ODD-PRIME EXTENSION: FOCUSED ORIGINALITY AND CLOSEST-METHODS REVIEW
2026-10-18. Independent literature review for the active research branch.
This is not a correctness certificate, publication clearance, or priority claim.
The proposed all-prime proof was supplied as a research outline; the sealed
qutrit manuscript and its SOURCE_AND_ORIGINALITY.txt were read for baseline.
No sealed artifacts or shared registry files were edited.

VERDICT
A complete arbitrary-mixed-input proper agnostic stabilizer learner for every
fixed odd prime is not identified in the inspected sources. Qi explicitly leaves
mixed-input extension open. A proof delivering that conclusion would represent
a substantive scope extension of Qi, and an extension of the present qutrit
result family, rather than a new independent learning architecture. Originality
is provisionally supported for the mixed-input escape estimate and its full
learner consequence. The measurement and bootstrap ingredients have substantial
prior art. The p=1 mod 4 specialization needs particularly restrained attribution.

PRIMARY COMPARISONS (versions checked on current arXiv abstract records)
1. Qi, Xu, Feng, Li, arXiv:2607.15559v1 (17 July 2026).
https://arxiv.org/html/2607.15559v1
Theorem 1 / Theorem 13 concern pure inputs in every odd-prime dimension.
Theorem 7 supplies pure-state subspace escape; Section III-A uses MUB geometry;
Section IV supplies qudit stabilizer bootstrapping. Section VI explicitly
identifies mixed-input distribution characterization and anticoncentration as
unresolved extension obstacles. The proposed purity-retaining local inequality
therefore addresses an actual scope gap, not an overlooked mixed hypothesis in
this version. The proposed learner should be called an extension of this method.
The pure MUB fidelity floor cannot simply be asserted for a mixed conditioned
block. Showing the mixed block estimate is the crucial new analytic obligation.

2. Chen, Gong, Ye, Zhang, arXiv:2408.06967v3 (5 December 2024).
https://arxiv.org/html/2408.06967v3
Mixed-qubit stabilizer agnostic learning and its quasi-polynomial bootstrap
architecture are prior work: Lemma 5.3 / Theorem 5.5, Section 6, Corollary 6.3.
The proposed result cannot claim invention of mixed stabilizer learning,
conditioning amplification, or proper agnostic bootstrapping. Ordinary embedding
of p-dimensional systems into qubits does not make the theorem an immediate
application: it does not identify p-ary stabilizer states with binary stabilizer
states, and an arbitrary binary output need not belong to the target p-ary class.
Purification also does not give an immediate reduction under copy-only access:
accessible copies of an arbitrary purification are not supplied, and its optimal
stabilizer overlap is a different optimization problem.

3. Allcock, Doriguello, Ivanyos, Santha, arXiv:2510.06848v3
(25 August 2026).
https://arxiv.org/html/2510.06848v3
Skewed Bell sampling, conjugation by register mixing, and sums-of-squares
arithmetic are established methods. The introduction and Corollary 44 explicitly
distinguish odd primes congruent to 3 and 1 modulo 4 and exploit a square root
of -1 in the latter class. Section 3.1 analyzes sampling distributions and their
submodule masses. Thus the weighted isotropic tensor representation satisfying
sum(t_j^2)=0 is closely related measurement algebra, and the two-weight
p=1 mod4 construction/four-copy difference sampler is an arithmetic specialization
of known ideas. A fourth-degree mixed escape estimate may still be a new useful
analytic consequence; copy count and square-root arithmetic alone are weak
novelty claims. No complete arbitrary-mixed-input optimizing-stabilizer agnostic
learner was identified here. Check normalized Fourier conventions when identifying
its marginal with the proposed sampler; structural equivalence is stronger than
an assertion of identical labels without that calculation.

4. Noeller, Tran, Gachechiladze, Kueng, arXiv:2510.08070v2
(1 September 2026).
https://arxiv.org/html/2510.08070v2
Section 4 measures commuting tensor-power Weyl operators for arbitrary density
operators and estimates Weyl amplitudes. Generalized/coarse-grained Bell PVMs
implement the measurement; independent outcome differencing is a standard way
to produce squared characteristic moments. This is direct prior art for the
qutrit six-copy primitive. General weighted commuting Weyls use the same
representation-theoretic mechanism. Its amplitude estimation task and lower
bounds do not by themselves supply an efficient proper optimizing-stabilizer
learner. Do not transfer its copy lower bound to the proposed different task or
claim a contradiction from the new constant-copy sampler.

5. Hinsche, Eisert, Carrasco, arXiv:2505.15770, current HTML accessed.
https://arxiv.org/html/2505.15770
Backward citation from Qi, reference 32. The hidden-stabilizer-group problem
assumes an actual symmetry subgroup and a correlation gap. The paper explicitly
anticipates generalizing agnostic learning by replacing Bell differencing with
its qudit measurement, but does not there give the full arbitrary-mixed optimizer
escape and proper learner asserted in the proposal. This is significant
conceptual precedent, which should be acknowledged if the Fourier viewpoint is
used. Shared-code-space input variants are not equivalent to arbitrary mixed
states and a closest stabilizer output.

6. Tang and Steckmann, arXiv:2610.03307v2.
https://arxiv.org/html/2610.03307v2
Noise-robust stabilizer-structure learning with promised/noisy low-nullity qubit
scope. Different target and hypotheses; not identified as the all-odd-prime
mixed proper learner.
Fan and Luan, arXiv:2610.14758v1.
https://arxiv.org/html/2610.14758v1
Mixed-qutrit three-copy Clifford invariant/testing algebra; not an identified
complete learner. These October leads were checked because the baseline cites
them and they postdate the central sampler papers.

CLAIM BOUNDARIES AND ROUTINE-COROLLARY RISK
- A=D^{-1}Tr(rho W_x rho W_x^dagger) is positive and normalized: the Weyl
  twirl gives sum_x W_x rho W_x^dagger = D I, hence sum_x A(x)=1.
  It is p_rho(x)=D^{-1}|Tr(rho W_x)|^2 whose total mass is Tr(rho^2).
  Factorization through scaled convolutions of A still requires consistent
  Fourier conventions; A itself is a probability law for every density rho.
- For weighted t=(1,a,b), sum squares zero gives commuting physical operators.
  Allcock already supplies the relevant arithmetic. New content must be the
  mixed lower bound and its use, not that existence lemma.
- The supplied g >= (p-1)/(4p) f^2 local estimate needs a fresh proof for arbitrary
  positive conditioned blocks and every odd prime, including p=3,5. The present
  review does not certify it, its constants, or the asserted F^4/F^6 escape.
- Once mixed escape and qudit projection amplification are proved, the full
  learner is a substantial consequence but mostly known-method composition.
  Track explicit p dependence. Fixed-p quasi-polynomial behavior is weaker than
  uniform polynomial dependence on p. Distinguish two/four/six simultaneous copies
  per primitive from total sample complexity and from conditioned-copy cost.
- If the all-prime proof uses only routine substitutions in the sealed qutrit
  proof, the increment over that private baseline is generalization and arithmetic
  cleanup, while the combined mixed-input theorem remains the research result.
  Preserve one result family and avoid counting p=3 and all-p as independent work.

SEARCH RECORD AND LIMITS
Actual Google accessed in the in-app browser with query
  "mixed" "qudit" "agnostic"
The principal relevant primary hit was Qi. Its AI Overview blurred mixed/pure
scope and was not relied upon. Google Scholar exact-title search returned Qi's
record and no visible cited-by link. An earlier attempted cites=arXiv identifier
URL is not a valid citation-graph audit and its empty result is NOT evidence of
zero citations. Generic web discovery additionally searched mixed qudit agnostic
learning, mixed-state variants, the Qi identifier, and fourth-copy prime mixed
sampling; leads were checked against primary papers. Backward coverage followed
Qi to Allcock/Chen/Hinsche and the baseline to Noeller and October leads.
Forward coverage is limited to search-discovered citing/related leads and
current versions, not a complete verified citation graph. No equivalent full
mixed learner was identified; this does not establish worldwide priority or
exclude unindexed, unpublished, or differently phrased results. A final package
review should refresh discovery and compare exact final theorem statements.

RECOMMENDED CONTRIBUTION LANGUAGE
We extend the qudit stabilizer bootstrapping method to arbitrary mixed inputs
in each odd-prime dimension by proving a purity-sensitive escape estimate.
Known multi-copy Weyl measurements implement the sampling step; a congruence-
dependent specialization gives fourth- or sixth-degree characteristic moments.
The qutrit theorem is retained as the p=3 case of the same result family.
This wording remains conditional on proof completion and independent verification.

CORRECTION NOTE (2026-10-18)
The initial version of the CLAIM BOUNDARIES normalization bullet incorrectly
assigned total mass Tr(rho^2) to A. This confused A with p_rho. The current bullet
corrects that error: A has total mass one by Weyl twirling, whereas p_rho has
mass Tr(rho^2). The parent review identified the error and reported agreement of
two independent analytic reviews and direct matrix checks; those checks were not
rerun as part of this correction. This correction does not endorse the proposed
all-prime proof or alter the bounded originality assessment above.
