R88 G02 challenge review — /root, not independent

Review object: the conditional compiler in proof-v1 and work-01..03. This is not independent certification of the R87 parent-gap proof.

Substantive correction made during review.
The first locality estimate used too short a separation margin. An omitted anchored term can extend inward by r0, and q_x' itself has radius r0. Its support distance is only R-3r0 from q_x'. Work-02 was corrected to R-4r0 throughout. The same polynomial radius and gate exponents survive after changing constants.

Other challenged interfaces and resolutions.
* Latest-time ordering: C'=g[B,C] places the largest time in the outermost commutator. The consolidated proof fixes this convention, rather than leaving the compiler to choose a reverse convention.
* Coherent path preparation: bounded sum of norms alone is insufficient. The order register is prepared from O(M) computable weights; each finite non-power-of-two center register uses prefix-count rotations. Sorting uniform times and coefficient flags avoid path enumeration. A power-of-two padding implementation must charge its per-step normalization factor; the proof provides the alternative without that factor.
* Imaginary-time nonunitarity: it appears only in an LCU oracle with summable normalization, never as physical successful filtering. The real-time simulation primitives are unitary.
* Truncated ground energy: truncation destroys exact zero-energy frustration freeness. The filter is evaluated on energy differences and the gap/eigenvector perturbation argument does not assume zero ground energy.
* Endpoint preparation: the beta=0 parent is the doubled Bell-product parent. At the join both paths have the same exact g=0 parent. Discarding the copy produces a mixture with the required global trace error.
* Gaussian filter: Fourier sign, normalization and excited-ground matrix elements were derived analytically. It is an approximate inverse frequency filter; no impossible exact Gaussian spectral cutoff is claimed.
* Patch restriction: no local restricted gap is used. Global gap is needed only for ground-state transport; local simulation is a real-time unitary problem.
* Near-linearity: directly nesting global SELECT would cost N squared. The outer locality decomposition precedes simulation, and each data scan is confined to a polynomial-size patch. The count C N is loose but sufficient, including finite-size whole-torus patches.
* Growing local dimensions: only the HHKL decomposition lemma is invoked. Every resulting patch operation is compiled with its actual data size and oracle normalization paid. The source's constant-range gate theorem is not blindly substituted.
* Time-dependent access: derivative bounds control discretization; superposed time parameters use reversible arithmetic with common normalization. There is no circuit separately compiled for each of the exponentially many grid labels.
* Classical preprocessing: Taylor/Dyson templates with elementary coefficients replace an unexplained QSP phase-optimization oracle. Special-function and rotation accuracy is polynomial in bit precision; no dense eigensystem is computed.
* Error accumulation: total errors add over unitary evolutions and oracle uses. Squaring top-left accuracy where necessary controls workspace leakage without free postselection. The resulting precision logarithms fit b+ell.
* Constants: the LCU construction can shrink the field window by an extremely small but fixed constant, such as 2^-48. This is mathematically permitted by the frozen existence target and must not be sold as a practically useful field threshold.

Primary-source overlap check.
Read the relevant scope and implementation statements of arXiv:2610.27939, including section II.4 and Theorems 1–2. It shares the auxiliary-parent mechanism but explicitly makes no elementary-gate efficiency claim and does not cover near-critical 2D Ising by its stated temperature domain. Existing fixed-beta preparation in arXiv:2610.03578v1 remains the essential baseline. General transport and simulation tools are attributed rather than counted as novel results.

Conclusion.
The compiler has a developed all-size conditional argument and closes an original-level implementation interface if R87 is correct. No further internal obstruction was identified in this review. That is weaker than acceptance of the complete G02 theorem: R87's quantitative stability chain remains a candidate dependency and no independent reviewer has checked either chain. Record central-gap change conditionally, route the combined chain to verification, and retain original_complete=false. No small numerical test is used to qualify the main attack.
