[Clear1nsight]

Problem and result

The retained outer layout and the newer actual-width root choose different chunk widths. The outer construction has d=floor(p^(1/40)), selects g=d-1 axes, and lays out chunks using K_d=floor(d^(1/500)). PR #3599 instead computes K_g=floor(g^(1/500)). At every nontrivial boundary d=k^500, the two widths are k and k-1. This changes the complete array extent and the selected physical bits. Enlarging a left extent to hide the cardinality mismatch still applies the wrong tensor.

This package proves the mismatch and constructs a matched layout, inverse layout and complete descriptors using K_g. It covers every common offset, top and bottom elementary round, singleton and mixed axes, and both directions. The common rounds already select consecutive equal-sized chunks, so this repair needs no additional general-support router. Layout movement and component-order conversion remain charged, and the old outer constructor still needs a correctly typed replacement.

The written counterexample survives final rounding: an admitted unit-disk impulse produces different p-grid outputs under the intended and naively substituted tensors. Exact checks also distinguish the production floor thresholds, including the actual caller's precisions divisible by six. The matched K>=k threshold is (k^500+1)^40, rather than k^20000.

Conditional layer theorem and published diagonal join

The proof establishes the actual caller's record-size and dimension admission. Completed normalised butterflies, truncation towards zero, and signed polynomial permutations preserve the unit disk on the p-grid throughout all rounds. Thus w=p+2 admits every required signed negation. PR #3611 already supplies the one-packet width observation; this result proves its complete-round implication.

With T=Mr coefficients, the retained ordinary movement exponent tau=99830289/10^8, and root exponent alpha=99827101/10^8, the conditional bound is

O(T p [d K + p K^(tau-1) + ell g^alpha log p]).

The remaining caller must provide the actual root/rounded return and a complete lifecycle bill Q <= C M R(rw+A+p^3)+poly(p), with fixed simultaneous buffers, restored borrows and heads, and consumed previous outputs. Here R<=ell and A=log2(M). Unknown charges are not zero. The narrower outer movement bottleneck and selected exponent remain unchanged.

During this investigation, Sagar Thakrar published PR #3617 at 4bf091f415d6470b60a5062a08b0a47e5b12dbd7 and handed its fixed-h pass to this complementary audit. A separate addendum retains all twelve predecessor files unchanged and executes that actual diagonal between explicitly unpriced H, rounding and layout oracles. It supplies the fixed-h enumeration, extraction/assembly, packet rearming and head-return portion of Q. Its 38 roles include both full streams; the full pass is one-shot, so packet reuse does not establish reuse across rounds. PR #3619's adjacent router is not silently substituted.

Evidence and limits

• Original component: ten complete small cubes, 50 completed-round comparisons, seven structural rejection controls, and two actual PR feat(research): execute encoded twiddle shape control #3593/research: consume encoded twiddle headers on signed packet tapes #3611 packet joins.
• Diagonal addendum: 12 positive completed rounds, 384 actual packet applications and 4,096 Gaussian coefficient comparisons. Positive diagonal tariffs total 19,566,850 actions. A separate 64-packet wrong-K pass disagrees at four coefficient positions.
• Both directions start from the same initial cube. This is not a forward/opposite full-transform round-trip claim. Fresh stage instances do not prove a physical all-round allocation schedule.
• Source-byte, strict typed-receipt, off-grid, one-shot and tape-lifecycle controls pass. Normal and optimised wrappers and independent same-session Git-free copies preserve bytes and modes.

The literal source executables cap ell at 32, while the nontrivial outer bands imply ell>=45,812,984,491. Finite fixtures corroborate the interfaces, not a production outer execution. No historical full diagonal suite, physical T74 production run, full supplier, formal-kernel proof or exponent improvement is claimed.

Registered reproduction and source-history commands:

GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/research_package.py --package research/twiddle-matched-layer
GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/check_research_commit.py --package research/twiddle-matched-layer --check-source-history

Public head 328c40966b650f60b1d62cfb0b1d67b2b755eb62 has tree 190e192e4ad13556740bbfd8adee025ce6c7ebeb, matching the reviewed local tree. All four registered commands, metadata/source pins, the 39-file committed-byte/source-history gate, and the official public export/check pass. An independent actual committed Git-free replay passes all four declared commands with empty stderr, preserving all 40 exported files, five directories, and the extraction-root mode. The 501,760-byte tar has SHA256 2019c49110359ee81e4c990b554c666d40e22b0b2f310018529096cf0e1e782b. The original and addendum receipts remain 33069d629d9684a9cdaa728641c6c6ee02424059a5ac58acf5e2c95599ebcae4 and 553be8d67783d69930768c8c8e94215eaed803cbcf60d527267291e46ac9a4dd. Hosted CI will be reported after its actual result.

Scope, provenance and handoff

This user-assigned uniform-transfer-audit continuation has changed, bounded scope under priority revision 6 and claim #19015428. Canonical main remained 20ecf2891d80b5acf18d980b2164fb44ea7faa90 at the fresh pre-submission fetch. The 10:24 API checkpoint covered every PR body updated since 09:58, with separate fresh visible Discussion reads; historical diffs and exhaustive Discussion pagination are outside coverage.

Only this package is added: 39 files comprising 25 retained inputs and 14 new proof, checker and metadata files. Original source pins and credit are retained; ancestor a71efb6cfb2a53df145e207ddccc63815c4aabb8 provides the source bytes in this PR's own history.

Three useful next obligations are:

1. Implement the typed actual-width outer wrapper with identical complete-array order/extent, bit-order conversion and one final rounded H return.
2. Connect the diagonal across all rounds with paid descriptor changes, framing, output consumption/reset and exact simultaneous stock.
3. Improve the remaining outer movement bill through a separately admitted construction, retaining precision/error, spectators, ownership and the complete transfer implications.

Credit Nick Petalas for PR #3493/#3593 and their lineage; Jose Manuel for PR #2298/#3599, retaining Hiroki Kumazaki's factory/rate work; Sagar Thakrar for PR #3611/#3617; and the retained positional, monomial and transform authors. Clear1nsight prepared this work with substantial OpenAI assistance from a root agent and three concurrent specialists. Same-session reviews are not independent human acceptance. New work is Apache-2.0; original licence and notice bytes are preserved.

[Clear1nsight]

Publication verification complete

Public head 328c40966b650f60b1d62cfb0b1d67b2b755eb62 and full tree 190e192e4ad13556740bbfd8adee025ce6c7ebeb match the reviewed package. The final committed-byte/source-history check covers exactly 39 files under research/twiddle-matched-layer/, with source-history commits main 20ecf2891d80b5acf18d980b2164fb44ea7faa90 and this PR's unchanged-source ancestor a71efb6cfb2a53df145e207ddccc63815c4aabb8. All 25 predecessor input files retain their original bytes and source-specific credit.

Hosted workflow 39120050038 completed successfully at 10:41:55 UTC on 18 October. Both jobs pass on CPython 3.12.15. The actual preview merge ea2a13de93e4c8ff746bd01f5b138041df6d1344 has parents main 20ecf28 and public 328c409, and complete tree 190e192e4ad13556740bbfd8adee025ce6c7ebeb, identical to the reviewed head. Logs contain all four registered CHECK entries, both original and both diagonal PASS markers, the registered partial outcome, and a successful final tracked diff check. This hosted workflow does not separately run the source-history/export gates or admit a physical whole layer.

Separately, official public export/check and an independent actual committed Git-free replay pass. All four declared normal/optimised commands exit 0 with empty stderr and their exact scoped PASS messages. Every one of the 40 exported files, five directory modes and extraction-root mode remains unchanged after each command. The tar contains 501,760 bytes with SHA256 2019c49110359ee81e4c990b554c666d40e22b0b2f310018529096cf0e1e782b. The original receipt remains 33069d629d9684a9cdaa728641c6c6ee02424059a5ac58acf5e2c95599ebcae4, and the diagonal receipt remains 553be8d67783d69930768c8c8e94215eaed803cbcf60d527267291e46ac9a4dd.

Independent same-session source/typed-receipt CLI controls reject a one-byte source change and Boolean-false to integer-zero substitution in each wrapper. Finite science covers the stated 50 original completed-round comparisons and 12 new arithmetic-H rounds with 384 actual diagonal packets; the separate wrong-K control is excluded from positive tariffs. No historical large source suite, physical H/root, all-round allocation/reuse/stock, complete invoice, independent human/formal acceptance or supplier admission is claimed.

The final 10:40:25 UTC canonical checkpoint still reads main 20ecf28, priority revision 6, with every checked guide and selected-record hash unchanged. A separate update-window scan through 10:40:03 read the newer PR3624 body as a conditional supplier-allocation lead only; its arithmetic and release were not imported or validated. It does not close the remaining caller/root/reuse interface. Frozen science and source inputs remain unchanged. The current claim and TASK.json give the precise handoff and predecessor credit.