M03-v3 — independent strict review, 22 October 2026

Judgments
Validity: supported internally; no proof gap or refutation found.
Original coverage: complete original, with its real symmetric gapped reference,
fixed physical jump list, admissible lowering filter, parity-even perturbations,
and even initial states. Complex hopping and a matching lower mixing bound are
outside the original and outside this verdict.
Source comparison: difference supported in the bounded primary-source search.
No identified unresolved covering theorem blocks this result. This is not a
claim that every publication or unpublished result has been searched.
External status: this review establishes no external expert acceptance and made
no submission or publication.

Frozen identity and exact target
Original: campaign/originals/M03.tex:6–24; candidate directory M03-v3 is frozen
in frozen-inputs.json. The text header says version 2; the directory and hashes,
not that stale heading, identify the reviewed inputs. The claim is an N-uniform
positive perturbation threshold, unique ground-state fixed point, and
C log(N/eta) trace-distance mixing for the specified dissipator.

Proof challenge and disposition
1. The particle–hole change alone is insufficient. I read the complete
locality-interface.txt and proof.txt, then the source interfaces. The real
projectors give canonical CAR modes and a unitary transformation of the FULL
2N jump-label list. This preserves the generator; it is not a replacement of
physical couplings by an assumed local eigenbasis. Exponential projector
locality and the bounded degree of each finite-support monomial give summable
shells after transformation, with constants independent of volume. The
interaction norm uses the sum over shell centres and support volumes; those
polynomial factors are absorbed by the exponential tail. See locality-interface.txt
and manuscript main.tex:108–170.
2. The fermionic localization lemma is for even observables. proof.txt:23–34
correctly applies it to K_i gamma_i, an even operator, then multiplies gamma_i
back. The exterior odd case uses the anticommutator, the even case the ordinary
commutator. Thus an even-only lemma is not being silently applied to an odd
jump. Finite-time Duhamel plus the integrable filter tail proves eta(lambda)
->0 uniformly, proof.txt:36–43; a global O(N) perturbation norm is unnecessary.
3. The shells are unital-annihilating, even superoperators in full induced
operator norm (45–57). The support identities in 69–81 depend essentially on
E_X(I)=0. Telescoping local CAR expectations on the even algebra supplies the
needed local bound. The homogeneous part in 87–90 is a sum of actual
Lindblad generators excluding site i and therefore is contractive. It is not
the semigroup of a shell difference, which need not be positive.
4. Summing the forcing requires two volume factors, both included in
kappa=6 C_b^2 sum_r(1+r)^(2D) epsilon_r at 94–102. Dominated convergence gives
a uniform threshold with kappa<=1/4. This supplies the missing perturbative
bridge rather than merely importing the positive-spectrum theorem.
5. The filter kills zero and positive Bohr frequencies, so all ground vectors
are dark (104–119). Even contraction gives a unique even stationary state;
choosing a parity basis in the ground space proves one-dimensionality. A
stationary state whose parity twirl is that pure state must equal it. The final
4N exp(-t/4) estimate and N>=2 give the claimed C=12 logarithmic form.

Primary-source comparison
• Zhan et al., 2503.15827v3, Theorem 11 and Appendix I, supplies the
positive-definite reference result and oscillator identities. Its hypothesis
M>Delta excludes a filled negative band. The reviewed locality/closure argument
is the substantive additional step. https://arxiv.org/html/2503.15827v3
• Nachtergaele–Sims–Young, 1705.08553v3, Theorem 3.1 and Lemmas 4.2–4.3,
supplies fermionic LR and even localization interfaces. The transformed even,
exponentially summable interaction satisfies their required decay norm.
https://arxiv.org/abs/1705.08553v3
• 2508.05703v3, supplement §S6.2, Theorems S13/S18, concerns free quadratic
preparation. Its N/accuracy-dependent algorithmic parameters and absence of
the interacting perturbation make it a different theorem.
https://arxiv.org/html/2508.05703v3
• The current finite-temperature Gaussian-mixture theorem 2609.35159v1,
Theorems A.1/A.2, is discussed in M07-review.txt; it does not provide this
zero-temperature fixed dissipator theorem.

Reproduction and manuscript
M03-CAR.log in both clean-run directories passes the candidate's finite CAR
controls. These check local algebra, not the uniform LR/perturbation argument,
which was reviewed analytically above. Manuscript M03-band-insulator/main.tex
Theorem 1.1 (94–106), locality lemma (126), jump lemma (174), local forcing
lemma (273), and stationary-state argument (312–361) match the checked route.
No unsupported manuscript strengthening found. Next action: retain as a
complete internally supported candidate; preserve the explicit real/parity/
filter assumptions in any release.
