INDEPENDENT CORRECTED-REVISION ATTRIBUTION AND PROOF-CONTINUITY REVIEW
October 18, 2026, America/Chicago

VERDICT: PASS within the stated source and review scope.

Mixed-state escape bounds and proper agnostic learning of stabilizer states
in odd-prime dimensions. Scott Schubr.

SOURCE BINDING
Corrected manuscript:
C:/Users/scott/OneDrive/Documents/ChatGPT/Math Lab/odd_prime_learner_publication_corrected_20261018/manuscript/main.tex
SHA256 63d71dce68ca261f600f91a048696b3b381c35f6c97781948e96219e7d49d04b
Compiled PDF at review binding:
SHA256 5f2799f141c9a052bdf6c0e04ef03d266bd0ca5840f45ae6ae2bdcc7c918cd27
This subreview identifies that PDF but does not claim visual/layout inspection.

Sealed all-prime baseline main.tex:
D:/LUMINARY ODDITIES LLC/AI Research/odd_prime_learner_prepublication_Riemann_A_20261018/manuscript/main.tex
SHA256 63f1a1a2400046d0083e8c654a5730a6239a713f09560fce83bcea06153b05b1
Original and corrected GENERAL_PROOF.txt are byte-identical:
SHA256 c041807f92005436abdfae2c10ec583f17453903c4acbc7d7ec0d5d2763b9ef8

METHOD AND ACTUAL COVERAGE
Read the complete corrected manuscript and complete unified source diff against
the sealed all-prime baseline. Read the complete GENERAL_PROOF checkpoint and
the previous independent proof-and-claims report, full-assessment report and
originality/value report. Reopened all three new primary papers and their arXiv
version histories online, reading the exact relevant statements and surrounding
definitions. This is a bounded attribution refresh and continuity review, not a
new exhaustive worldwide-priority search or independent full computational run.
No original or corrected manuscript was edited by this reviewer. Review output
is external to the preserved originals. Code, replay and PDF presentation are
separate assigned checks.

THREE NEW REFERENCES
1. Vishnu Iyer and Daniel Liang, Tolerant Testing of Stabilizer States with
Mixed State Inputs, arXiv:2411.08765v2. The version history records May 12, 2025;
use that archive date, although the HTML body displays a later automatic date.
Lemma 2.12, Remark 2.13 and Facts 2.14--2.15 support the earlier mixed-qubit
Fourier-dual overlap identity and its positivity/normalization. The corrected
paper appropriately credits this precedent and describes its own Weyl identity
as standard, preserving the relevant normalization distinction.
https://arxiv.org/abs/2411.08765v2
https://arxiv.org/html/2411.08765v2

2. Isaac Holt and Sathyawageeswar Subramanian, Learning quantum symmetries,
arXiv:2609.38085v2, September 30, 2026. Lemma 8.4 treats Fourier-difference
sampling. Section 9 and Theorem 9.27 address exact mixed-state stabilizer-group
learning; the group is defined by P rho=rho, with phaseless labels having
unit-modulus Weyl expectation. This differs from finding a best pure comparator.
The correction makes that distinction without repeating an unqualified
total-copy complexity claim. The full-rank depolarized-stabilizer example
illustrates the distinction correctly.
https://arxiv.org/abs/2609.38085v2
https://arxiv.org/html/2609.38085v2

3. Lennart Bittel, Jens Eisert, Weiyuan Gong, Antonio Anna Mele and Louis
Schatzki, Adaptivity is all you need: Optimal stabilizer learning using just
single-copy measurements, arXiv:2610.02031v1, October 1, 2026. Theorem III.1
allows mixed qubits with a known overlap floor strictly above sqrt(2/3).
Theorem A.1 learns pure prime-dimensional stabilizer states exactly. These
scopes are stated accurately in the correction; no necessity of multi-copy
access is asserted. Bibliographic authors, version and date are correct.
https://arxiv.org/abs/2610.02031v1
https://arxiv.org/html/2610.02031v1

PROOF AND CLAIM CONTINUITY
All eight theorem/lemma/corollary environment bodies are exactly unchanged in
the source comparison. All numbered and aligned mathematical displays are
exactly unchanged. The abstract, two theorem statements, local inequality,
hyperplane lift, weighted sampler, constants, thresholds, algorithm steps,
explicit budgets, operation model and unknown-optimum corollary retain the
baseline content. The GENERAL_PROOF supporting source is unchanged.

The only proof prose change defines the auxiliary favorable witness explicitly:
active only while its prefix has target-fixing low-correlation jumps; absorbed
at first recording of the optimizer; killed on another continuation or abort.
This is sufficient and matches the previously audited stopped coupling.
Every active code fixes the original optimizer, so its original-copy weight is
at least F>=tau; no zero-weight wrong-prefix ideal state is required. The cap
loss bound Q exp(-tau K)<=s0/4 is therefore unchanged. The physical algorithm
still caps all branches and retains candidates after aborts. This clarification
changes neither the algorithm nor its success/resource guarantee.

The fresh comparison reveals no new proof gap, enlarged claim or uncredited
ingredient. Known sampling/arithmetic/bootstrapping remains credited. The
identifiable contribution remains the mixed local estimate, operational
all-odd-prime escape and complete proper mixed-input learner analysis. The
previous specialist-publication merit judgment remains applicable, with
provisional external novelty and no practical/optimal-resource claim.

RELATIONSHIP AND LIMITS
The preserved qutrit paper is the p=3 special case of this same consolidated
family, not a second independent publication. This correction does not create
another theorem family. Exact Clifford/coherent measurement assumptions, finite
diagnostic limits, no finite-universal-gate robustness theorem, and distinction
between internal AI assistance and external human refereeing remain explicit.
No claim is made that internal review proves worldwide priority. This report
does not certify mathematical facts by hash or authorize publication itself;
current human release instructions and the separate final package checks govern
handoff.
