[
  {
    "id": "ARR-2026-483TABVBKH939V3Q-v1",
    "type": "article",
    "title": "Operational Influence Proxies in a TFIM Surrogate: Non-Monotonicity and a Controlled ω = 0 Witness Floor Mechanism",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          1,
          8
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-483TABVBKH939V3Q",
    "version": "v1",
    "genre": "Archived manuscript",
    "URL": "https://airr.science/papers/ARR-2026-483TABVBKH939V3Q/versions/v1/",
    "note": "Archived manuscript; ARR-2026-483TABVBKH939V3Q v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.",
    "abstract": "We study spatial influence detection in a transverse-field Ising chain (TFIM) subjected to localized Markovian noise. Using an operational one-site trace-distance influence proxy computed from TEBD combined with Monte Carlo wavefunction (MCWF) sampling, we test whether remote dissipation produces an identifiable nonzero asymptotic influence offset (a \"floor\") as a function of separation epsilon. Uncertainties are estimated by trajectory bootstrap and model selection is performed between exponential decay and exponential-plus-offset forms using both BIC and the finite-sample corrected criterion AICc. In the TFIM surrogate regimes explored, we find no robustly identifiable floor for both dephasing and amplitude-damping channels; instead, the influence proxy is non-monotone in separation, consistent with coherent finite-size structure superimposed on average attenuation. To demonstrate that floors can exist as a controlled mechanism independent of fragile spatial fits, we present a Davies/witness stress test: for nonzero zero-frequency bath weight gamma(0) > 0, a commutator witness yields a strictly positive lower bound on an effective decay envelope. Exact-diagonalization calculations show this lower bound is robust to enlarging the observable support and to variations in inverse temperature. v2 adds: a synthetic-injection power analysis showing that over the sampled one-octave window epsilon in [16,32] with n = 5 points, a constant floor is nearly degenerate with a slow exponential -- AICc essentially never detects a floor and even BIC requires D0 ~ 30 sigma -- so \"no identifiable floor\" is in part a design limitation, now stated as such; a fully declared exact-diagonalization benchmark for the witness (v1 did not record its ED parameters), regenerable from scratch by the shipped suite; a null case showing the witness switches off (kappa_min ~ 1e-29) for couplings with vanishing omega = 0 component; an invariant-subspace caveat for the envelope interpretation; and series cross-references."
  }
]