M15-v1 — independent strict review
Date and literature cutoff: 22 October 2026
Reviewer: /root/top3_strict_independent (fresh-context child agent; no further agents)

VERDICT
Validity: supported internally.
Original coverage: complete original, with the original's fixed d,k and inverse-polynomial error range.
Literature: difference supported relative to the checked sources; substantial inherited components.
External status: no external acceptance or submission receipt established by this review.
Blocking gaps: none found. This is a fallible analytic review, not expert certification.

FROZEN IDENTITY AND REVIEW SCOPE
Original: campaign/originals/M15.tex
Original SHA256: 90e149a4c8f28f1bfb5e71eabf62986895cd1aa5ed05d119d0700c5cc87d9482
Candidate: campaign/continuation-R41-R60-2026-10-22/candidates/M15-v1
proof.txt SHA256: 04d5fe897e6291fcd1bbbe08329d61202484b32119aaf748c04154eeba741ab1
All candidate files, originals and bundled dependencies are in frozen-inputs.json.
I read the exact original, full 314-line proof, claim, mapping and relevant dependency interfaces before using earlier review code. Earlier verdicts and internal PASS labels were not evidence. The full proof and candidate were not modified.

EXACT ORIGINAL MAPPING
Objects and operations: n-qubit depth-d circuits, arbitrary connectivity, disjoint one/two-qubit gates within each layer. The proof uses light-cone overlap, not lattice geometry. Algebraic gate descriptions and their explicit bit length b are retained.
Quantifiers: d and k are fixed positive integers. The promise is max_x p(x)>=n^(-k); no heavy string is given. Rational epsilon lies in the original n^(-k) to 1/4 range. The algorithm finds an approximate marginal-majority center itself.
Success: a uniform classical randomized algorithm with worst-case polynomial(n,b) work for fixed d,k and total variation error <=epsilon. A capped rejection loop establishes bounded worst-case work, rather than only expected work.
The proof does not establish a polynomial whose degree is uniform in growing depth, arbitrary k, or exponentially small epsilon. Those are not requirements of the frozen original.

DECISIVE ANALYTIC AUDIT
1. Dependency and concentration, proof.txt:27-65.
Disjoint backwards light cones give joint independence of separated vertex sets, the strong dependency property needed later. Coloring with K=4^d permits Holder's inequality and exponential-moment bounds. Approximate marginal comparisons need not identify exact ties. The high-marginal core has O(log n) vertices and the remaining total marginal mass is O(log n). This uses the peakedness promise without supplying its maximizer.

2. Good-zero evaluation and precision, proof.txt:76-123.
The deletion recurrence controls the polymer polynomial on a fixed complex disk. The connected-support coefficient enumeration uses r=O(log n) for the analytic truncation. Later acceptance arithmetic increases precision at this fixed r; it does not rerun the cluster algorithm with r proportional to log(1/w) and thereby change polynomial work into quasipolynomial work. Coefficient error amplification exp(O(r^2)) calls for O(log^2 n) guard bits, which is still a polynomial bit cost at fixed d,k. The zero-free disk makes evaluation of the truncated exponential legitimate.

3. Global L1 regrouping, proof.txt:127-163.
The dangerous step is summing errors over all output strings. Here S and T are disjoint good-vertex sets, and regrouping by D=S union T gives only subset multiplicities. Summing the core outcomes J gives the unconditional moment mu(D); it does not introduce an inverse probability of a core event. Consequently the tail is bounded by 2^(-R) E[5^W] and the zero-evaluation contribution by eta E[3^W]. No factor equal to the size of an O(log n) Hamming ball appears. I checked the combinatorics independently in an exact finite law.

4. Positive dominating proposal, proof.txt:168-224.
For connected C, choosing a root and an independent color class outside its neighborhood controls the sum of mu(C) by a constant times the total rare marginal mass. Thus Lambda=O(log n). Enumerated core choices have polynomial total mass, bounded using 2^|H| E[2^W]. Positive rational upper weights add controlled total slack. Their product normalization is at most exp(Lambda), hence polynomial.
The unique valid representation is forced by the connected components of S: components meeting H belong to D; all other components are precisely the active polymers. The validity predicate rules out overlapping or adjacent alternatives. Domination uses factorization of unconditional moments of separated sets, not an unjustified factorization of the target output probability. It yields w>=mu(J union S)>=p(J,S).

5. Normalization and bounded runtime, proof.txt:228-263 and 289-294.
Pointwise clipping into [0,w] cannot increase distance from a target value already in that interval. The unnormalized L1 estimate controls both total mass and the normalized sampling law. The success lower bound is inverse polynomial because the envelope normalization is polynomial. Rejection is capped, with fallback probability charged to TV error. Positive upper-weight flooring supplies w>=nu^(h+1), so evaluating an acceptance coin to the required additive precision costs only polynomially many bits. Finite dyadic randomness and arithmetic errors are explicitly budgeted.

FRESH CONTROLS AND REPRODUCTION
The supplied author checker was inspected and replayed twice in its ordinary and --parity modes. The bundled owner check.py was also inspected and replayed twice; top-level M15-v1/check.py does not exist, so the actual provenance path was used. All exits were zero, and corresponding stdout matched. These programs compute rational identities, not just print a claimed status.

My new targeted-controls.py uses a six-cycle dependency law with rational latent Bernoulli probabilities and XOR/OR outputs, H={0,5}, and actual support cutoff h=2. It enumerates the complete finite proposal space: 24 cores, seven polymers, 44 valid supported outputs, exactly one representation for each. Omitted mass is 1762/81719 and invalid proposal mass is strictly positive, so this is not an all-supported/vacuous rejection case. It checks proposal-weight identities, domination and global L1 bounds for four distinct tail cutoffs. All assertions use exact rational arithmetic. This is a dependency-law bottleneck control, not a new shallow-circuit realization theorem or an asymptotic proof.
The independent supplied six-qubit noncommuting circuit control separately checks the circuit-to-moment interface. Neither finite test substitutes for the analytic concentration, counting and bit-complexity estimates.

LITERATURE AND NOVELTY JUDGMENT
Read source entries M15-S1 and M15-S2 in source-comparisons.txt/json for exact locators and primary URLs. The new claim is the globally controlled polynomial sampler. Neither a point-probability approximation nor a quasipolynomial sampler covers that statement. The recognizable inherited ingredients are dependency concentration, rooted inclusion-exclusion and cluster/zero-free evaluation. The additional work is the global L1 regrouping together with a polynomially normalized positive envelope and implementable bounded rejection.
No precise unresolved equivalent formulation or source theorem was found that would already imply this complete sampler. Search non-exhaustiveness remains; a historical-priority guarantee is not claimed.

NEXT JUSTIFIED ACTION
Retain the unchanged candidate as supported for a release assessment, preserving fixed-parameter qualifications and source attribution. This review neither changes catalog status nor authorizes publication.

