Manuscript Em04-A@2 · Em04-A-v2.tex · section · f5b28abc

Revision and citation-role notes

Revision and citation-role notes · lines 1994–2025

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Version 2 makes the following substantive corrections:

  1. It separates reported source availability from completed source inspection and from executed verification.

  2. It includes every partial-transpose eigenvalue and zero multiplicity, including the zero cross-block case.

  3. It states the finite-coordinate hypothesis and supplies the physical-time expansion at zero dissipation.

  4. It uses the trapezoidal constant for the reported trapezoidal implementation, retaining the midpoint rule only as a labeled alternative.

  5. It includes arithmetic errors, a positivity repair for rounded quadrature matrices, and a bin-independent completed-law bound.

  6. It distinguishes residual accuracy from positivity, provides whole-cell entrywise certificates, and charges any repair.

  7. It corrects the reconstruction norm notation and avoids interpreting a perturbation bound as a sharp-threshold theorem.

  8. It moves unrelated programme identifiers outside the main proof.

The foundational semigroup references support the framework; they do not prove this chain's invariant-sector calculation. Wootters and Vidal–Werner supply diagnostic definitions, while the specialized matrix formulas are derived here. Baumgratz–Cramer–Plenio supplies the basis-coherence framework. Watrous supplies finite-channel background. Johansson supplies a rigorous-integration methodology, not a completed numerical enclosure. QuTiP and latexmk documentation support the proposed execution interfaces, not mathematical accuracy or a successful run.

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