R87/G02 current-agent challenge review
Not independent; no original-solution acceptance.

Checked and corrected:
- Shell ancillas are free in the canonical restricted Hamiltonian. Earlier assumptions imposing their mismatch penalties are not used.
- Off-diagonal quantum observables are controlled by an exact common boundary-mixture channel, not by diagonal correlation decay alone.
- LTQO carries a support-size factor. The relative-form argument explicitly pays its square root after applying it to A^*A.
- Polynomial critical gap extension uses monotonicity of FK crossings, not spectral-gap monotonicity.
- The subcritical recursive geometry is restricted to bounded-aspect rectangles. Arbitrarily thin-domain crossing domination is unnecessary and not claimed.
- Two torus-to-box reductions use the source's periodic-boundary coupling, avoiding an unproved global torus physical-cluster assertion.
- Block updates run at rate1 each; site clocks at rate1. The recursion retains a gap near1 so logarithmically many scales do not cost a power of system size.
- Finite-g Gram terms remain separate; grouping the reference projections is only a g=0 device.
- Every spectral filter has fixed moments with displayed powers of gamma. The spectral-flow interaction is made small before its LR exponential is used.
- Filter differences retain J through a Duhamel derivative. Subtracting two independent locality estimates would lose J and is not used.
- The local-energy filters need not individually fix h_x. Only the sum identity T(H)=H is used.
- The finite-size remainder annihilates the reference ground. Small tori are covered by an explicit polynomial cutoff and Weyl bound, not discarded.
- The all-size gap candidate is not conflated with a compilable Gibbs preparation circuit.

Controls already run: check-local-parent.json tests the shell-conditioned heat-bath transform and the full reduced-density-matrix boundary mixture, including off-diagonal entries. These are consistency checks only. No repeated numerical controls were added after they passed.

Residual confidence limit: the argument is a multi-lemma current-agent derivation. A separate expert/agent proof audit has not occurred; the user chose sequential work. The finite-gap candidate is suitable as a precisely scoped next-round input, with the derivation attached. G02 remains open and unpublishable as a claimed complete solution.

Source comparison: the downloaded primary critical-Ising and stability papers supply the structural ingredients explicitly attributed in proof-v1.txt. A fresh targeted search also found arXiv:2610.27939, whose abstract concerns sufficient local-channel phases rather than the claimed near-critical gate bound; arXiv:2604.07214 gives detectability-lemma methods; and the 2025 Nature Communications weak-interaction Fermi-Hubbard paper uses a different reference model. These searches are not an exhaustive novelty certificate. The new-channel paper's full theorem and implementation assumptions should be read before any later algorithmic novelty claim.
