Research paperHistorical importARR-2026-2VT5B14BC88EG9TD · v1
Lluis Eriksson
We study whether recovery-based operational distances exhibit a distinctive finite-size signature near quantum criticality. For a tripartition A-B-C of a 1D chain with a collar B of width w separating A from C, we compute a Petz-based reconstructed state and the recovery error E_Petz(w) = -log F (squared Uhlmann fidelity), and define an effective recovery distance d_eff(epsilon) as the minimal collar width achieving error below epsilon, stabilized by E_best(w) = min over w' <= w of E_Petz(w') and reported with explicit censoring. Using exact diagonalization of the transverse-field Ising chain at N = 11 with |A| = 2, we sweep hx across the critical region at hz = 0 and compare to a longitudinally perturbed control hz = 0.5: pronounced growth and extensive censoring of d_eff(epsilon) appear in the critical region at low temperature, while the control remains comparatively featureless; an extended-collar spot-check yields d_eff(1e-3) of about 7.6-7.7 at beta = 12 near hx in {0.96, 1.00}. v2 adds (no v1 result is changed): an explicit |C|-shrinkage caveat -- at fixed N, growing w also shrinks C, so the absolute scale of d_eff near w_max conflates buffer growth with a shrinking reconstruction target, while fixed-geometry comparisons across hx (the criticality signature) are unaffected; a window-relativity remark (epsilon, beta, N jointly set what is resolvable: at smaller N the beta = 12, epsilon = 1e-3 window censors even off-critical points, consistent with v1's own zoom); delivery of v1's "future work" item: a CMI-based distance computed on the same sweep shows the same criticality signature at its own threshold (CMI decays about half as fast as the Petz error, cf. 2601.0035); series positioning; and a fully regenerable verification suite.
Research paperHistorical importARR-2026-4303A7YGN9957T0V · v1
Lluis Eriksson
We define an operational notion of effective distance from approximate quantum state recovery. Given a tripartition A-B-C with B a collar of width w separating A from C, we compute a Petz recovery reconstruction error E_Petz(w) = -log F(rho_ABC, rho_Petz(w)) (squared Uhlmann fidelity) and define an emergent distance d_eff(epsilon) as the minimal collar width such that the best-achieved error up to w falls below a threshold epsilon. Using exact diagonalization for the transverse-field Ising chain at N = 11, hx = 1.05, |A| = 2, we find that d_eff(1e-3) grows strongly with inverse temperature beta in the unperturbed case (hz = 0), from 1.00 at beta = 0.5 to 3.57 at beta = 5.0, while remaining near-minimal in the longitudinally perturbed case (hz = 0.5), close to 1.0 across the same range. We also introduce a discrete curvature diagnostic based on second differences of log E_Petz(w) on a pre-floor window, reported only when identifiable. v2 (no v1 number is changed): the garbled reproducibility paragraph of v1 is replaced by a real, regenerable verification suite, which reproduces the beta-sweep to two decimals already at N = 9 (d_eff = 1.00, 1.00, 1.51, 2.11, 2.82, 3.55 vs 3.57 at N = 11; mu_prefloor endpoints 8.44 to 1.35 vs 1.33; PSD-projection sensitivity 3.3e-8 vs about 3e-8) -- independently confirming the finite-size robustness of the appendix; the mild |C|-shrinkage caveat is stated with cross-references to its quantified analysis in the companions; and series positioning is added.
Research paperHistorical importARR-2026-5BJDY6QKSH9QBTQS · v1
Lluis Eriksson
In algebraic quantum field theory (AQFT), local algebras are typically Type III factors, so density matrices and von Neumann entropies are unavailable for bounded regions. We formulate a B-minimal continuum analog of the lattice "collar => Markovness => recovery" mechanism by combining: (i) the split property as the mathematical replacement of a buffer (collar), (ii) Araki relative entropy to define a split-regularized conditional mutual information I^N(A:C|B) relative to fixed Type I interpolating data N, and (iii) modular/twirled Petz recovery as an explicit candidate recovery channel. Assuming an FR-type recoverability inequality in the fixed-split setting, we obtain quantitative recovery bounds in a fidelity-based error metric (purified distance). We conclude with a conditional holographic remark. v2 corrects the fidelity-convention factor in the assumed FR-type inequality: with the squared (Bures/Uhlmann-squared) convention used throughout, the importable finite-dimensional motivation gives -log F <= I, not -log F <= I/2; v1's half-form is strictly stronger than its motivation and is refuted as a finite-dimensional anchor on 40/40 random tripartite states (the corrected form holds on 40/40) -- the same factor-2 correction applied in 2512.0101 v2 and 2601.0020 v2. The recovery theorem's constant changes by sqrt(2); the exponent is unaffected. v2 further adds series positioning, a compatibility remark with the split-regularized CMI of 2601.0020, a concrete demonstration that I^N can be negative for unfavorable split data -- nonnegativity of I^N is part of the good-split-data regime, not automatic -- and a finite-dimensional verification suite for every checkable ingredient of the dictionary.
Research paperHistorical importARR-2026-7RASMSMHWW8PM9S8 · v1
Lluis Eriksson
We present a quantitative clustering-recovery bridge for interacting quantum many-body systems that is intrinsically non-Gaussian, organized around conditional mutual information (CMI). For a geometric tripartition A-B-C in which B is a collar of width w separating A from C, an exponential geometric Markov bound I(A:C|B) <= K e^(-alpha w) implies exponentially accurate recovery of rho_ABC from rho_AB in the theorem-facing metric -log F, by combining the Fawzi-Renner inequality with an elementary conversion to fidelity error bounds. We obtain a proved interacting lane (shielded small-region geometry, arbitrary temperature) by invoking recent local Markovness results for finite-range lattice Gibbs states. Numerically, we benchmark the mechanism in the transverse-field Ising chain with longitudinal field, comparing integrable (hz = 0) and non-integrable (hz = 0.5) regimes, and evaluate the explicit Petz recovery map with a censored log-plotting and fit protocol. v2 corrects the Fawzi-Renner factor under the squared-fidelity convention used throughout (-log F <= I, not I/2; fourth occurrence of this correction in the series), with a substantive empirical consequence: v1's headline "mild overshoot" of Petz over the FR scale (r of about 1.23-1.26 in the non-integrable, low-temperature, minimal-collar regime, including rotated and twirled controls) was measured against the incorrect half scale; against the corrected scale the overshoot disappears entirely (r of about 0.62), and the v1 conclusion of "a genuine gap between explicit Petz-type constructions and the existential optimal-recovery scale" is withdrawn. The corrected conclusion is stronger: explicit Petz satisfies the FR scale throughout the dataset, with at least about 40 percent margin even at the hardest point. A fully regenerable verification suite reproduces the pipeline from scratch. Finally, we state a conditional application to entanglement wedge reconstruction, separating proved information-theoretic content from bulk-boundary interface assumptions.
Research paperHistorical importARR-2026-34XCH3HCWK9ENB44 · v1
Lluis Eriksson
We study when geometric separation in gapped quantum systems yields a genuine reduction in thermodynamic resources required to maintain coherence against uncontrolled open-system dynamics. Our analysis separates three layers. First, in a regularized Gaussian split regime motivated by algebraic QFT, we state an explicit static reconstruction bound: collar suppression of vacuum cross-correlations enables approximate state recovery via a conditional-reattachment covariance rule with fidelity error controlled by a cross-block recovery norm. Second, we show why static recoverability does not automatically imply suppression of dynamical decay rates: fixed-point structure and Bohr-zero (omega = 0) channels can generate obstructions invisible to static clustering alone. We formalize this using an exact omega = 0 Dirichlet identity and implement finite-size commutator-witness diagnostics in the transverse-field Ising chain, finding no evidence of a size-independent omega = 0 floor in that benchmark regime for tested sizes. Third, we give an autocontained finite-dimensional core linking coherence loss to incremental maintenance power under an explicit battery-assisted thermal-operations model with paired strategies, and we state a typed rate-inheritance hypothesis identifying precisely what additional dynamical input is required to propagate collar suppression into power suppression. We conclude with a Type III blueprint. v2 corrects two points and adds verification: (i) the recovery rule of the static layer is conditional reattachment -- not the Petz map for correlated Gaussian references (aligned with 2601.0007 v2 and 2512.0060 v2), with an explicit admissibility hypothesis; (ii) the v1 work-cost bookkeeping (its Eq. (25)) carried a sign error -- the work cost is the battery free-energy decrease -- which made v1's one-step work lemma false as printed (random energy-conserving unitaries violate it in 57/100 draws) while its own proof chain and everything downstream hold verbatim with the corrected sign; this is the same error class repaired in 2512.0061 v2. v2 further adds a GNS/KMS convention bridge to the companion witness papers, series positioning, an updated status of the rate-inheritance hypothesis, and a verification suite.
Research paperHistorical importARR-2026-483TABVBKH939V3Q · v1
Lluis Eriksson
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.
Research paperHistorical importARR-2026-79JR2RMHHP93RVAD · v1
Lluis Eriksson
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.
Research paperHistorical importARR-2026-1HR3DENYAZ9S8VCR · v1
Lluis Eriksson
We propose an entropic interface between locality, recoverability, and dynamical decay rates across a geometric collar. The central scalar invariant is the conditional mutual information (CMI) I_rho(A:C|B), where B is a buffer separating A and C. In finite dimension (Type I algebras), the Fawzi-Renner theorem implies that small CMI yields a quantitative recovery channel acting on B. We formulate a volume-uniform geometric Markov bound with a boundary prefactor, I_rhoLambda(A:C|B) <= sigma(dB) g(w), and summarize recent literature inputs establishing exponential CMI decay in shielded/high-temperature regimes. On the dynamical side, we formulate a Rate Inheritance Principle (RIP) for Davies/KMS-symmetric generators: static Markovness across the collar constrains decay rates on the fast sector F-perp modulo the fixed-point algebra F = ker L (the omega = 0 floor), with a dynamical input stated as a Poincare inequality for a local collar Dirichlet form. The only remaining nontrivial link is isolated as an explicit Dirichlet comparison assumption. We verify a diagonal (classical) heat-bath comparison and derive a diagonal subsector corollary with an explicit transfer coefficient. Finally, we define a split reduction datum and a split-regularized CMI target quantity for an AQFT lift and include finite-size illustrations/diagnostics. v2 corrects two points and adds verification: (i) the Fawzi-Renner factor under the squared-fidelity convention is -log F, not -2 log F (as in the companion 2512.0101 v2), so the geometric recovery bound reads 1 - F <= sigma(dB) g(w); (ii) the v1 bulk-collar comparison for diagonal heat-bath observables is false as stated -- exact-enumeration counterexamples are exhibited -- and is replaced by a proved version with the collar extension taken on the enlarged neighborhood B^(+2r) (commuting-projection argument). A full verification suite (exact enumeration, N = 9 Ising-Z) ships with the paper, checking the corrected comparison (0 violations), the transfer constants, the exact vanishing of CMI for the 1D Markov field, and the corrected FR factor on random tripartite states. Throughout, the target RIP theorem remains conditional on the bulk-collar comparison assumption; the diagonal heat-bath result verifies only a corrected commuting-subsector comparison, and also exhibits a 1D degeneracy of the transfer constant.
Research paperHistorical importARR-2026-0QAD31QJAM84YR08 · v1
Lluis Eriksson
We prove a quantitative clustering—recovery bound for centered quasi-free (Gaussian) states in a finite-mode bosonic CCR (Weyl) setting. Motivated by split inclusions in algebraic quantum field theory, we work in a regularized framework where Gaussian states are parametrized by finite covariance matrices and a recovery map admits an explicit covariance block formula. Using a perturbative Gaussian fidelity input and explicit coercivity bounds for inverse covariances, we control the recovery error in terms of a vacuum cross-correlation factor, a cross-correlation perturbation parameter, and a recovery-error matrix norm ||DeltaGamma||_HS with an explicit quadratic+quartic structure. In a distinguished class (Family A, X = X0), this reduces to a bound in terms of the cross-block error ||Delta12||_HS. We include ancillary numerical sanity checks verifying the perturbative regime, a collar-envelope decay model, a dimension sweep n1 = n2 in {1,2,3}, and phase-diagram checks of the perturbative domain. v2 adds: a collar-suppressed recovery corollary making the "clustering suppresses recovery error" mechanism a single displayed inequality; an upgraded discussion of the fidelity constants (the local coefficient 1/8 is shown numerically to be a directional benchmark, not a uniform bound, and an empirical constant is certified on the sampled domain); an independent verification suite in pure NumPy/SciPy implementing the Banchi—Braunstein—Pirandola fidelity formula with closed-form anchors, with all proved inequalities tested on random draws (zero violations); positioning remarks relative to the companion notes 2512.0060 and 2512.0101; and, aligning with 2512.0060 v2, corrected Petz-identification language (the recovery rule is conditional reattachment, with Petz agreement only in the factorized case) plus an explicit admissibility hypothesis for the recovered covariance.
Research paperHistorical importARR-2025-42P63ZKJP39JK98S · v1
Lluis Eriksson
This note reports a replicated, high-resolution Bell-transport experiment on IBM Quantum superconducting hardware using a prefix-path protocol that controls spatial heterogeneity across transport lengths. A single physical qubit chain is fixed and increasing transport length L is realized via prefixes of that chain, so that L changes depth while keeping qubits nested rather than switching to different qubit subsets. We reconstruct the Bell-state fidelity F(L) from Pauli correlators E_XX, E_YY, E_ZZ and apply a minimal drift correction using interleaved full-Phi+ control blocks. Beyond a single-chain sweep, we perform a comparative geometry test across three disjoint physical chains on the same backend: the effective decay scale differs significantly across chains (with >10 sigma separations under fit uncertainties), providing operational evidence that the transport decay scale is geometry-dependent under fixed compilation constraints. Motivated by the Rate Inheritance Principle (RIP) framing, we also investigate whether a phase-sensitive static correlation metric measured on idle chains can predict dynamical transport decay. A curated three-chain set exhibits an ordering agreement between a static Ramsey-X nearest-neighbor covariance metric and the transport decay scales mu measured on the same chains; however, scale-up studies over n=18 randomly sampled chains and a preregistered out-of-sample prediction test do not show statistically significant monotone association under permutation testing. We interpret the static—dynamic ordering agreement as conditional and geometry-specific, while the geometry dependence of dynamical decay is robust. v2 adds: a fitting-choice caveat with a synthetically validated re-analysis pipeline for future variant tables, a power bound showing the negative preregistered test excludes a strong device-wide static—dynamic law (from published quantities alone), an all-lengths rate proxy specification, small-sample and estimator caveats, context references, and an offline re-analysis script with documented schema for a future data revision.
Research paperHistorical importARR-2025-2SZN7M8RMR9D18W8 · v1
Lluis Eriksson
We derive the local one-loop contribution proportional to the scalar curvature R in the Euclidean effective action obtained by integrating out matter fields on a curved background. Using a Schwinger proper-time cutoff epsilon = Lambda^(-2) and the Seeley—DeWitt coefficient a_1, we extract the quadratically divergent term multiplying int d^4x sqrt(g) R. We fix a single Euclidean convention for the Einstein—Hilbert action, state an explicit Laplacian convention, and write the Laplacian—Lichnerowicz identity in a sign-robust form so that the fermionic contribution is unambiguous. We provide a unified bookkeeping coefficient A_1^(eff), and hence an induced Newton coupling G_ind via comparison with the Euclidean Einstein—Hilbert action. We also include the minimal gauge+ghost package in background Feynman gauge, a species table, and a reproducible verification suite. v2 adds: the equivalence of the species table with the classic counting 1/G_ind = (Lambda^2/12pi)(N_0 + 2N_(1/2) - 4N_1), gauge- and scheme-dependence caveats for the vector sector, a Weyl/Majorana caveat, corrected Wick-rotation wording, and an exact-spectrum numerical verification of every a_1 entry against closed-form spectra on S^4.
Research paperHistorical importARR-2025-6NR077ZRZ19NJ8RG · v1
Lluis Eriksson
We formulate a non-Gaussian, finite-volume and uniform-in-Lambda version of the Clustering-Recovery bridge for interacting lattice systems. We introduce an explicit collar geometry, a CMI formulation via Fawzi-Renner, and an operational (Heisenberg-picture) quasi-locality strengthening for the recovery map. Version 2 corrects one identity: v1's "CMI as relative entropy" equation equated I(A:C|B) with the relative entropy to the normalized Markov-product state; the exact identity holds for the unnormalized product M = exp(log rho_AB + log rho_BC - log rho_B), and the normalized version underestimates the CMI by -log Z >= 0 (Z <= 1 by Lieb's triple-matrix inequality). We also fix the Fawzi-Renner factor: with the squared-fidelity convention used throughout, the bound is I(A:C|B) >= -log F (not -2 log F). All numerical claims of v1 (Petz slope table; prefactor-slope trade-off; crossover w*=3) have been independently reproduced from scratch by a NumPy-only verification script that ships with this paper.
Research paperHistorical importARR-2025-6D5NJKE4WT856RS8 · v1
Lluis Eriksson
We derive the local contribution proportional to the scalar curvature R in the Euclidean one-loop effective action obtained by integrating out matter fields on a curved background. Using a Schwinger cutoff epsilon = Lambda^{-2} and the Seeley-DeWitt coefficient a1, we extract the quadratically divergent term multiplying the integral of sqrt(g) R. We fix a single Euclidean convention for the Einstein-Hilbert action, state an explicit Laplacian convention, and write the Lichnerowicz/Weitzenbock identity in a sign-robust form so that the fermionic contribution is unambiguous. We provide a unified bookkeeping coefficient A1_eff such that W_R^total = -(A1_eff / 32 pi^2) Lambda^2 integral sqrt(g) R, and hence an induced Newton constant G_ind via comparison with the Euclidean Einstein-Hilbert action. We include the minimal gauge+ghost package in background Feynman gauge, a species table, and a reproducible symbolic check of every entry.
Research paperHistorical importARR-2025-4MV7NKFB2G9KXV82 · v1
Lluis Eriksson
Cognitive systems are resource-limited, but "resource limitation" is often invoked without distinguishing one-shot costs (forming a representation) from sustained costs (keeping it usable under noise). We argue that the availability of internal state features for control, integration, and report is constrained by their maintainability under finite budgets. As a technical anchor we cite a companion preprint deriving an operational maintenance inequality in explicit thermodynamic control models: incremental maintenance power has a non-arbitrary lower bound tied to dynamical fragility (in its corrected form, against efficient baselines, with an unconditional entropy-production floor beneath). This motivates an operational cut: a feasibility boundary separating maintainable from unmaintainable state features. We develop an auditable bridge argument (maintainability to stability to availability), propose a neutrality-friendly principle of maintenance-feasibility bias, and show how it can be incorporated into active inference (the Free-Energy Principle) as a maintenance penalty or constraint, aligning secondarily with Global Workspace accounts of access stability. We address objections and offer falsifiable predictions for synthetic agents and neuromorphic systems, plus an explicitly exploratory psychophysics subsection framed in terms of reportability and stability rather than phenomenology. We do not propose collapse mechanisms, do not derive the Born rule, and make no claims about phenomenological consciousness.
Research paperHistorical importARR-2025-2AQXS44H6Z8GQAG2 · v1
Lluis Eriksson
We present a logically explicit operational program connecting three themes: geometry as suppressibility of cross-region influence, membranes as engineered interfaces implementing that suppressibility, and life as sustained maintenance of internal organization under finite resources. The program composes: (i) a law-grade thermodynamic inequality relating incremental maintenance power to the instantaneous loss rate of an organization functional, imported in its corrected operational hierarchy; (ii) a static geometric suppression layer in which cross-interface leakage admits an envelope f(eps) ~ poly(m eps) e^{-m eps} (with K_nu(m eps) as a canonical representative in massive homogeneous models); and (iii) a dynamical hinge (the Rate Inheritance Principle, RIP) connecting static suppression to separation-dependent effective dynamical rates. This version distinguishes upper and lower rate envelopes kappa_up(eps) and kappa_down(eps) to avoid sign/quantifier errors -- a distinction now vindicated by the companion series -- separates a law-grade Delta-track (energy pinching) from a conditional biology-grade E-track (general conditional expectations), and adds two interface anchors: a recoverability layer via conditional mutual information (CMI) and the Fawzi-Renner guarantee, and a minimal Davies interface lemma showing how correlator envelopes imply Davies-rate upper envelopes (supporting RIP-U microscopically in standard weak-coupling settings). A concrete electrical testbed using membrane-embedded spin probes is proposed to measure dephasing-rate envelopes and detect near-zero-frequency floors that create a resource horizon. A dependency and falsification matrix makes the logical structure audit-friendly.
Research paperHistorical importARR-2025-199995HEM58RZAPN · v1
Lluis Eriksson
Maintaining quantum coherence against uncontrolled open-system dynamics is a control task with unavoidable thermodynamic cost. In a finite-dimensional setting with battery-assisted thermal operations at bath temperature T, we present the corrected operational hierarchy for maintenance power: an unconditional lower bound P_min(rho) >= k_B T sigma(rho) with sigma(rho) the entropy production rate of the target (proved in the appendix); the coherence-power bound P_min >= k_B T Cdot_loss(rho) under diagonal contraction; and incremental (extra) power bounds relative to thermodynamically efficient population-maintenance baselines, which become assumption-free exactly when the pinched target is stationary -- e.g. under pure dephasing, the very dissipator used in this paper's numerical protocol. Here C(rho) = S(rho||Delta[rho]) is relative-entropy coherence to energy pinching and Cdot_loss(rho) := -d/dt C(rho_t)|_{t=0}. These statements are operational, observer-independent, and geometry-free. We then present the Rate Inheritance Principle (RIP) as the falsifiable dynamical bridge between static clustering and decoherence rates, with its status: weak form a lemma under explicit hypotheses; strong form derived, with a frequency-resolved squared-amplitude exponent, in an exactly solvable quasi-free local-sink class; failure through near-zero Bohr-frequency channels realized within the secular Davies class. We provide falsifiable protocols distinguishing one-shot work from sustained maintenance power, including a numerical stress test (distance-independent influence floor without an interface vs collar-induced suppression) in a transverse-field Ising chain with remote dephasing. Finally, an explicitly speculative Outlook connects the resource boundary to the Free-Energy Principle for resource-limited agents, at a methodological (non-phenomenological) level.
Research paperHistorical importARR-2025-1D8QJ84MY09CNBJ8 · v1
Lluis Eriksson
In gapped quantum many-body systems, static correlations decay exponentially with distance. A common heuristic expectation is that this geometric suppression carries over to dynamical decoherence rates induced by local environments; this expectation has been isolated as the Rate Inheritance Principle (RIP). We stress test RIP in a fully specified Davies-type Markovian setting: a gapped transverse-field Ising chain weakly coupled to a thermal bosonic bath through a strictly local operator. RIP is formulated operatorially through two spectral envelopes of the Dirichlet form on operators supported at distance eps from the coupling region: a ceiling kappa_sup(eps) (v1's envelope) and a floor kappa_perp(eps) (smallest nonzero rate, new in v2 — the quantity a maintenance no-go actually needs; v1's inference from ceiling saturation to a power floor was a non sequitur and is corrected here). Numerically, rate inheritance remains conditional: for energy-exchange-dominated coupling the ceiling decreases with separation, while for near-zero-Bohr-frequency coupling it saturates — and, more importantly for the no-go, the projected floor also persists in that regime. Version 2 adds the diagnostic that the series' methodology demands: the near-zero-frequency Bohr components of the local coupling are strongly delocalized at finite size (about 90 percent of their weight beyond the coupling site), so the saturation is established within the Davies model class, whose secular construction is nonlocal; the exactly solvable local-sink model of the companion paper shows genuine geometric suppression, and the two results bracket the physics. Combined with the corrected maintenance bounds of the companion work theorem, a persistent projected spectral floor yields a quadratic-proxy resource horizon; the corresponding relative-entropy no-go is stated with its required uniform-Cdot_loss / MLSI-type hypothesis explicit.
Research paperHistorical importARR-2025-13JDAZFXPP81EBY4 · v1
Lluis Eriksson
Maintaining quantum coherence against uncontrolled open-system dynamics is an operational control task with unavoidable thermodynamic cost. In finite dimensions, explicit lower bounds on the minimal power required to stabilize coherence can be derived under standard Markovian assumptions, independently of geometric or field-theoretic structure. At the same time, static correlations in gapped systems are geometrically suppressed, raising the question of how such suppression influences dynamical decoherence rates and, consequently, coherence-maintenance power. Bridging the two domains requires dynamical input that static clustering alone does not provide.This note introduces no new technical results. It provides a logical closure of the program by separating (i) results proven without additional structure, (ii) conditional interfaces, and (iii) dynamical hypotheses — and, new in this version, it updates the status of the central hinge. In v1, rate inheritance — the relation between static correlation envelopes and effective decoherence rates — was identified as the unique unresolved hinge. Since then it has been partially resolved in both directions anticipated by v1's scenario analysis: it is now a derived, frequency-resolved law in an exactly solvable quasi-free local-sink class (2512.0064 v2), and the failure scenario through near-zero-frequency channels has been realized within the Davies model class, with the persistent floor computed and the secular nonlocality of that construction quantified (2512.0070 v2). The imported maintenance bound is restated in its corrected v2 form (2512.0061 v2), whose v1 formulation was vacuous. The framework's design goal — robustness under partial refutation — has thus been exercised in practice, twice.
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.
Research paperHistorical importARR-2025-7GXFT1VQV98JNA6Q · v1
Lluis Eriksson
We prove that exponential clustering of vacuum correlations enables approximate reconstruction of global quasi-free states from local data in algebraic quantum field theory. The reconstruction is an explicit Gaussian procedure — conditional reattachment through the vacuum's regression structure — which coincides with the output of the Petz recovery map when the reference state factorizes across the split, but not in general: for a pure reference the Petz map returns the reference itself for every input, and version 1 of this paper incorrectly identified the two. For quasi-free states of a massive scalar field satisfying natural constraints, including a symplectic-gap (mixedness) condition on the reference state and an admissibility (no-steering) condition on the split geometry, we prove 1 - F <= C(d,kappa) / [eps^2 (1 - (eta_vac + delta)^2/eps)^2] * ||Delta12||_HS^2, where Delta12 is the reconstruction error, eta_vac <~ e^(-mr) is the vacuum correlation factor, delta controls cross-correlation perturbations, and C(d,kappa) = C_k(6+C_k)/(16 min(c1,c2)^2) with C_k = (1+kappa)^2/(kappa(kappa+2)) determined by the symplectic gap kappa > 0. A finite-rank corollary with explicit factor 2n recovers physical intuition. All counterexamples and bounds are verified by an exact truncated-Fock numerical suite distributed with the paper. Applications to holographic reconstruction are discussed.Version 2 makes three corrections to v1: (i) the reconstruction map of v1's Proposition 2.14 is not the Petz map — its "marginal preservation" step fails for correlated references — and the main theorem is restated for the reconstruction procedure the proof actually controls; (ii) the simplified constant is corrected (3/8 to 7/16 in the strongly mixed limit); (iii) a symplectic-gap hypothesis is added to the Gaussian fidelity lemma, shown necessary by an explicit counterexample.
Research paperHistorical importARR-2025-76C3S3SSMP8HJ8NF · v1
Lluis Eriksson
We derive operational lower bounds on the minimal thermodynamic power required to maintain quantum coherence against uncontrolled open-system dynamics. Work is defined as the consumption of non-equilibrium free energy stored in an explicit battery at bath temperature T, namely W := F_W(sigma_W) - F_W(sigma'_W) with F_W(sigma) = k_B T S(sigma||gamma_W), and allowed controls are battery-assisted thermal operations implemented by energy-conserving global unitaries. Coherence is quantified as a relative entropy to a conditional expectation, C_E(rho) := S(rho||E[rho]). Our main proved results are: (i) an unconditional maintenance bound P_min(rho) >= k_B T sigma(rho), where sigma(rho) >= 0 is the entropy production rate of the target under the uncontrolled semigroup (Spohn), which splits via the pinching Pythagorean identity as sigma = F_diag + C_loss; (ii) the coherence-power bound P_min >= k_B T C_loss(rho) under a diagonal-contraction hypothesis satisfied by Davies generators; and (iii) extra-power bounds for coherence stabilization relative to thermodynamically efficient population-maintenance baselines — version 1's "assumption-free" paired-infimum formulation is shown to be vacuous (the unlinked-pairs infimum is minus infinity), and the corrected statement is genuinely assumption-free precisely when the pinched target is stationary (e.g. pure dephasing), where the baseline is free. We further provide a conditional extension to general conditional expectations and a Type III split blueprint, with external geometric inputs encoded as explicit two-sided interface assumptions. All finite-dimensional claims are verified by an exact numerical suite distributed with the paper. These results provide an operational resource criterion for quantum-to-classical behavior, not a collapse theory.Version 2 corrects a sign error in the work definition and in the final step of v1's Appendix A, replaces v1's vacuous extra-power definition, and strengthens the main bound to an unconditional entropy-production form.
