCE_INTERFACE

The three decisive checks passed in normal and optimized Python. All six fresh receipts equal their frozen receipts byte for byte. The independent publication review repeated the six jobs in a cold copy. The checks cover all 704 formal input columns, physical helper endpoints, exact native-event preservation, and original owner binding. Controls reject wrong operator order, omitted cleanup or signs, and replacement of the required output Q^-1 by Q.

The raw content map, dense native phase compiler, and complete old owner-axis history remain pinned inherited premises; this replay does not rerun them. No selected-construction replay, full changed data-controller check, complete supplier invoice, or precision proof was run. Two portable scripts only change source roots and archive-member reads. The adaptation record retains the originals and exact diffs.

The packaging base is b58ad9ef4d4e861b0eaa5dba41742bdc072dca51, which selects PR #4470. The consumed gauge44/t16 source remains historical commit bce54fb3f895cbe5cd4c0eb477c3afeed100190f. This PR does not transfer the theorem to the newer selected construction.

The retained source notices credit @icekylinx for the gauge and supplier pipeline, Hao Yan (@FanPUYen) for t16 construction and integration, Jeremy Kothe (@jeremykothe2) for the PR #799 X4 word, Chafik Boukhalfa (@chafreaky) for the PR #741 frames and PR #685 owner construction, and Rohan Arun (@rohanarun) for the native exact-complex recurrence correction. The full preceding lineage and Apache-2.0 notices remain. Substantial OpenAI Codex assistance was used for the construction, proofs, separate agent checks, and publication package.

The independent publication review was performed by a separate Codex agent; no human peer review is claimed.