Research paperHistorical importARR-2025-528FY1PGWT8QEVWQ · v1
Lluis Eriksson
In gapped open quantum systems with localized couplings, static correlations across an operational interface of width eps are exponentially suppressed by the mass gap. Independently, the energetic cost of maintaining quantum coherence is governed by the rate at which coherence is lost under uncontrolled dynamics. The Rate Inheritance Principle (RIP) is the hypothesis connecting the two: effective coherence-loss rates inherit the suppression envelope of static correlations across the interface. We distinguish a weak upper-envelope form — stated here as a short proved lemma under explicit integrability hypotheses — from a stronger envelope-class conjecture, and we record what is now known: the strong form is derived, with a frequency-resolved exponent, in an exactly solvable quasi-free local-sink class, where the rate inherits the square of the static amplitude envelope, kappa(eps) proportional to e^(-2 q(omega_b) eps) — confirming the squared-envelope caveat anticipated in v1 — and it fails through near-zero-frequency channels within the secular Davies model class, whose delocalized jump operators sustain a persistent rate floor. Version 1's surrogate decay-curve evidence is withdrawn: it belonged to the uncontrolled proxy class whose failure mode was exposed by the critical-point control of the companion paper, and it is replaced here by the exact Liouvillian-rapidity evidence. Failure modes (now including secular delocalization), a proxy-validated falsification protocol, and the conditional operational consequences for the quantum-classical resource boundary are stated with explicit scope.
Research paperHistorical importARR-2025-03RW5SHK35815BZR · v1
Lluis Eriksson
SUPERSEDED BY AI.VIXRA:2601.0023V2. This replacement preserves public version 1 and adds an explicit correction and supersession record. The exact omega=0 statements and witness mechanism of version 1 stand unchanged, and Proposition 4.4 survives with a repaired proof. What is superseded is the false general plain-commutator Bohr decomposition, the suppression proof route using a false KMS submultiplicativity bound, the associated constants and claim of avoiding an inverse-smallest-eigenvalue factor, and the inline listing. ai.viXra:2601.0023v2 supplies the exact general decomposition, corrected c_sigma-dependent bounds, pinning identity, explicit hypotheses and verification suite. No thermodynamic, continuum or universal resource-boundary theorem follows from the finite tests. The preserved version 1 follows the two-page notice unchanged.
Research paperHistorical importARR-2025-1Q29S482V08T1VV0 · v1
Lluis Eriksson
We revisit the proposal that the Heisenberg cut is best understood operationally, as a resource boundary: a superposition counts as effectively classical for an agent once the power required to maintain its coherence against decoherence, P_extra >= k_B T Cdot_loss, exceeds that agent's budget. Version 1 supported the key dynamical ingredient — the rate-inheritance hypothesis, that decoherence rates transmitted through a gapped buffer of width eps are suppressed as poly(eps) e^(-m eps) — with a windowed numerical proxy on a transverse-field Ising chain. Two things change in this revision. First, rate inheritance is now derived in an exactly solvable quasi-free model and verified against exact Liouvillian rapidities: for a probe mode of renormalized sub-gap frequency omega_b coupled through a Kitaev buffer to a Markovian loss, the exact Liouvillian rapidity obeys kappa(eps) proportional to e^(-2 q(omega_b) eps) with cosh q(omega) = (mu^2 + 4 - omega^2)/(4 mu), verified to four decimal places over ten decades of kappa; the exponent is the squared (amplitude^2) one, resolving Remark 8.1 of v1, and it closes continuously at the band edge. Second, the central numerical evidence of v1 (its Fig. 1) is withdrawn: an exact critical-point control shows that the co-moving-window proxy decays faster when the gap is removed, so what it measured was arrival kinematics, not gap physics. We identify the mechanism with photonic-band-gap suppression of emission and evanescent atom-photon bound states, restate carefully what is imported versus what is new, derive a logarithmic law for the resource cost of coherence lifetime, note that the protected object is a sub-gap subalgebra rather than a spatial region, and state the interacting-buffer conjecture that would take rate inheritance beyond the quasi-free class. The non-claims of v1 stand unchanged: nothing here derives the Born rule or selects single outcomes.
