FINAL MANUSCRIPT ORIGINALITY, ATTRIBUTION AND SCOPE REVIEW
18 October 2026 (America/Chicago). Independent AI review.

DISPOSITION: PASS within the stated literature/attribution scope, conditional
on the separate exact-source analytic review. No originality blocker found.
The manuscript is an appropriate focused specialist follow-up. This does not
certify worldwide priority, external peer review or publication permission.

EXACT SOURCE
Read all six manuscript files. Fresh SHA256 checks matched every entry in
evidence/manuscript_source_review1.json:
geometry.tex 044c471f72eace8a3a115af6db4cb66ecee1fb5579e909e91d3c79c2eb419823
inference.tex 1c8c7bd26da5424767dc1def4137ae780d9c0127eba1d3e0cfd34d94bc11475e
main.tex 87b2bf549bbd99c3898c8ad322195f3a79921592c32f847027663137a32a7a26
references.tex b9a56069f940bb459fdf8994db45ca45402f183f2a0b855b2734f35bda25a194
stopping.tex 3219540581a156a2176e8c7ed5b705ef455d29110e096d80d687dd7184074acf
trajectory.tex 8f37894e57f6b1bc1a2759456b190733936ccdaa1bc867eea026b7d856cd35fb
The preserved analytic baseline has SHA256
7d2ed0072718a9fbb84581ed4c67fe75d4781468592bafa3198e163bbcd12edd;
the stopped calibration findings have SHA256
db4525f5344d5add32130cbd253bb3106a8fe90ed86187bd0a83c474c7171de8.
These hashes identify reviewed bytes; they do not prove the theorem.

LITERATURE COVERAGE AND FINAL REFRESH
reviews/publication_literature_review.txt is preserved as the initial full
record. It records actual Google discovery and refreshed primary checks of
Kokot, Mordant, Feydy, Wormell--Reich, Cheng--Landa, Celisse--Wahl,
Maeda--Yao--Nitanda, the prior Schubr publication and relevant recent work.
At this final checkpoint actual Chrome Google discovery was refreshed for
  "Sinkhorn" "score" "first" "stopping".
Its visible results did not identify a directly covering theorem. A recent
diffusion/attention lead was checked on the primary AAAI abstract page:
Kwanyoung Kim, Toward the Frontiers of Reliable Diffusion Sampling via
Adversarial Sinkhorn Attention Guidance, AAAI 40(7),5682--5690 (2026),
https://ojs.aaai.org/index.php/AAAI/article/view/37488
It concerns attention guidance; its full PDF fetch timed out. No detailed
theorem-comparison claim is made from that abstract alone. This final search
supplements, rather than replaces, the substantive predecessor checks in the
initial review. Search coverage is focused, not an exhaustive citation census
or access to unpublished work. UW live fetch limits and the reused archived
primary Kokot text/metadata are explicitly recorded in the initial review.

ATTRIBUTION CHECK
The related-work section expressly credits Kokot Chapter 3 for Gaussian-RKHS
scaling differentiation, the self-diagonal plus-resolvent and a fixed-epsilon
Hilbert CLT, and Section 4.4.1 for two-update population matching. Those
attributions agree with the inspected primary statements/proofs. The paper
does not present these mechanisms as newly invented.
The algorithm is cited to Feydy2019 and Mordant2026 where introduced. The
primary Feydy equation (25) is the averaged symmetric update after changing
to scaling coordinates. Mordant's Euclidean score-limit setting is separated
from this exact periodic Gaussian model. The bibliography uses the title
printed on Mordant v2's PDF; its abstract metadata has a different title,
as documented in the initial review.
The paper credits existing normalization/operator theory (Wormell--Reich),
approximate normalization at statistical accuracy (Cheng--Landa), combined
statistical/iteration bridge error (Maeda et al.) and spectral discrepancy
stopping (Celisse--Wahl). It does not claim the first statistical stopping
principle, first Sinkhorn finite-iterate analysis or new self-transport
algorithm. All citation keys resolve, and all nine bibliography entries are
cited in the frozen source.
Schubr2026 cites the actual observed public edition 1 and identifies the
earlier arbitrary-candidate certificates/sharpness witnesses. The present
actual-trajectory theorem is a follow-up within the same family, not a
republication of those witnesses as a new stopping result.

EXACT CONTRIBUTION AND MATHEMATICAL VALUE
The combined theorem concerns a fixed positive C6 density on T^d,d=1,2;
the exact integral-one periodic Gaussian; deterministic bandwidth satisfying
epsilon->0,n epsilon^(3d/2)->infinity,n epsilon^(d/2+3)->0; the same iid
sample for scaling, residual and point query; standard initialization b0=1;
and the first projective residual hit at n^-1/2 epsilon^-gamma for each fixed
strict 0<gamma<d/4. It establishes an attained residual bounded below by c
times that threshold for every fixed 0<c<1/2, the leading count
(d/4-gamma)log(1/epsilon)/log2, negligible score error at the same random
index, and the exact empirical true-score Gaussian law. The endpoint result
is a uniform-density class counterexample for the coefficient-one threshold
at/above gamma=d/4; it is not necessity for every density or every prefactor.
The frozen manuscript retains these domains, sufficient windows, strict
endpoints and quantifiers. It does not assert gamma=0 or gamma_n results.

No inspected predecessor establishes this combined actual sampled nonlinear
first-hit result. The identifiable increment is the empirical trajectory and
relative residual crossing analysis, including the dimension-two normalized
row cancellation, decaying commutator, common stochastic errors and lower
residual concentration. That is a meaningful specialist contribution. The
geometric count inversion, standard spectral/CLT tools and Slutsky confidence
regions are useful parts of its explanation, not independent breakthroughs.
The paper appropriately keeps editorial originality ratings and speculative
impact out of the manuscript. Wider priority remains provisional.

FIXED-QUERY INFERENCE VERSUS FINITE-SAMPLE HONESTY
The feasible pivot uses the same-sample positive periodic KDE consistently;
Slutsky needs no independence from the stopped score. The confidence ball
has limiting coverage at each fixed density and predetermined query. Neither
data-selected query coverage nor simultaneous spatial bands is asserted.
The short sine example gives score q e1 at x0 exactly and one-sample total
variation |q|/(2 pi^2 m); the displayed n-sample bound follows by the product
TV inequality. The alternatives can remain between1/2 and3/2 while their
derivative norms diverge. For fixed n, uniform honesty would require coverage
of each q under uniform data; almost-sure boundedness contradicts this as
|q| tends to infinity. Dufour1997 is properly used as an established general
discontinuous-functional mechanism, not a direct new theorem credited here.
This limitation does not withdraw the fixed-f asymptotic result. It is not
marketed as an additional original publication contribution. The omitted
quantitative-class salvage remains outside the paper.

APPLICATION AND CLAIM LIMITS
The supported use is choosing observable residual tolerances while retaining
pointwise uncertainty for the logarithmic density gradient; predetermined
zero-gradient tests follow. The final scope section excludes unknown-mode
location, selected queries, global spatial/path guarantees, boundaries,
vanishing densities and higher dimensions. Iteration counts are explicitly
separated from wall-clock claims. No finite-sample calibration or practical
coverage study is implied. The two bandwidth conditions indeed conflict
at d=3. These statements are coherent with the exact theorem.

No manuscript, predecessor evidence or prior edition was changed during
this final review. Pure layout changes require a source-diff rebind; any
mathematical or consequential attribution change requires substantive review.
