M24-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, using the explicitly identified external affine entropy theorem.
Original coverage: complete original; the candidate treats finite 1:m and includes the requested nonsymmetric 1:2 case.
Literature: difference supported for generic 1:m saturation/extraction; the two-mode lower bound and Gaussian covariance roof are inherited.
External status: no external acceptance or submission receipt established by this review.
Blocking gaps: none found. The external affine theorem is an imported mathematical result, not an independently reproved result of this review.

FROZEN IDENTITY AND REVIEW SCOPE
Original: campaign/originals/M24.tex
Original SHA256: 108df172b97692b9d89679b8ae02bd6353ad19afdc98614999ecd1ec3436e0a3
Candidate: campaign/continuation-R41-R60-2026-10-22/candidates/M24-v1
proof.txt SHA256: 73c89e36b4677c5b2c57e7d016458b756c1d3f97ee0ed8291881176ddc72f483
All inputs and bundled dependencies are frozen in frozen-inputs.json.
I read the entire 251-line proof, original, claim and maps before earlier review code. No internal verdict or finite control was used as evidence of generality. The candidate was not modified.

EXACT ORIGINAL MAPPING
The original asks whether unrestricted entanglement of formation equals its Gaussian restriction for every finite-energy Gaussian state with one Alice mode and two Bob modes, without Bob-swap symmetry. The candidate proves that equality for one Alice mode and any fixed finite number of Bob modes.
It allows arbitrary real quadrature cross correlations, first moments removable by local displacement, non-strict physical boundaries, and arbitrary pure-state probability measures. It does not replace the unrestricted convex roof by a finite ensemble, nor impose a q/p block-diagonal form on the mixed state. Its result does not settle generic m:n with both parties multimode.

DECISIVE ANALYTIC AUDIT
1. Gaussian roof and compactness, proof.txt:18-43 and 233-251.
The feasible pure covariance set Gamma<=V is compact: purity gives reciprocal eigenvalue control in terms of the upper bound by V. The minimum therefore exists. The pure seed, not the mixed covariance, is put in local Gaussian Schmidt form with one entangled pair and Bob vacuum spectators. The nonlocal whitening is an algebraic coordinate step, not an allowed physical local operation. The a=1 product-seed branch is separately trivial.
The arbitrary Gaussian-measure roof argument is not merely an assumption that all decompositions have a common covariance. The proof's Gaussian moment-generating-function domination forces component covariances <=V almost everywhere; the displaced fixed-seed ensemble gives the reverse construction.

2. Nonconvex stationarity qualification, proof.txt:45-80.
A convex Slater argument would be invalid for the pure-covariance manifold. The actual proof instead sets K=ker(V'-I) and proves K intersection JK={0} from strict physicality. If a nonzero v and Jv both belonged to K, the corresponding complex vector would violate strict positivity of V'+iJ.
With P_K the orthogonal projector, X0=J P_K J^T-P_K belongs to the pure tangent space and has strictly negative compression to K. This is an explicit strict feasible tangent direction. In the conic separation argument it excludes an abnormal multiplier alpha=0; normalizing the objective multiplier is therefore justified. This supplies W>=0, range(W) subset K and the displayed stationarity relation. The argument genuinely uses strict physicality.

3. Disjoint-range rank step, proof.txt:82-100.
The multiplier ranges lie in K and JK and are disjoint. For positive semidefinite P,Q with disjoint ranges, (P-Q)x=0 implies Px=Qx belongs to their intersection, hence Px=Qx=0. Therefore ker(P-Q)=ker(P) intersection ker(Q) and rank(P-Q)=rank(P)+rank(Q). This justifies rank(W-JWJ^T)=2 rank(W), without incorrectly assuming the ranges are orthogonal.
The objective's antisymplectic part has rank four on the entangled pair. Thus W has rank two, and the same range equality localizes its support to that pair. I checked this algebra and its support consequence independently.

4. Witness shape and admissible gain, proof.txt:102-157.
The scalar diagonal blocks and stationarity constrain the off-diagonal block to xI+yJ-kappa Z. Positivity and rank two force its two singular values equal; since kappa is nonzero, x=y=0. After undoing whitening, the witness has the EPR Gram form.
The inequalities A0-qB0=u/c>0 and B0-qA0=v/c>0 imply q<t<=1 after choosing the orientation of the retained pair. Thus the proof does not use the external inequality outside its allowed gain region. Complementary slackness makes the EPR expectation exactly d_t(q). The covariance convention contributes the required 1/4 trace factor and additive (1-t^2)/2.
Discarding Bob's spectator modes supplies a lower bound through monotonicity. There is no assertion that the noisy mixed covariance factors into one pair and spectators. That stronger statement would generally be unjustified and is unnecessary here.

5. External inequality and arbitrary decompositions, proof.txt:145-157 and 204-232.
The Adesso theorem uses the same finite-energy, 0<q<t<=1 regime and affine dependence on the EPR expectation. Applying an affine inequality to pure components and integrating gives the mixed lower bound without any Jensen-direction issue. Finite average energy controls entropy and EPR moments. Tonelli and the explicit number-basis refinement handle arbitrary probability measures and tracing out Bob modes. The imported theorem was read with its conventions and measure extension; its long source derivation was not reconstructed from first principles.

6. Physical boundary, proof.txt:159-175.
The strictly physical KKT argument is not extended by assertion to pure or rank-deficient boundaries. Adding independent local noise gives strict physicality. Local noise monotonicity yields a lower bound on the original EF, while compactness of pure feasible covariances gives convergence of the Gaussian minimum. This avoids assuming unrestricted EF continuity in infinite dimension. The limiting inequalities close in the correct direction.

FRESH CONTROLS AND REPRODUCTION
The supplied author's exact-controls.py and bundled owner's check.py were each inspected and replayed twice in isolated directories, including the latter's snapshot input. All exits were zero and paired stdout matched. No top-level M24-v1/check.py exists; the provenance script was used.

My fresh rational three-mode control takes q=3/5, t=7/10 and constructs nontrivial noise in the EPR-witness kernel. All six leading principal minors of V'+iJ are strictly positive. It verifies multiplier rank two, rank difference four, negative tangent compression, slack saturation and the exact EPR expectation 841/1600. A local Bob shear introduces q/p cross correlations while retaining the identities. The pure D=0 negative control gives X0=0, correctly showing that this interior qualification cannot be used at the boundary.
These are exact rational admissibility and algebra checks, not a search over all covariances and not certification of the external entropy inequality.

LITERATURE AND NOVELTY JUDGMENT
See M24-S1 through M24-S4 in source-comparisons.txt/json. The precise new bridge is a generic 1:m covariance optimizer producing a rank-two saturating witness supported on one extractable Bob mode. Known two-mode EPR/canonical-form results, Gaussian covariance minimization, bisymmetric reductions and PPT/separability do not supply this bridge.
I specifically checked the newer source's tensor-product and discord corollaries; neither is a hidden generic 1:m formation theorem. Older generalized-EPR literature supplies substantial conceptual precedent and must be credited.
No actual unclosed interface or specific unresolved prior-coverage lead remains in this review. The conclusion is a supported distinction from checked sources, not a worldwide novelty certificate.

NEXT JUSTIFIED ACTION
Retain the unchanged candidate for release assessment, prominently crediting the imported affine theorem and limiting the new theorem to finite 1:m. This review does not change publication or catalog status.

