PRIMARY-SOURCE COMPARISON — 22 October 2026

Each entry identifies what was actually compared. 'Difference supported' means that the inspected sources leave a precise step supplied by the candidate. It is not a guarantee of historical priority. Primary theorem interfaces, not search snippets or internal labels, carry these judgments.

M15-S1: Coudron, Gullans, Nelson, Rajakumar and Tan
https://arxiv.org/html/2610.02146v1
Read: Theorem 1.1; Theorem 4.1; rooted expansion Eqs. (7)-(10); Section 3.3; introduction after the comparison table.
Classification: partial overlap / inherited method.
Polynomial additive point-probability evaluation is supplied. The rooted expansion and good-zero cluster machinery overlap substantially with the candidate. The source explicitly distinguishes sampling from pointwise estimates. It does not construct the candidate's global L1 error bound, polynomial dominating proposal, or normalized worst-case polynomial sampler. Those are the relevant additional steps.

M15-S2: Bravyi, Gosset and Liu
https://arxiv.org/html/2309.08405v1
Read: Theorems 1, 1a and 2; introduction's concentration argument.
Classification: partial overlap.
The arbitrary-connectivity peaked sampler has quasipolynomial size dependence; the polynomial sampling case imposes two-dimensional geometric locality. Peakedness-to-concentration and shallow-circuit dependency ideas are inherited. Neither statement covers the candidate's polynomial sampler for arbitrary connectivity at fixed depth and inverse-polynomial accuracy.

M24-S1: Adesso
https://arxiv.org/html/2608.01909v3
Read: Theorem 1, Eqs. (8)-(9); Supplement S2, especially (S54)-(S63); S3 Lemma S3; Theorem 2; S10 Corollary S10.
Classification: imported theorem / partial overlap.
The finite-energy affine two-mode EPR entropy inequality, including q<t<=1 and arbitrary-measure extension, supplies the candidate's lower-bound interface. Its two-mode covariance argument and bisymmetric consequences do not supply generic 1:m saturation. The tensor-product result and restricted discord corollary likewise do not imply that missing reduction. The candidate's stationarity, rank-two multiplier and extraction argument are additional.
Limitation: The imported affine theorem was read at its actual interface; its long independent source proof was not re-proved in this review.

M24-S2: Wolf, Giedke, Krueger, Werner and Cirac
https://arxiv.org/html/quant-ph/0306177v2
Read: Proposition 1, Eq. (9), and its proof; pure-state mode decomposition discussion.
Classification: known-covered component.
The Gaussian convex-roof covariance minimization is inherited. This reduces the Gaussian roof, not the unrestricted roof, for generic multimode states. It therefore does not prove M24. The candidate additionally explains why arbitrary Gaussian probability measures yield the same covariance minimization.

M24-S3: Ivan and Simon
https://arxiv.org/html/0808.1658v1
Read: Propositions 1 and 3; Conjecture 1; Proposition 5.
Classification: partial overlap.
Generalized EPR correlations and the two-mode canonical form are older. The two-mode formation claim here explicitly depends on Conjecture 1. This is not an unconditional generic 1:m result and does not provide the candidate's multiplier argument. It is useful attribution for the EPR mechanism, not full prior coverage.

M24-S4: Lami, Serafini and Adesso
https://arxiv.org/html/1612.05215v3
Read: Theorem 5; Section IV; Section VI.
Classification: related result, not equivalent.
One-versus-many PPT/separability and mono-symmetry reductions concern separability, the zero-entanglement case. They do not determine the positive entanglement convex roof for arbitrary nonsymmetric 1:m states. In particular the separation criterion is not the candidate's quantitative saturation theorem.

M05-S1: Rouze and Stilck Franca
https://arxiv.org/html/2610.03578v1
Read: Theorem 3.11 and Remark 3.12; Appendix B.1; Proposition 3.4; Theorem 4.4 and (4.16)-(4.17); Propositions 5.7-5.8; (5.18), (5.22), (5.31)-(5.32); Appendix A after (A.13).
Classification: substantial inherited architecture / precise implementation gap.
This supplies QBP resets, correction, locality and DS mixing. Remark 3.12 already proposes recursive purification and collective jump encoding, while leaving the detailed single-exponential implementation analysis open. Thus the architecture itself is not new. The candidate fills the charged implementation gap, with explicit bit costs and a temperature-dependent logarithmic exponent. The exact discrete contraction theorem allows its preparation schedule. Input and clustering parameters match; the Appendix A cutoff includes the k-dependent denominator.

M05-S2: Leeseok Kim
https://arxiv.org/html/2610.01190v1
Read: Theorem 6.1; Corollary 6.2; Appendix C.2, Eqs. (203)-(207).
Classification: partial overlap / inherited implementation technique.
At fixed temperature and block parameters, the source supplies nearly linear gate preparation and polynomial classical construction. Its theorem does not state the candidate's explicit single-exponential temperature prefactor with nearly linear classical assembly. Ordered Dyson LCU, including repeated grid nodes, is inherited. The candidate has to charge the recursive reset and actual oracle construction separately.

M05-S3: Low and Wiebe
https://arxiv.org/html/1805.00675v2
Read: Theorem 3; Corollary 4; Lemma 6; Eqs. (20)-(25).
Classification: imported algorithm.
Interaction-picture simulation is oracle-relative. It does not give a free local simulator for an unbounded onsite Hamiltonian. The candidate supplies fixed-dimensional onsite diagonalization, controlled phase arithmetic and the local interaction oracle, with their bit costs. The cited dependence on the interaction normalization and logarithmic fast-evolution scale is consistent with that construction.

M05-S4: Chen, Gao, Wang and Zhou
https://arxiv.org/html/2609.18757v1
Read: Definition 1.1; Theorem 1.2; Lemma 6.3, Eqs. (81)-(83); Section 7.2; Sections 9.2-9.4, Algorithm 2 and (132)-(139).
Classification: imported algorithm.
The simulator accepts a Hermitian involution and projected rectangular jump stack, normalized by alpha_H+alpha_B^2. Coefficient support is O(q), and binary time indices avoid a J-entry table. The candidate constructs exactly these interfaces and charges arithmetic, label preparation, oracle calls and their inverses. This source does not itself construct the Gibbs reset/correction or prove the candidate's temperature cost.

M05-S5: Kuwahara, Alhambra and Anshu
https://arxiv.org/html/2007.11174v2
Read: Section IV.1, Theorem 3, Eqs. (23)-(25).
Classification: related algorithm, weaker size dependence for this target.
The constructive MPO cost is n beta exp(Q_epsilon), where Q_epsilon includes sqrt(beta log(n/epsilon)) times a logarithm. For fixed positive temperature and inverse-polynomial precision this overhead exceeds every fixed polylogarithm. Its quasi-linear n^(1+o(1)) terminology therefore does not imply the N polylog(N/epsilon) target here.

M05-S6: Bilgin and Boixo
https://arxiv.org/html/1008.4162v2
Read: Abstract; recursive merging construction around Figure 1 and Eq. (1).
Classification: older recursive architecture / partial overlap.
Recursive merging of thermal regions is older. The stated dominant size cost N^(||h||/T) does not provide the candidate's nearly linear size dependence at arbitrary fixed temperature. This is additional reason not to claim recursion as new; the explicit integrated implementation and resource bound are the candidate's distinction.

Search scope: exact claims and equivalent formulations included peaked-circuit sampling versus probability estimation; dependency-graph/moment/polymer sampling; Gaussian one-versus-many formation, EPR witnesses, separability, discord and local extraction; and one-dimensional thermal preparation, recursive purification, single-exponential temperature cost and quasi-linear tensor-network algorithms. Current versions were checked where material: 2610.02146v1, 2608.01909v3, 2610.03578v1, 2610.01190v1 and 2609.18757v1. Secondary summaries were leads only. No specific unresolved overlap was found that blocks these three candidates. Ordinary non-exhaustiveness remains.

