INDEPENDENT PUBLISHER CODE AND COMPUTATIONAL REPLAY ASSESSMENT
October 18, 2026, America/Chicago

PACKAGE
Mixed-state escape bounds and proper agnostic learning of stabilizer states in
odd-prime dimensions. Sealed source:
D:/LUMINARY ODDITIES LLC/AI Research/odd_prime_learner_prepublication_Riemann_A_20261018
ZIP SHA256: 35e4dffd9a95256ba90cb957dc6e261e53aa99e9086ee3e8cea7ad7b051a18ef
main.tex SHA256: 63f1a1a2400046d0083e8c654a5730a6239a713f09560fce83bcea06153b05b1
main.pdf SHA256: bff8ecbc813a36fed79653fe0420209f7e9bfa83c93b4dbc66e09e145b01b80b

VERDICT
PASS for the stated finite computational evidence and documented reproduction
commands. All three reproduction modes were freshly executed successfully.
No arithmetic, convention or tested-dimension enumeration defect was found.
Two modest verifier-hardening recommendations remain below. This code assessment
does not prove the all-n analytic theorem, implement the complete learner, or
establish external novelty. Publication authority is separate and absent here.

WHAT WAS READ AND RUN
Read README, REVIEW_REQUEST, all three executable verification sources, manifest,
producer replay/preservation receipts, earlier CODE_AUDIT, relevant manuscript
computational-scope passages and shared project/assessment instructions.
All fresh execution occurred outside the sealed package in
publisher_review_odd_prime_20261018/independent_replay, with further scratch
created by the copied verifier. Original files were not executed in place.

Runtime: bundled CPython 3.12.14, NumPy 2.3.5; Python -B (assertions enabled).
OPENBLAS_NUM_THREADS, OMP_NUM_THREADS, MKL_NUM_THREADS, NUMEXPR_NUM_THREADS,
VECLIB_MAXIMUM_THREADS and BLIS_NUM_THREADS were limited to 1. No global runtime
or system configuration changed. No pycache was generated in original packages.

Fresh commands against a byte-identical isolated source copy:
  python -B verification/verify_package.py           PASS, return 0
  python -B verification/verify_package.py --dense   PASS, return 0
  python -B verification/verify_package.py --full    PASS, return 0
The full mode itself runs both the entire finite suite and the dense PVM check.
Its execution took approximately 2.75 seconds in this runtime. This is fresh
execution, not adoption of the producer's saved PASS or a partial resumed run.
See independent_replay/replay-receipt.json and verify-*.log.

IDENTITY AND PRESERVATION
An independent checker, separate from supplied verify_package.py, confirmed:
- 28 unique manifest entries plus manifest itself = exactly 29 source files.
- Every manifested digest matches; handoff ZIP, source and PDF hashes match.
- Exactly 29 unique non-directory ZIP members, same complete file set; all CRCs
  pass and each archive member has exactly the corresponding source-file bytes.
- Relative manifest paths are normalized, do not contain '..', and are not
  absolute. Duplicate entry/member names were explicitly rejected by this audit.
- The preserved qutrit original has all 39 manifest entries and all 40 files,
  with sizes/hashes matching and all 40 archive bytes matching. Original qutrit
  ZIP hash remains 2afda27faa4b26a86e96cd04da481075c093109115c67d0a498b246c62589e75.
- Before/after snapshots of both complete originals and both ZIP hashes match;
  the isolated source copy also remained byte-identical after reproduction.
This is identity/preservation evidence only, not a proof of mathematical claims.

FRESH FULL SUITE COVERAGE
One-system cases p=3,5,7,11,13,17,19 each cover 22 densities: maximally mixed,
one enumerated stabilizer and 20 seeded random densities of varying rank.
Two-system cases (p,n)=(3,2),(5,2) each cover 12 densities: the two fixed inputs
and 10 random densities. Total: 178 input states.
Only the first FOUR states per case undergo direct affine-orbit physical-law
checks: 36 physical batch laws. This is not 178 physical-law reconstructions.
The exact rational grid contains 101 f values for each of ten primes
3,5,7,11,13,17,19,23,31,101: 1010 Fraction factorization/sign identities.
Grid tests corroborate algebra at those points; they do not prove its continuous
sign, which the analytic factorization must establish.

The suite freshly confirms sampled auxiliary-kernel Fourier identity,
normalization/positivity, all tested maximizing Lagrangian/hyperplane escape
inequalities, one-system local inequalities and complex physical characteristic
functions. Maximum direct physical characteristic residual was 1.09e-14, below
the stated 1e-8 numerical acceptance tolerance.
All random inputs use seed 2026101803. These are ordinary complex128 diagnostics,
not interval certificates, exhaustive mixed-state tests or a formal proof.

CODE LOGIC AUDIT
The Weyl matrix action is |q> -> omega^(a.q+a.b/2)|q+b>, consistent with the
manuscript's omega^(-a.b/2) Z^a X^b convention and symplectic pairing. The
einsum computes Tr(rho W), while the inversion matrix is omega^[x,u]/D^2.
Its conjugate transpose times D^2 is the forward transform. Comparison against
the generally complex product of chi, not only its absolute square, materially
checks signs. The auxiliary matrix-overlap kernel is computed directly and
checked against Fourier inversion rather than assumed equal by construction.

For n=1 the enumerator contains all p+1 isotropic lines and p eigenstates per
line. For n=2 it spans all commuting independent pairs of projective lines and
deduplicates spans; counts are 40 and 156 Lagrangians and 360 and 3900 stabilizer
states for p=3,5. Its hyperplanes are all lines of each 2D Lagrangian. Near ties
within 1e-8 include every matching optimizer owner, over which the minimum is
taken. The generic-looking setup(...,n) else-branch only spans TWO generators:
it is valid for the documented n=2 tests, not an arbitrary-n enumerator.

The affine physical_batch implementation partitions the input computational
basis into free simultaneous weighted-translation orbits. Each orbit contains
D elements. Their Fourier vectors form an orthonormal refinement of the joint
commuting Weyl PVM. The weights are nonzero and have sum of squares zero in all
tested branches. The code separately compares the resulting measurement's
complex characteristic function with the product of input Weyl amplitudes.

FRESH INDEPENDENT DENSE CHECKS
The supplied independent_dense_pvm.py was freshly replayed in both --dense and
--full. It independently constructs Weyls via powers of X,Z and character-sum
projectors, bypassing affine orbit construction. It tests all projector
Hermiticity/idempotence/orthogonality, completeness, minimum eigenvalue, trace,
all probabilities and characteristic function for a fresh random mixed state
in each of p=5,t=(1,2),dimension 25 and p=3,t=(1,1,1),dimension 27.
All residuals <=5.62e-15; full-law discrepancies <=2.78e-17.

This Publisher auditor added a third independent dense case to check nontrivial
unequal three-register weights: p=7,n=1,t=(1,2,3), joint dimension 343.
All 49 character projectors and outcome probabilities were independently built;
Hermiticity, completeness and traces were checked for all sectors, while matrix
idempotence/orthogonality were checked on three selected sectors. One fresh
full-rank mixed input (seed 181027) was tested. The complex characteristic error
was 1.11e-15; the full outcome-law discrepancy with the original affine method
was 2.78e-17; maximum matrix residual was 1.62e-14, below 1e-10.
This supplements, rather than replaces or enlarges the claims of, the finite
178-state suite. See independent_replay/additional-checks.json and its script.

NEGATIVE CONTROLS AND HARDENING RECOMMENDATIONS
All mutations below were made only in disposable isolated copies outside the
originals. Supplied verify_package.py rejects a changed file and rejects the
simultaneous missing/extra file case. A deliberately false escape coefficient
kappa=10 is rejected by ordinary diagnostic execution, as it should be.

1. The diagnostic source has 11 Python assert statements and the independent
   dense script has one. Python optimization removes these acceptance gates.
   In a copied negative control, kappa=10 nevertheless emitted a PASS JSON under
   direct python -O execution. The supplied documented -B commands use ordinary
   assertions and passed honestly here. A parent -O flag alone is not inherited
   by verify_package.py's fresh subprocess, but inherited PYTHONOPTIMIZE can
   disable gates there, and users can directly run diagnostics with -O.
   Recommendation: explicit runtime errors for failed numerical acceptance, or
   fail fast when sys.flags.optimize is nonzero. This is a robustness issue for
   unsupported execution modes, not evidence of a failed ordinary replay.

2. Supplied verify_package.py converts manifest paths to a set, so a duplicate
   manifest entry is silently accepted. A copied duplicate entry was accepted
   with return 0. The actual sealed manifest is unique, and the independent
   Publisher audit verified uniqueness and exact ZIP/file identities. Recommend
   rejecting duplicate/noncanonical/traversing manifest paths explicitly.

These are minor verification engineering recommendations. No manuscript theorem
repair or mathematical blocker follows from them. Do not silently edit the
sealed source; any authorized hardening belongs in a new revision.

EVIDENCE LIMITS
No full learner simulation, conditioning/capture experiment, empirical sample
complexity, finite-universal-gate compilation or arbitrary-n verification is
implemented in these scripts. Their finite scope is disclosed in the manuscript.
The proof must carry global optimizer preservation, adaptive/stopped favorable
witness coupling, rejection caps, exact operation model and growing-p bounds.
Producer's first memory-limited partial suite is transparently labelled as
partial; this review's complete rerun independently supersedes it for fresh
finite replay purposes. No novelty, practicality, minimum-copy optimality or
external human refereeing is inferred from code, file hashes or assistant PASS.

Review outputs and negative-control examples remain outside both originals.
