INDEPENDENT MANUSCRIPT PROOF REVIEW
Date: October 18, 2026
File reviewed: manuscript/main.tex
SHA256: 63f1a1a2400046d0083e8c654a5730a6239a713f09560fce83bcea06153b05b1
Related analytic checkpoint: ../riemann_A_odd_prime_extension_20261018/GENERAL_PROOF.txt
Checkpoint SHA256: c041807f92005436abdfae2c10ec583f17453903c4acbc7d7ec0d5d2763b9ef8

SCOPE AND METHOD
Read the entire actual manuscript anew, including both theorems, all lemmas,
algorithm and parameter formulas, corollary, and operation-model limitations.
Retraced mathematical implications rather than treating the checkpoint's earlier
review verdict as evidence. Compared the manuscript's formulas and hypotheses
with the actual analytic checkpoint previously read in full. No manuscript,
baseline, original package or registry was edited. This report is an internal
AI-assisted mathematical audit, not external human refereeing, formal proof
verification, a literature-priority clearance, or a rendered-PDF layout review.

VERDICT
No material mathematical or transcription defect found in this exact source.
The arbitrary-mixed-input escape bounds and proper additive learner follow in
the stated exact prime-dimensional Clifford/coherent-measurement model for all
odd primes and n>=1. The explicit resource accounting supports both fixed-p and
conservative growing-p claims. The source is suitable to advance to separate
Publisher assessment; this audit does not grant release permission.

CLAIM-BY-CLAIM CHECKS

Normalization and conventions.
The stated X,Z conventions give the displayed Weyl product phase. For A,
positivity and twirling yield a probability law even when rho is mixed.
The explicit inversion expression D^-2 sum_v |chi(v)|^2 omega^[x,v] has the
correct Fourier sign and normalization. The manuscript correctly distinguishes
A from the generally subnormalized characteristic weight D^-1 |chi|^2.
This distinction is essential and is preserved through the sampler argument.

Local estimate and hyperplane lift.
The complete-MUB second moment 1+Tr(tau^2), maximum-probability bound, and
diagonal Cauchy bound give the displayed two quadratic factorizations.
The common leading coefficient is exactly (3p-1)(p+1)/(4p(p-1)).
The first auxiliary root exceeds one and the second is <=2/(p+1);
hence both closed-interval sign arguments hold.
For the hyperplane formula, summing diagonal Weyl characters enforces equality
of the last n-1 coordinates; the factor p^(n-1)/D is 1/p. Summing all of S
enforces equality of all coordinates, giving the stated difference formula.
Positivity makes every other block contribution nonnegative. The target block
normalization t cancels quadratically, and its one-system stabilizer optimality
follows from the original global optimization. The explicitly stated n=1 case
also works. No purity assumption or loss depending on n appears.

Weighted PVM, arithmetic and escape.
The condition sum t_i^2=0 cancels the tensor-Weyl commutator phase and produces
an ordinary representation. Character projectors have rank D^(k-2); they form
a complete PVM. Its Fourier statistic has the sign shown. Subtracting two
independent outcomes gives a product of squared moduli, and A_t(x)=A(t^-1 x)
is the correct scalar pushforward without additional normalization factors.
The physical measurement uses commuting joint operators and preserves their
eigenspaces. It does not call for conjugated input states or a sampler for A.
For p=3 mod4, the square-set intersection gives two nonzero coefficients;
for p=1 mod4, a^2=-1 gives the two-register construction. The p=5 exception
is handled correctly. The factor-space convolution events are disjoint and
sum into S minus H, proving precisely the stated constants and copy counts.
Enlarging T to a hyperplane correctly weakens the event. At p=3 the bound
is F^6/18. The manuscript makes no copy-optimality claim.

Conditioning.
Stabilizer projection closure sends a pure stabilizer to zero or a scalar
times another pure stabilizer. The squared scalar c<=1 bounds its unnormalized
overlap by F, while the chosen optimizer attains F. Thus the conditioned
optimum is exactly F/w. Since P fixes that optimizer, w>=F. This handles
tied optimizers and justifies using original-copy code acceptance on every
favorable prefix.

Thresholds and finite precision.
Delta>=8/p^2 and eta=1/(4p^2) give the 29/32 probability lower bound.
The noncommuting spectral-projector identity EGE=E/p remains valid for
degenerate n-qudit eigenspaces; the resulting norm bound <7/4 excludes
two high noncommuting labels. Code-supported states have zero expectation
on noncommuting labels. The reverse triangle inequality gives the q bound
on every spectral probability at correlation <=1-eta.
For estimation, true and empirical means both have modulus <=1, so the
coordinate Hoeffding errors imply squared-modulus error <t0/2. Adding
deterministic rounding error <=t0/2 achieves the advertised t0. Only
O(log p) accuracy bits beyond ordinary counter/accumulator arithmetic are
needed. The retention threshold and margin are rational. The manuscript
explicitly permits conservative computable parameter bounds, avoiding a
requirement to decide exact transcendental ceiling equalities. This statement
is understood in its ordinary dependency order: choose J, recompute s0, choose
later budgets, and use constant-factor/slack upper bounds to retain the
claimed asymptotics, rather than arbitrarily enlarging a budget.

Adaptive capture.
All sampled G labels are retained on the estimation event; retained labels
have correlation >1-9eta/4>1-3eta and commute with C. Their span is isotropic
and can be extended to H. The matrix-column-span bound p^(4n^2) covers every
possible data-dependent output H. Missing a fixed violating G minus H has
probability <=exp(-am). The two 1/8 failure budgets give success >=3/4.
No unimplemented mass test or knowledge of the optimizer is assumed.

Learner, stopped witness, and caps.
When a good H equals S, the original-copy basis measurement lists the chosen
optimizer with probability F. Otherwise escape on S intersect H gives
outside-H target mass >=2a; high-correlation removal loses at most a.
The remaining target labels are low and commute with C; correct eigenvalue
selection costs 1/p. The conditional progress bound b0 is valid even for
data-dependent H. Each nonabsorbing favorable jump amplifies by at least
1/q. J such jumps are impossible because tau q^-J>1; rank-n termination
on a favorable path already lists the optimizer. Recording is legitimately
treated as absorbing since candidates are preserved.
The capped coupling is restricted to this stopped favorable witness:
its code acceptance on original copies is >=tau before recording. The bound
Q exp(-tau K)<=s0/4 therefore subtracts from ideal success without imposing
any acceptance assumption on wrong branches. Such branches, including
zero-weight codes, still consume at most their caps. No free postselection
is used by the actual algorithm.
Each outside-H label is independent of C since C is contained in H; thus its
eigenvalue extension defines a nonzero code even if rho has zero code weight.

Validation, resources and endpoints.
There are <=R(J+1) candidates. Independent repetitions miss the optimizer with
probability <=delta/2. Fresh-copy validation permits conditioning on the list;
Hoeffding and its union bound give simultaneous epsilon/2 accuracy with the
remaining delta/2 budget. Largest estimated overlap loses at most epsilon.
The formula RQK+RJ+Nv accounts for all original copies; Q has sufficient
conditional-request slack. The displayed J,m,h,kappa and log(1/s0) estimates
imply exp(O(p^2 L(L+log p))) times the stated polynomial. Exact Clifford
and field overhead is explicitly polynomial in p, not log p. At fixed p,
the dependence simplifies to the claimed quasipolynomial overlap dependence.
The tau=1 endpoint has J=1 and is compatible with the same proof.
For unknown F, tau=epsilon works: below that promise every output already
meets the additive target, and polynomial inverse-epsilon factors fit the
stated exponential. The interpretation is 0<epsilon,delta<1 as in the parent
theorem.

OBJECTIONS AND DISPOSITION
No blocker or required mathematical correction identified.
The attribution paragraphs and cited results' exact literature scope were not
freshly externally verified here. Their assessment belongs to the separate
originality/Publisher review and cannot be inferred from this proof verdict.
The finite checks mentioned in the manuscript are corroboration, not analytic
premises; this review did not replay them or test the complete learner.
No approximate-gate robustness, composite-dimension theorem, optimal constant,
practical implementation claim, or publication permission follows.

PRESERVATION AND VERSION BINDING
This review binds only the manuscript SHA256 above. Any subsequent substantive
source change needs an appropriately scoped recheck. The qutrit baseline and
the original analytic checkpoint were not modified. The prior sealed qutrit
package identity is provenance rather than a freshly recomputed hash in this
review.

