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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
