[
  {
    "id": "ARR-2026-79JR2RMHHP93RVAD-v1",
    "type": "article",
    "title": "Finite-Dimensional Davies Interface Lemmas and TFIM Witness Tests for Separation-Dependent Decoherence Rate Envelopes",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          1,
          8
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-79JR2RMHHP93RVAD",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-79JR2RMHHP93RVAD/versions/v1/",
    "note": "Archived manuscript; ARR-2026-79JR2RMHHP93RVAD v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We develop a finite-dimensional technical core for relating separation to effective decoherence-rate envelopes in Davies-type open-system dynamics. We work with energy pinching Delta and quantify coherence by C(rho) = S(rho||Delta[rho]). We import a maintenance inequality P_extra(rho) >= k_B T dC_loss(rho) -- in the corrected operational sense of its source (paired strategies against efficient/free baselines, 2512.0061 v2) -- as an external input. On the operator side we prove: (i) an exact omega = 0 Dirichlet identity yielding a witness-based lower bound on instantaneous decay envelopes, (ii) a Bohr-channel Dirichlet decomposition for a single-channel Davies generator under quantum detailed balance -- corrected in v2: the v1 form (1/2) sum_w gamma(w) ||[S(w),O]||^2 is false as an identity (numerical deviations of order 20%); the exact form is sum_w gamma(w) e^(beta w/2) Re , which reduces to (i) at omega = 0 and is nonnegative pairwise in +-omega -- and (iii) envelope suppression lemmata under infrared exclusion and quasi-local spectral tails, reproved in v2: the v1 proofs used a KMS submultiplicativity step that is false in general (a one-qubit counterexample saturates the corrected constant); the corrected constants carry c_sigma^2 = (lambda_max/lambda_min)^(1/2) and sup_w gamma(w)e^(beta w/2), and the e^(-2 eps/xi) exponent survives via a new positivity-pinning argument: for S = S_near + delta S_tail and far-supported O, detailed balance at every delta forces E_delta(O) = delta^2 E_tail(O) exactly. Consequently Lemma 4.13's v1 claim of a lambda_min-free prefactor is downgraded to a quadratically improved dependence. On the state side we give an asymptotic linearization on Bohr-block perturbations with fixed diagonal, yielding a direction-dependent effective decay rate. Finite-size TFIM witness diagnostics are provided, and every corrected statement is verified to machine precision by the shipped suite."
  }
]