Manuscript Oai265-A@2 · Oai265-A.tex · section · c0a34a45

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Oai265-A sharpens the Family 265 comparison into a quantitative audit and a non-identification theorem. It freezes the induced-graph boundary and the full-system gap, proves a terminal two-family entropy certificate, and identifies the missing uniform information charges needed to price an area-law constant. PEPS existence remains separate from tensor production, contraction, and preparation. Locally proved complete-isometry examples show that identical selected spectra can coexist with recovery errors and , while uniformly gapped low-bond ground-state families permit different entropy paths. The external 265-01 and 265-02 claims are not verified by these comparisons. No graph-cut bound is identified with a horizon, island, quantum extremal surface, replica wormhole, or time-dependent radiation entropy.

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