Research paperAcceptedARR-2026-1D2QYXPCVY9H7ANB · v1
Lluis Eriksson
We give a unified exact rate–distortion theory for retaining the complete rank-one Born-probability field of a Haar-random pure state in complex projective space. A constrained root count, a sharp centered power-sum theorem, and Newton's expansion prove an all-degree spectral result: at fixed traceless Frobenius norm the projective Laplace transform is maximized by a one-positive-spike spectrum. This reduces the unrestricted Shannon rate–distortion function to an exact scalar complex-Bingham envelope in every dimension, with covariant channels and independently flagged coexistence mixtures attaining every distortion. For dimension at least three, directional information turns on discontinuously; the qubit curve and the all-dimensional high-fidelity constant are explicit. We then solve the full fixed-normalized-distortion limit. If y_* > 2 solves y_* - 1 = 2 log y_*, the limiting free energy has a unique coexistence point, and the information cost per dimension is a closed two-piece function with a nontrivial linear face. The finite-dimensional onset multiplier equals alpha_* d minus [alpha_*/(2 log y_*)] log d up to an O(1) remainder. Finally, a pointwise Hilbert projection converts every measurable scalar reporter into a physical density-matrix reporter without increasing risk for any pure input. Hence the exact worst-state channel capacity equals the Haar rate–distortion function, arbitrary joint n-state memories cost exactly n times the one-state frontier, and transitivity forces zero rate dispersion with an exponential finite-blocklength strong converse. These results concern reusable calibrated probability fields, not click-only simulation, state update, or intrinsic randomness.
Research paperHistorical importARR-2026-32DEQJM8W59JXSQT · v1
Lluis Eriksson
Four balanced spin kicks along the vertices of a regular tetrahedron generatean order-dependent eight-pulse echo. We prove that all 24 echo orders have oneconjugacy class in SU(2). Haar randomization of only the global orientationtherefore gives an order-law-independent, self-adjoint random-unitary channelon every spin-j matrix algebra. Its exact eigenvalues are normalized SU(2)characters, lambda_l=U_{2l}(q)/(2l+1), with multiplicity 2l+1 and an explicitfinite-pulse architecture polynomial q=1-A/2. The maximal link-reflection-positive interval connected to zero is alpha<=pi/(4j+1), with an exact endpointequation and a finite OS Hamiltonian under strict inequality. In the doublescaling N=4j+1, y=xi/sqrt(N), the full tower converges uniformly tosinc(8xi^2u). This gives the sharp full-tower boundary xi_c=sqrt(pi/8), acritical boundary law N lambda_top -> 3pi/8-2s, an explicit scaled mass profile,and an ultraviolet heat-trace integral. The fixed-rank limit recovers the fuzzy-sphere Laplacian. Poissonization yields a genuine CPTP semigroup and an exactmany-body connected nuclear profile exp(3e^-c)-1. Symbolic and deterministicmatrix certificates accompany the manuscript.The Haar average also has explicit exact finite implementations. A classicalpositive Gauss--Legendre/trapezoidal cubature at bandlimit 4j needs(4j+1)(2j+1) order-conditioned frames, or (4j+1)^2(2j+1) frames when the sameframe list must be order oblivious.The common-class proof reduces the 24 orders to the even and odd A4 orbits.For finite implementations, a separate stability bound controls l1 weighterror, orientation displacement, and pulse perturbations; total variationagainst Haar is not used for discrete frames.
Research paperHistorical importARR-2026-3M1EEG1T689ADSMW · v1
Lluis Eriksson
For a prescribed traceless Hermitian four-level target F, we determine exactly the least product of Hilbert-Schmidt norms of Hermitian A,B satisfying -i[A,B]=F. With ordered eigenvalues lambda_1 >= ... >= lambda_4, the answer is the maximum of four explicit linear spectral forms. The lower bounds are Horn-Littlewood-Richardson certificates and four closed constructions attain them. On every nonzero spectral stratum, the least optimal rank is exactly max(n_+(F),n_-(F)), closing all chamber walls and degenerations. We also prove a finite-dimensional Horn linear-program reduction, the sharp tax 1 <= kappa_4/(||F||_1/2) <= 2 with complete equality cases, and the exact balanced three-kick action S_2^2=12 sqrt(3) kappa_4. Exact symbolic and deterministic LP certificates accompany the manuscript.
Research paperHistorical importARR-2026-3SDH8JSK73925RXK · v1
Lluis Eriksson
A balanced sequence of short Hamiltonian kicks has no first-order drift, but its order-dependent commutator holonomy survives when the order record is discarded. We prove that a reversal-symmetric average of complete order/reverse echoes is a self-adjoint random-unitary transfer operator and obeys the nonperturbative bound cos(4|y|S) I <= T_y <= I for |y|S < pi/8. This yields site and link reflection positivity and a finite-dimensional Osterwalder-Schrader Hamiltonian. The physical transfer approaches the curvature-frame generator with an explicit sixth-order remainder, giving quantitative O(y^2) convergence of its mass gap. For the regular tetrahedral qubit loop, we derive the exact finite-pulse depolarizing eigenvalue, isolate its first positivity zero at y = 0.455698535295322..., and obtain the mass expansion. We then prove a complete finite-depth Hausdorff criterion for visible transfer edges, with uniformly sharp depth r-1, and give an exact rational four-kick certificate: the true frame gap 10/3 is certified while the false claim 4 has rational witness value -1/64. A Wishart-Loewner band supplies finite-sample type-I control for independent Gaussian correlator sketches, including adaptive witnesses. Exact symbolic and deterministic numerical certificates accompany the manuscript.
Research paperHistorical importARR-2026-1PT4297HNX9T4RBD · v1
Lluis Eriksson
A balanced sequence of short Hamiltonian kicks has zero first-order drift but retains an order-dependent commutator holonomy. For a traceless qutrit target with ordered eigenvalues, we solve the inverse Hermitian-commutator problem exactly: its minimum product Hilbert-Schmidt norm is the larger adjacent spectral gap, equivalently half the trace norm plus the absolute middle eigenvalue. This yields the exact minimum action of a balanced three-kick realization and identifies a middle-eigenvalue cost tax between 1 and 3/2. Among four equal-norm balanced qubit kicks, the forgotten-order curvature gap is at most `S^4/108`, with equality only for a regular tetrahedron. Its 24 orders generate exactly the six Pauli holonomies, so the finite twirl is depolarizing and an explicit inverse-cosine schedule realizes any depolarizing semigroup exactly at every finite step count. We then derive the diffusion limit from complete echoed, pinched physical words, obtaining an explicit `O(n^-1/2)` diamond-norm bound. Off-block pulses of size `y^(1+beta)` produce a sharp trichotomy: irrelevant for `beta>1`, additive at `beta=1`, and Zeno-projective for `0<beta<1`; a quantitative compression bound gives uniform convergence away from zero and an explicit initial-layer profile. The complete implementation has serial action proportional to `n^(3/4)`. Exact symbolic and deterministic numerical certificates accompany the manuscript.
Research paperHistorical importARR-2026-2JJFS9HNTT87DAGC · v1
Lluis Eriksson
A balanced ordered loop of retained Hamiltonians generates a second-order geometric Hamiltonian. We solve its higher-rank action problem and determine what remains when the order record is erased. For every matrix dimension and every number of kicks `m >= 3`, a gauge-invariant operator action obeys a sharp, dimension-free polygonal bound on the spectral diameter of the geometric Hamiltonian; regular two-level polygons attain the constant in every dimension. A target-sensitive Hilbert--Schmidt companion bound is controlled by the trace norm and has equality exactly for sign-paired nonzero spectra. These laws yield exact diamond-norm ceilings with a physical state witness. For a uniformly forgotten order, we derive an exact `1/12` commutator-frame covariance. The resulting reversal-symmetric random-unitary product converges in diamond norm at rate `O(n^-1)` to a GKLS frame Laplacian whose fixed algebra is the joint commutant of the pair commutators. A tetrahedral Pauli architecture gives exact primitive depolarization with gap `64/3`. Finally, fixed laboratory time `T` and bounded kick amplitude `Lambda` impose a sharp curvature ceiling proportional to `T^2 Lambda^2/n`; maintaining nonzero holonomy requires `Lambda=Omega(sqrt(n))`. Exact symbolic and deterministic numerical certificates accompany the paper.
Research paperHistorical importARR-2026-5GGH8B5GDA89RRHX · v1
Lluis Eriksson
Lower bounds do not determine which resource profiles are physically attainable. We close the continuous inverse problem for passive subspace transport. Let two rank-k subspaces in C^N, N >= 2k, have ordered canonical angles beta, and let q_j be the integrated leading eigenvalues of a positive generator Q = -iS* dS/dt. We prove the exact equivalence: q is attainable if and only if 2 beta is weakly majorized by q. Every feasible profile has a compiler using at most k+1 mutually commuting positive generators of rank at most k, with constant ordered top spectrum. Analytic rationality adds an integer-valued resource: for two boundary frequencies, the least McMillan degree of an inner matrix sending a fixed input subspace to two prescribed output subspaces equals the number of nonzero canonical angles. We also give a fail-closed finite-error certificate for both resources from noisy projectors.At multiple frequencies, Wigner-Smith delay is only the block diagonal of a boundary de Branges-Rovnyak Pick matrix. This positive matrix is the Gram matrix of frequency-excited internal states and has rank bounded by the McMillan degree. Its spectrum yields robust degree certificates and unavoidable model-reduction tails. An exact example exhibits identical local proper delays for degree-one and degree-two devices while their Pick ranks distinguish them. Deterministic code reconstructs the compilers, tests 2,240 randomized theorem interfaces, checks the strict separation, and independently replays the certificate.
Research paperHistorical importARR-2026-0FF03PQCTD89KBTM · v1
Lluis Eriksson
The order of short operations is normally a microscopic detail. We show that a fixed degenerate measurement turns it into an operational curvature with an exact macroscopic readout. Let E retain a block matrix algebra, and let two words apply the same short Hamiltonian kicks in different orders, with the same nonselective pinching after every kick. Their leading difference is `-i tau^2 ad(F) E`, where F is the sum of `i[h_j,h_k]` over pairwise inversions. This gives a discrete non-Abelian Stokes law. Its diamond-norm coefficient is exactly the largest spectral diameter of a block of F, and therefore fixes the leading optimal channel-discrimination advantage. Under first-order balance, all permutations have the same dissipator while their geometric Hamiltonians differ exactly by F, so local curvature integrates into distinct diffusive quantum Markov semigroups. We characterize contextual invisibility, the rank-one classical boundary, and inverse-success amplification under postselection. Every retained Hamiltonian modulo the block center is realizable by a balanced three-kick loop. For a qubit block we prove the sharp action law `kappa <= S^2/[m tan(pi/m)]`, attained by regular planar kick polygons. An integer-Pauli four-kick architecture saturates the bound and supports primitive dissipation. Symbolic, semidefinite, and convergence certificates accompany the paper.
Research paperHistorical importARR-2026-3A3YP2CEH79D4RV0 · v1
Lluis Eriksson
Repeated projective measurements are usually discussed either in the ballistic Zeno scaling or after reduction to classical outcome probabilities. We study a different regime in which each nonselective measurement retains a full matrix algebra inside every degenerate outcome block. Let E(X)=sum_a P_a X P_a, let E_tau be its rotation by exp(-i tau H), and close one cycle by Phi_tau=E E_tau E. We prove, uniformly on compact time intervals and in diamond norm, that Phi_{sqrt(t/n)}^n converges to exp(-tK)E, where K=E ad_H(1-E)ad_H E=C_H^* C_H. The limit is a genuinely quantum Markov semigroup on the direct sum of the block matrix algebras, with explicit jumps sqrt(2) P_b H P_a. Beyond upper bounds, we identify three exact local obstructions for the unprocessed physical product. The cubic map M_H produces a nonzero n^{-1/2} coefficient; after it vanishes, the quartic product obstruction J_H produces a nonzero n^{-1} coefficient; after both vanish, the quintic obstruction P_H produces a nonzero n^{-3/2} coefficient. If all three vanish, the error is O(n^{-2}). All three coefficient transforms are injective. An exact three-record algebraic example has M_H=J_H=0 but P_H nonzero, proving that the third branch is attained. The fixed algebra is A intersect {H_off}', and the least singular value of the commutator frame C_H defines a noncommutative connectivity gap. In the primitive case that gap is the exact exponential mixing exponent in diamond norm and is Lipschitz robust under Hamiltonian perturbations. Rank-one blocks reduce exactly to twice the squared-coupling graph Laplacian. An eight-dimensional rational architecture with four qubit blocks is certified irreducible; its gap is the unique root in (0.4545,0.4547) of an explicit quartic. Symbolic certificates, semidefinite diamond-norm replays, and convergence tests accompany the paper.
Research paperHistorical importARR-2026-127X6SRKAV9ZSVFM · v1
Lluis Eriksson
A subspace quantum speed limit usually records only the largest canonical angle. Passive scattering theory usually records either the largest proper delay or their total trace. Both compressions discard how a rank-k routing event is distributed across modes. We derive the missing vector law: the integrated spectral-spread vector weakly majorizes twice the canonical-angle vector. More strongly, for every symmetric gauge Φ and every pair of k-subspaces in N ≥ 2k dimensions, we solve the variational problem exactly: the minimum spectral-spread action is 2Φ(β). The same value holds for the leading-proper-delay action under positive generators, and one constant coupled-mode path minimizes all gauges simultaneously. The Ky Fan members recover the bandwidth limit, strengthen the trace-action law, and expose every intermediate modal budget. An exact nonnegative slack decomposition separates common-mode delay, inefficient spectral coupling, and nongeodesic subspace motion. Robust corollaries convert heterogeneous pass/stop leakage spectra and finite tomography errors into certified Lorenz curves for delay and, for rational inner networks, McMillan-degree lower bounds. A deterministic artifact tests 8,192 random generators, 1,536 time-dependent paths, sharp equality families, and 2,048 noisy tomography instances.
Research paperHistorical importARR-2026-6352FQW52B9AGB8Z · v1
Lluis Eriksson
Exact interpolation can force the internal degree of a passive network, but laboratory calibrations are approximate. We prove a sharp frequency-domain speed limit requiring neither exact zeros nor analytic continuation away from the measured frequency axis. Let (S(e^{itheta})) be an absolutely continuous unitary scattering path with positive Wigner—Smith generator (Q(theta)=-iS(e^{itheta})^astpartial_theta S(e^{itheta})succeq0). If a fixed (k)-dimensional input subspace is routed approximately between complementary output sectors with amplitude leakages (varepsilon_p,varepsilon_s), define (alpha=[pi/2-arcsinvarepsilon_p-arcsinvarepsilon_s]_+). Every transition then requires Wigner—Smith trace action at least (2kalpha) and largest-proper-delay action at least (2alpha). Costs add over disjoint frequency arcs. For a rational inner network of McMillan degree (n), (M) alternating pass/stop pairs imply (nge 2Mkalpha/pi), recovering (nge Mk) at zero error. An explicit (2k)-port interferometric family attains the bounds for every admissible error pair. A tomography-error corollary converts finite scattering measurements directly into certified degree and delay lower bounds. Reproducible certificates audit equality cases, positive-block inequalities and random Blaschke—Potapov products.
Research paperHistorical importARR-2026-07EH3CZRD89YC8JN · v1
Lluis Eriksson
How many internal passive modes are required to transmit prescribed quantum noise channels without loss while suppressing all signal directions elsewhere? We prove an architecture-independent answer for finite-dimensional rational networks. Let a causal rational inner scattering matrix S have McMillan degree n, signal block G, and complementary loss block C. At distinct regular boundary frequencies, suppose that G is isometric on input subspaces of dimensions k_j. If G is a strict contraction at one other frequency, then sum_j k_j ≤ n.Every lossless direction lies in the kernel of C; a nonzero maximal minor of C therefore has a zero of multiplicity at least k_j. Exterior powers of a minimal Blaschke—Potapov factorization show that no minor can have more than n zeros. The same factorization yields the exact topological delay identity(1/2π) ∫ tr Q(θ) dθ = deg_McM S = n,where Q = −i S* ∂θS is positive semidefinite. Thus lossless calibration multiplicity is bounded by integrated Wigner—Smith delay. The bound is sharp in every dimension. We establish robustness under analytic passive perturbations, prove why unstructured approximate samples cannot imply a degree bound, and show that a previously constructed six-port reservoir filter is universally optimal up to six internal states. Proofs and numerical certificates are reproduced by the linked public repository.
Research paperHistorical importARR-2026-4F7SF8FXM18ANAXH · v1
Lluis Eriksson
We study whether passive reservoir filtering can suppress decoherence more effectively when its channel mixing is irreducible, even after fixing the passband responses and rational complexity. For every integer S ≥ 5, we construct an explicit causal inner six-port network with three signal and three vacuum-loss ports. Its signal block is a rational Schur transfer satisfying 3(S−1) delayed full-spark tangential calibrations and exhibiting exponentially small leakage on two stop arcs. In contrast, every transfer of the same bidegree possessing a constant nontrivial reducing channel and satisfying the same calibrations retains unit stopband norm.We strengthen this exact separation with a quantitative finite-error obstruction: for calibration defect δ and sampled reducing-line defect β, comparator leakage is bounded below by [1−C_S(δ+β)]_+, with C_S given explicitly by finite singular-value margins. A scalar Schur construction proves that every bound of this form must deteriorate at least as 2 exp(9S/20)(1+o(1)); hence uniform robustness is impossible for the chosen clustered calibrations.For uniformly nondegenerate bath spectra, the signal-level separation is squared at the Kossakowski-rate level. A closed Markov pure-dephasing model includes all auxiliary vacuum ports exactly, producing an architecture-independent measurable baseline and an explicit total Ramsey-rate advantage. Finally, we prove that strong passive suppression requires large dwell time: under a peak-delay budget D, the rate-improvement factor is asymptotically at most quadratic in D/S. The construction therefore moves the coherence-maintenance resource into passive memory, vacuum noise and conditioning rather than eliminating it. All certificates, figures and numerical audits are publicly reproducible.
Research paperHistorical importARR-2026-6YFENMGGBY9PPBF1 · v1
Lluis Eriksson
Soft spectral filtering has a more severe effect at finite filling than in a dilute edge-mode code. We consider two odd Su-Schrieffer-Heeger (SSH) rails, fill every negative-energy orbital, and encode one additional fermion in the zero mode of either rail. The code has fixed total number and supports physical coherence. For a boundary transfer at a site with zero-mode weight w_x, the desired logical Davies line has squared matrix element w_x^2. We prove the exact many-body leakage identity W_leak^filled(x) = (1 + 2w_x - 3w_x^2)/4. At the remote boundary, w_x = Theta(zeta^(2 ell)), so the logical line is Theta(zeta^(4 ell)) while the summed particle-hole leakage tends to 1/4. This differs qualitatively from the dilute identity w_x(1 - w_x) = Theta(zeta^(2 ell)).For a Davies filter whose off-target tail is epsilon_ell = exp[-q ell + o(ell)], the bounded-latency exact-refresh power obeys the exponent law lim_(ell to infinity) -(1/ell) log P_(ell,tau) = min{4m,q}, where m = -log zeta, under explicit uniform-envelope and resource-ledger assumptions. A width-independent tail, a special case with q = 0, produces a nonzero maintenance floor rather than merely halving the membrane exponent. More generally, q = 0 means only that the decay is subexponential. Every nonzero tail also makes the exact rapid-refresh limit logarithmically singular at each fixed width.The floor is not a free-fermion accident. For arbitrary interacting number-conserving rails, we prove an exact static identity expressing leakage as a local occupation product minus the logical matrix element. Uniform finite filling and remote-edge indistinguishability force a positive leakage floor. A new local spectral-window lemma places a fixed fraction of that weight in a width-independent Bohr-frequency window using only a commutator norm. Consequently, any bath tail bounded below on that window yields an interaction-stable Davies leakage floor. Quasi-local spectral flow shows persistence in a neighborhood of a symmetry-preserving gapped SSH phase. Exact diagonalization of the interacting spinless SSH chain shows that repulsive and attractive interactions change the observed edge-localization exponent while the leakage is already driven close to 1/4 at accessible widths.
Research paperHistorical importARR-2026-2PYSR8HXMA8RD8RV · v1
Lluis Eriksson
Exact rapid maintenance behaves singularly at the boundary of quantum state space. Let a finite-dimensional target rho have support projector P, and let an uncontrolled quantum Markov semigroup have outward support-leakage rate a = Tr[(1-P)L(rho)]. We prove that, whenever a > 0, the nonequilibrium free-energy loss has the universal short-time form F(rho) - F(exp(tL)rho) = k_B T a t log(1/t) + O(t). Under an explicit fresh-resource-cell ledger, the optimal period-t exact-refresh power therefore diverges as k_B T a log(1/t). For GKLS generators, a is a positive sum of squared support-crossing jump amplitudes. We prove the complete dichotomy: a > 0 gives logarithmically infinite rapid power, while a = 0 gives finite rapid power even when Hamiltonian rotation produces population outside the fixed initial support at second order. We also define a periodic threshold-reset corridor and prove its sharp k_B T a log(1/r) + O(1) small-corridor law.The general singularity has an unexpected geometric consequence. In a fixed-parity dual-rail SSH code, a boundary transfer has desired logical weight w_x^2, but its exact summed zero-mode-to-bulk weight is w_x(1-w_x). At the remote boundary, these scale respectively as Theta(zeta^(4 ell)) and Theta(zeta^(2 ell)). Thus a soft spectral tail changes the exponential rate of bounded-latency refresh from 4|log zeta| to 2|log zeta| unless the tail itself is suppressed at least as zeta^(2 ell). We prove the general rate formula min{4m, 2m+q}, where m = -log zeta and q is the exponential suppression rate of the spectral tail. Exact rapid maintenance and the wide-membrane limit do not commute: every nonzero tail gives infinite rapid power at fixed width, while fixed-period power still vanishes exponentially with width. The result turns perfect filtering from a technical convenience into the sharp boundary between finite and singular exact maintenance.
Research paperHistorical importARR-2026-4GJP1XS78A95XS6H · v1
Lluis Eriksson
The tangent cone of quantum state space at a rank-deficient density matrix is known to have a positive exterior block, and recent work identifies all of its directions with Lindbladian velocities. We derive a quantitative stabilization consequence of this geometry. Let rho be a finite-dimensional target with support projector P, set Q = 1 - P, and let an uncontrolled GKLS generator L have outward support-leakage rate a = Tr[Q L(rho)] > 0. Every additive GKLS controller, including a bounded time-dependent controller, has its own nonnegative outward rate at rho and therefore cannot cancel a. Consequently, no finite-rate additive Markovian controller can keep the system exactly at the target. The conclusion persists for arbitrary finite-dimensional autonomous ancillas, provided the adverse system generator remains additive and local to the system.Under induced trace-norm bounds ||L|| <= M and ||K_t|| <= Gamma, we prove the dynamic corridor inequality limsup ||rho_t - rho||_1 >= 2a/(M + Gamma), without assuming convergence to a stationary state. An autonomous Poisson-reset generator supplies a matching inverse-rate upper bound, establishing the order-optimal minimax law Theta(Gamma^{-1}).For a soft-filter dual-rail SSH family, the microscopic leakage coefficient scales as exp[-(2m + q)ell + o(ell)], whereas the ideal logical disturbance scales as exp[-4m ell + O(1)]. We derive the exact controller-growth threshold g_min = max{0, 2m - q}. Thus, below the filter threshold q = 2m, retaining ideal logical accuracy requires an exponentially growing autonomous correction intensity.
Research paperHistorical importARR-2026-77MR0BB1E487CAYR · v1
Lluis Eriksson
Lower bounds based on the instantaneous free-energy loss of a target state are often interpreted as lower bounds on the power required to maintain that state. We show that this interpretation depends decisively on the control task. If maintenance only requires exact restoration at periodically sampled endpoints and the intervention period is unrestricted, the infimal average power can vanish even when the target has strictly positive instantaneous entropy production. A full-rank dephasing qubit gives an exact energy-conserving SWAP counterexample. We repair the formulation by separating endpoint restoration, bounded-latency maintenance, and continuous holding.For continuous-time finite Markov chains we adopt the established trajectory-relative-entropy holding cost and review the known reversible optimizer and Dirichlet-form representation. Our first composition result is then an exact geometric additivity theorem for suppressible and persistent generators sharing a detailed-balance reference. A two-state counterexample shows that this hypothesis is essential: channels with incompatible equilibria can cancel at a finite membrane width. A dual-rail pair of odd fermionic SSH chains supplies the microscopic layer: exact edge modes, a uniform bulk gap, and an explicitly filtered number-conserving Davies coupling produce two-sided holding-cost bounds without an assumed rate-inheritance bridge. The logical basis has fixed particle number and parity, so arbitrary logical coherence is physical under fermionic superselection. Finally, under a fully axiomatized resource-cell ledger, fresh target-state cells and energy-conserving SWAPs saturate the fixed-period free-energy bound; the correctly ordered rapid-control limit closes the SSH theorem for coherent logical targets. The fresh-copy construction is related to earlier collision-model stabilization work and is not claimed as a work-only controller. The remaining frontier is autonomous work-only control without preloaded target copies.
Research paperHistorical importARR-2026-2695DMHYEK9NEBXD · v1
Lluis Eriksson
This replacement restores the paper originally submitted as version 1 and retracts its claimed unconditional closure of the weak-coupling lattice Yang-Mills mass-gap chain. The principal-logarithm construction in Lemma A.1 fails at central elements such as -I in SU(2), and the printed argument does not establish the required measurable conditional kernel. The proof of Lemma 6.2 applies the Holley-Stroock comparison in the wrong direction: it does not give a coupling-uniform per-block log-Sobolev bound on the unbounded range beta >= beta_0. A bounded beta window can control that per-block estimate, but it does not prove Lemma 6.3, which separately requires an inter-block contraction hypothesis. Three numerical samples and an upper bound on the oscillation are recorded only as numerical evidence; they do not prove linear growth of the optimum or a vanishing infimum. The remaining horizon-transfer, analyticity, and boundary-uniform interfaces are classified as conditional or not established. Corollary 7.3 and the abstract's unconditional mass-gap conclusion are withdrawn. No numbered lemma is declared false unless the corrective note supplies the stated counterargument; otherwise the status is expressly "not established."
Research paperHistorical importARR-2026-00YSQD5FFQ8Y99ZZ · v1
Lluis Eriksson
This replacement restores the corrected Morse-Bott revision that was previously placed on another public record and adds an erratum delimiting its valid scope. The original manuscript used one symbol for both total loop holonomy and per-link angle, losing factors of L in the covariant symbol and metric. It also contained an incorrect sine identity, Fourier labels and normal-bundle statements that fail independently, and a determinant convention that double-counted the Faddeev-Popov factor. The replacement withdraws the claims that hypothesis (H1) was discharged and that (H-FACT) by itself replaced (H2); it records the resulting dependency loop with ai.viXra:2602.0033. What remains is a qualitative fixed-volume positivity statement, conditional quantitative implications under explicitly named hypotheses, and numerical evidence in the tested finite-volume case. The numerical checks printed in the historical revision are treated as author-reported evidence because the cited companion verifier is not present in the audited package. No unconditional continuum or infinite-volume mass-gap theorem is claimed.
Research paperHistorical importARR-2026-4F24313TF996VSTG · v1
Lluis Eriksson
This replacement withdraws the global orbit-space Ricci lower bound and the spectral-gap corollaries derived from it. The printed proof of Theorem 3.1 traces O'Neill's horizontal sectional-curvature identity as though the total-space Ricci tensor contained only horizontal directions. The correct trace also subtracts the mixed horizontal-vertical sectional curvatures. For the bi-invariant product metric these terms are nonnegative before subtraction, so the omitted contribution has the unfavorable sign; the manuscript does not prove that the positive O'Neill term dominates it. Accordingly Theorem 3.1 is not established, rather than asserted false, and Corollaries 3.2-3.3 are withdrawn. The correction also separates a finite-dimensional orbit-space statement from later RCD results formulated for a different measure and operator, and records the broken dependency on a version of ai.viXra:2602.0035 that was not present in its public record. The local geodesic-convexity results and the independently stated structural obstruction are retained only within their stated scope.
Research paperHistorical importARR-2026-0PJHG1P2B09S2SXM · v1
Lluis Eriksson
This replacement corrects the title and headline scope while preserving public version 2 in full. For the simplified quadratic Gribov-Zwanziger lattice measure defined in the manuscript, the zero-momentum propagator obeys the stated volume-uniform bound and its thermodynamic-limit value is computed. Finiteness of D(0) is only the necessary condition identified in Definition 4: it does not by itself prove exponential clustering, a transfer-operator spectral gap, a mass gap for the simplified measure, or a mass gap for Wilson Yang-Mills theory. The former title's phrases "Mass Gap" and "A Non-Perturbative Proof" are withdrawn. No continuum-limit or Clay-problem conclusion is claimed.
Research paperHistorical importARR-2026-7PY68QESR297W938 · v1
Lluis Eriksson
We establish a conditional reduction of the Yang-Mills mass gap problem to a concrete spectral inequality involving the gradient flow. Main result (informal): for pure SU(N) Yang-Mills theory, if the gradient flow beta-function satisfies a uniform strict asymptotic freedom condition |beta_GF(g)| >= delta g^3 for large g, and a Tauberian regularity condition holds for the spectral density, then: in d = 3 the theory has a mass gap Delta > 0; in d = 4 the infrared trace anomaly vanishes, a_IR = 0, ruling out a conformal infrared fixed point -- combined with the phase exclusion of the companion paper, this reduces the mass gap to explicit spectral conditions. However, the spectral argument is marginal in d = 4 and requires additional non-perturbative input. The proof uses a spectral representation of the gradient flow energy E(t) with the monotonicity identity R'(t) = -2 Var_t(lambda) <= 0, the Komargodski-Schwimmer a-theorem, and a gradient flow Poincare inequality connecting functional inequalities to exponential clustering. We verify all perturbative inputs: the free-field calibration gives R_free(t) = 2/t in d = 4 and the one-loop correction has the correct sign. We identify the indefiniteness of the Weitzenbock curvature term as the precise technical barrier in d = 4. v2 (no v1 numbered statement is changed): the fixed-measure spectral representation is retagged as an explicit hypothesis (H0) for the nonlinear interacting flow (equivalent to complete monotonicity of E(t), proven only for the linearized flow; the status table is retagged accordingly); an unresolved citation is repaired; the Holley-Stroock route claimed in v1 to give the Poincare inequality unconditionally at finite beta is corrected (its constant is exponential in the volume, so the L-uniform statement remains conditional outside the two controlled regimes); the a_IR = 0 phase classification behind the d = 3 mass-gap corollary is retagged as imported physical input; the Karamata attribution is replaced by the elementary direct bound actually used; and a verification suite adds numerical evidence: exact spectral machinery, lattice free-field calibration, the quantified d = 3 vs d = 4 dichotomy on synthetic spectral densities, and a first in-framework SU(2) Wilson-flow Monte Carlo diagnostic (8^4, beta = 2.4: c(t) = t^2 rises 42 percent across the measured window and R(t) < 2/t pointwise, i.e. beta_GF < 0 throughout -- numerical support for Hypothesis B' in a controlled lattice window, evidence not proof).
Research paperHistorical importARR-2026-7R7V1N2Y1K877A8T · v1
Lluis Eriksson
We present a reproducible pipeline to compute region algebraic entropies and conditional mutual informations (CMI) in a tiny truncated Hilbert space (here dim = 8) indexed by discrete fusion-like descriptors desc = (x, mu) on L = 4 cells. To generate nontrivial ground states within the descriptor-labeled subspace, we introduce an effective Hermitian mixing Hamiltonian based on a weighted k-nearest-neighbor (kNN) graph Laplacian over configuration labels. Across a parameter sweep, we identify a strong-mixing regime where the participation ratio approaches dim (consistent with Laplacian-dominated ground states on connected graphs) and algebraic CMI diagnostics become extremely small (down to 10^{-6} and below) for the chosen algebraic factorization, while region algebraic entropies remain O(1) and exhibit near-quantized values ~ n log 2. We stress that the mixing term is an ansatz used to probe information-theoretic diagnostics and is not claimed to coincide with a Kogut-Susskind plaquette operator. v2 (no v1 number is changed): the reproducibility gap of v1 is repaired -- v1's pipeline loaded an unshipped basis file (descs.pkl) that was never specified, so the v1 dataset was not regenerable from the paper; v2 prints a canonical self-contained basis whose pipeline reproduces every structural finding, keeping v1's Table 1 as an archival dataset; two empirical observations are upgraded to proved statements -- the descriptor-to-key map is injective, making S_alg a genuine von Neumann entropy of a sector (center-type) decomposition, and in the strong-mixing limit the ground state converges to the uniform superposition where the quantization S_alg = n log 2 and the vanishing of both CMIs are exact; the additional experiments recommended in v1 (Haar baseline, kNN ablations, finer t_mix grid) are executed -- the Haar median of I_sum is 0.39, five to six orders of magnitude above the strong-mixing point, so the small-CMI regime is nontrivial; and the verification suite is fully self-contained (no Drive dependencies).
Research paperHistorical importARR-2026-1T29MY5N4J9ZHVQ5 · v1
Lluis Eriksson
We study approximate quantum Markov structure in a Z2 lattice gauge ground state using the conditional mutual information (CMI) I(A:C|B(w)) and the performance of Petz recovery across a family of tripartitions (A, B(w), C) parameterized by a buffer width w. We consider a 2x4 plaquette lattice with open boundaries and qubits on links, restricted to a gauge-invariant (Gauss-law) physical sector, at coupling g = 1.0. For each w we compute reduced density matrices, the entropies entering the CMI, and a Petz-recovered state sigma_ABC = (id_A (x) R^Petz_{B->BC})(rho_AB), reporting fidelity F(rho_ABC, sigma_ABC) via the recovery error E_rec(w) = -log F. The Overleaf project includes the plot, a formatted table, raw CSV outputs, and a hash-based manifest; the appendix typesets raw artifacts. We also report numerical cross-checks (dense vs. low-rank method agreement and trace stability) to support validity. v2 (no v1 number is changed): the star-operator definition is corrected -- with the Hamiltonian convention used here (single-link Z terms), the Gauss stars must be G_s = prod Z_l; v1's printed prod X_l anticommutes with the Z_l terms of H (the code used the consistent convention: an independent reconstruction from the manifest alone reproduces the CSV ground energy to 7x10^{-15} and every CMI of Table 1 to machine precision); two interpretive remarks are added -- the CMI rise at w = 2 tracks the shrinking traced-out complement (|D|: 8 -> 2 -> 0), so the profile is not a shielding-decay curve, and the w = 2 ~ w = 3 plateau is the buffer-saturation identity of the companion 2601.0050 (v2); the apparent Petz-over-CMI excess at w = 1 (E_rec > I) is shown to be the delta = 10^{-6} regularization floor -- regenerating with delta = 10^{-12} restores E_rec <= I at every w in the regenerated dataset; and a verification suite replicates the full pipeline from the manifest data alone.
Research paperHistorical importARR-2026-7X027P5YTZ9M88CK · v1
Lluis Eriksson
We study an information-theoretic notion of locality -- approximate quantum Markov behavior -- via the conditional mutual information (CMI) I(A:C|B(w)) in a semi-infinite geometry of the 1D transverse-field Ising model (TFIM). Using infinite matrix product states (iMPS), we compute I(A:C|B(w)) as a function of the collar width w separating two semi-infinite regions. In a representative gapped point (h = 1.5), we observe clean exponential decay and a rapid plateau of the local effective-length estimator, yielding an early-decay length xi_rec^(early) comparable to the iMPS transfer-matrix correlation length xi_corr. Near criticality (h = 1.005), the local estimator increases throughout the accessible range, indicating a pre-asymptotic regime; we therefore report a fixed-window effective length and a window-sensitivity range as a systematic uncertainty. All generated assets used here (two JSONL data streams, the figure, and the LaTeX table snippet) are included in the Overleaf project. v2 (no v1 number is changed): Appendix A is repaired (in v1 the data-source filenames were typeset in math mode and the near-critical entry was missing entirely); Table 1 is re-typeset (collided columns in v1); the Colab scripts of Appendix B are shipped as runnable files in the series repository rather than as listings; series positioning is added -- this paper is a numerical instantiation of the A-CMI hypothesis of the contract note ai.viXra:2601.0066 in a semi-infinite 1D geometry; and an independent verification suite (free fermions via Jordan-Wigner, no tensor networks) reproduces the gapped point of Table 1 exactly (xi_rec^(early) = 1.149 on the main window, window sensitivity [1.149, 1.158], both matching v1 digit for digit), verifies the operational identity I = 2 S_cut - S(B(w)) to 10^{-11}, and reproduces the rising near-critical xi_local(w); a TeNPy cross-check reproduces the free-fermion I(w) pointwise to 5x10^{-5} relative.
Research paperHistorical importARR-2026-53WA9C4RB39JRRXF · v1
Lluis Eriksson
We isolate the dynamic hinge in typed separation-to-rate-to-power pipelines within the Davies (weak-coupling, Markovian) setting in finite dimension. First, we formulate an upper-envelope statement (RIP-U): under an explicit factorized bath-correlation envelope with separation-dependent amplitude f(epsilon) and integrable time profile, Fourier-transformed Davies rates inherit an O(f(epsilon)) envelope. Under additional regularity assumptions preventing trivial degeneracies, this yields a worst-case bound kappa_up(epsilon) <= C f(epsilon) for the instantaneous relative loss rate of a coherence-like functional. Second, we isolate a structural obstruction to lower-envelope statements: we prove an exact identity for the omega = 0 contribution to the Davies Dirichlet form, E^(0)sigma(O) = (gamma(0)/2) ||[S(0),O]||^2{2,sigma}, and derive a witness mechanism showing how omega = 0 channels can enforce a non-vanishing dissipation contribution for suitable observable families. We emphasize directionality: RIP-U (upper) does not imply a positive lower envelope kappa_down(epsilon) without additional family-qualified input. All assumptions are explicit and accompanied by falsification routes. v2 (no v1 number is changed): two v1 assumptions are upgraded to proved statements in their canonical instances -- Delta-MONO holds unconditionally for the energy pinching (Davies covariance plus data processing), and a sufficient bridge with an explicit constant is proved; the cross-reference labels are repaired (in v1 every assumption and theorem was typeset as "Definition x.y"); Table 1 is re-typeset (overlapping text in v1); the omega = 0 identity is placed within the corrected Bohr-channel decomposition of the companion 2601.0023 (it is exactly the omega = 0 sector, and the plain-commutator form provably fails at omega != 0); and a verification suite reproduces every proved item numerically, including the identity at machine precision and an explicit family with kappa_down much smaller than kappa_up under the same envelope.
Research paperHistorical importARR-2026-3QBZE3EYPV8Y6RPX · v1
Lluis Eriksson
Local algebras in relativistic quantum field theory are typically Type III, so reduced density matrices and von Neumann entropies are not available without additional structure. We give a B-minimal, audit-friendly interface for recoverability in Type III AQFT: we fix a collar geometry and a split datum N (an intermediate Type I factor) and define (i) a split-regularized conditional mutual information (CMI) and (ii) a Bures-fidelity-based recovery error for normal states. We isolate, as explicit assumptions, the two hard bridges needed for an exponential recoverability statement in Type III: (a) existence of an omega_0-preserving conditional expectation onto N (a Takesaki-type condition) and (b) an FR-type inequality in the fixed split implementation. We prove a conditional theorem: if split-regularized CMI decays exponentially in the collar width and an FR-type inequality holds in that split, then recoverability error decays exponentially, with constants tracked explicitly. This paper makes no Clay mass-gap claim and does not invoke von Neumann entropy on Type III algebras without split regularization. v2 (no v1 number is changed): the cross-reference labels are repaired (in v1 every assumption and theorem was typeset as "Definition x.y") and Table 1 is re-typeset; a direction slip in the recovery candidate is corrected -- under CE the GNS-adjoint of the conditional expectation is provably the inclusion iota: N into M, so the operational candidate aligned with the recovery task is the predual of the conditional expectation itself; the finite-dimensional reduction is proved rather than remarked, including the equivalence of the two split-regularized CMI definitions and c_FR = 1 in the fixed conventions; a constructive instance of CE with product reference state is proved; series positioning is added; and a verification suite instantiates the entire contract end to end in the Type I regime (gapped transverse-field Ising collar: CMI decay with alpha ~ 1.06, Petz-type reconstruction satisfying E_rec <= I^(N) at every width in the generated dataset, and the omega_0-adjoint identity E^# = iota at machine precision).
Research paperHistorical importARR-2026-4G5E4HG7NM8YGB7S · v1
Lluis Eriksson
We present an audit-friendly logical contract for a multi-layer program connecting (i) static locality/Markovness, (ii) recoverability bounds, (iii) separation-dependent dissipation rates, and (iv) thermodynamic maintenance power. Each interface is typed with explicit quantifiers, tagged as [PROVED]/[IMPORTED]/[ASSUMED]/[CONJECTURED], and paired with falsification routes. We do not claim a proof of the Clay Yang-Mills mass gap; we separate a Clay (closed-Hamiltonian) track from an operational (open-system/maintenance) track. As a fully closed lane inside this paper, we prove that an exponential conditional mutual information (CMI) decay hypothesis implies exponential recoverability via an imported Fawzi-Renner inequality, with fidelity conventions fixed explicitly. v2 (no v1 number is changed): the cross-reference labels are repaired (in v1 every assumption, lemma, theorem, remark and corollary was typeset as "Definition x.y") and Tables 1 and 2 are re-typeset; the constant-alignment step of Appendix A is executed rather than prescribed -- in the locked conventions (squared fidelity, E_rec = -log F) the Fawzi-Renner import yields c_FR = 1 exactly; the deferred interfaces of Appendix B are now concrete series papers and are cited as such (the Type III interface is ai.viXra:2601.0065, the Davies/RIP-U dynamics note is ai.viXra:2601.0064, the benchmark infrastructure lives in the series repository); the BATO-LAW upgrade path of Appendix C records the partial progress of ai.viXra:2601.0031; and a verification suite instantiates everything instantiable: the closed recoverability lane end to end on a gapped transverse-field Ising collar (I ~ 0.20 e^{-1.06 w}, E_rec <= I at every width in the generated dataset, full 1 - F <= E_rec <= c_FR K e^{-alpha epsilon} chain), the exact-Markov example at machine precision, and the dephasing example with an explicit kappa_up/kappa_down spread of two orders of magnitude illustrating the directionality golden rule.
Research paperHistorical importARR-2026-6XR3EE53GH8E49RH · v1
Lluis Eriksson
We provide a finite-size benchmark testing whether a CMI-based recoverability proxy correlates with Wilson-loop confinement diagnostics in Z2 lattice gauge theory in 2+1 dimensions, computing ground states by sparse exact diagonalization on 2x2 and 2x3 open lattices (link qubits, Gauss-law penalty verified by ~ 1) and evaluating entropic quantities by pure-state Schmidt/SVD. We state a conditional bridge from a spatial area law to an operational "information horizon" via explicit hypotheses (H1)-(H4), with two recovery-length conventions (absolute, and normalized by the boundary prefactor Sigma_B(w) = |dB(w)| log 2). v2 (no v1 number is changed) adds a structural lemma that v1's own Table 1 was exhibiting unnoticed: for a pure global state, when the collar saturates (B = (A u C)^c) purity forces I(A:C|B) = I(A:C|empty) -- this is exactly why v1's Table 1 shows I(w=2) = I(w=0) = 0.4992999 to seven digits; the saturated row carries no buffer information, and the informative range of that benchmark is w in {0, 1}. v2 also anchors the non-monotonicity of CMI under collar enlargement as geometry-dependent (v1's wall geometry shows growth at w=0 to 1; a BFS-patch geometry on the same states decays monotonically -- there is no data-processing theorem in that direction); cross-links the CMI benchmark to the Petz-error twin on the same lattices (densified n = 8 sweep: Spearman rank-trend +1.00, permutation p = 1e-4, against both 1/sigma_eff and the inverse spectral gap -- so, as in the twin, confinement specificity is unresolved at these sizes); harmonizes the fidelity convention (v1 correctly uses root fidelity with I >= -2 log f, equivalent to the companions' squared-convention I >= -log F); removes an internal phase label leaked into v1's Section 1 title and a duplicated heading; and adds series positioning and a regenerable verification suite. The conditional proposition and its hypotheses are unchanged.
Research paperHistorical importARR-2026-29YZ0PQA699GV8T9 · v1
Lluis Eriksson
We provide reproducible finite-size benchmarks testing whether a Petz-type recoverability proxy correlates with Wilson-loop confinement diagnostics in Z2 lattice gauge theory in 2+1 dimensions: an exact-diagonalization benchmark on 2x2 and 2x3 plaquette lattices (Gauss penalty, ~ 1 verified), and TeNPy DMRG ladders 2xL, L in {4, 6, 8}, chi_max = 96, with a warm-start bond-dimension stability check (chi = 96 to 192 stable to all shown digits). In the tensor-network part, E_rec is reported as a function of contiguous buffer size |B| in MPS site ordering (a declared proxy), not the BFS collar of the ED part. v2 (no v1 number is changed): the broken Appendix A.1 of v1 -- whose published PDF literally prints "Missing file" where the ED reproduction script should appear -- is repaired by pointing to the series repository, where that script and a full verification suite for the ED benchmark already live with the companion paper; internal working titles leaked throughout v1's scripts and captions are removed; the MPS-ordering proxy is sharpened with new evidence -- on an exact Z2 ladder the geometric admissible buffer decays cleanly (5e-4 to 3e-8) while the contiguous-ordering proxy starts orders of magnitude higher and saturates, and a from-scratch DMRG replication (reduced chi, Lx = 4) reproduces both the trend direction of the money plots and v1's own buffer inversion E_rec(|B|=2) > E_rec(|B|=1), confirming it as a property of the contiguous proxy rather than a numerical accident; the confinement-vs-gap degeneracy established for the ED twin applies verbatim to the ladder money plots and is now stated; and series positioning is added. All conclusions remain finite-size benchmark statements.
Research paperHistorical importARR-2026-2KDX6T0J7Y9348TM · v1
Lluis Eriksson
SUPERSEDED BY AI.VIXRA:2601.0051V2 FOR THE CONSOLIDATED BENCHMARK. This replacement preserves public version 2 and makes the series relation explicit. The exact-diagonalization benchmark remains a valid finite-size component, but the successor is the authoritative combined source because it retains that benchmark and adds tensor-network ladder calculations and further scope controls. The reported Petz/Wilson rank alignment is not a confinement-specific or thermodynamic theorem: absolute recovery errors remain prescription dependent, and an equally strong spectral-gap covariate leaves confinement specificity unresolved at the tested sizes. The preserved version 2 follows the two-page notice unchanged.
Research paperHistorical importARR-2026-7B37HVCEAD9A1BWQ · v1
Lluis Eriksson
We propose an operational route from recoverability data to effective geometry. Given a tripartition A-B(w)-C and a collar width w, we consider a Petz-type recoverability error E_rec(w) defined via fidelity and extracted from a fixed collaring rule (A, C, w) -> B(w). We define distance-like functionals from the minimal buffer needed to suppress E_rec(w) below a threshold, and from exponential fit scales when such a regime exists; these are organized into a (generally non-metric) dissimilarity matrix on coarse regions, symmetrized when needed, and embedded via multidimensional scaling or diffusion maps. The paper emphasizes precise definitions (collaring rule, symmetrization, censoring below numerical floors) and falsifiable diagnostics (approximate triangle inequalities, robustness to thresholds and regularization). A minimal control experiment in the 1D transverse-field Ising model illustrates the pipeline and the growth of a recoverability length near criticality. v2 (definitions unchanged) adds: a regenerable suite replacing the "representative run" of v1 -- the control table is regenerated from scratch, its g = 0.5 row is flagged as unstable by the paper's own fit-window policy, and a three-point-fit caveat is stated; the first in-model test of the tracking conjecture -- from the same ground states, xi_rec/xi_corr in {0.98, 0.53, 0.52} across regimes, same order of magnitude throughout; a first numerical illustration of the embedding machinery (four coarse regions, MDS recovering the chain order exactly, triangle violations bounded by discretization), which also surfaces an operational lesson: tracing out the region between B(w) and C fakes separation and inverts monotonicity, so the separation condition of the collaring rule is essential, and profiles below the separating width are not admissible; the observation that the fixed-|A|,|C|/traced-environment design of the control is precisely the fixed-target protocol that resolves the |C|-shrinkage confound identified in the companion d_eff notes; and series positioning.
Research paperHistorical importARR-2026-4P264G2DC08DTTKP · v1
Lluis Eriksson
We propose a numerical protocol and falsifiable conjectures relating quantum-information recoverability measures to confinement diagnostics in lattice gauge theories. For a tripartition A-B-C and collar width w, we define a Petz-type recovery error E_rec(w) and extract a recoverability length from threshold and fit criteria. Since gauge constraints obstruct naive factorization, the protocol is formulated in an extended-Hilbert-space (EHS) prescription by default, with an algebraic (gauge-invariant) variant outlined together with its subtleties (centers, sectors). We conjecture that E_rec(w) decays exponentially in gapped phases and that its scale tracks confinement scales set by Wilson loops. v2 executes the testbed that v1 only specified: on a Z2 ladder of four plaquettes (14 links, Gauss law enforced exactly, = 1 to 1e-6), the suite computes E_rec(w) and Wilson decay on the same ground states across five couplings. Findings: the pipeline runs end to end; xi_rec is identifiable at three of five couplings and nearly coupling-independent (0.21-0.31, spread x1.4), while the Wilson decay length varies strongly (0.38-6.9, spread x8.6): no tracking at ladder level. Because height-one ladders degenerate area and perimeter, the Wilson scale there is not a pure confinement scale, so this first dataset is inconclusive-but-cautionary for the tracking conjecture rather than a falsification -- and it sharpens the requirement: a genuine 2D lattice is needed. v2 further flags the TFIM control row shared with the companion framework note as unstable under regeneration, and adds series positioning. No v1 definition is changed.
Research paperHistorical importARR-2026-5HG8P9BAQ78C5AB2 · v1
Lluis Eriksson
We formulate an operational notion of recoverability in algebraic quantum field theory for type III local von Neumann algebras. Fixing a faithful normal KMS reference state and assuming a state-preserving conditional expectation, we define the recovery channel and, working in a fixed split implementation for each separation r, we assume (i) exponential decay of split-implemented conditional mutual information and (ii) a CMI-to-recovery inequality. Under these explicit bridge assumptions we obtain a conditional exponential recoverability bound E_rec(r) <= g(C1 e^(-m r)). v2 corrects the duality underlying the construction: v1 defined the Petz-type channel as the "Accardi-Cecchini adjoint" via the pairing omega(Z R(X)) = omega(eps(Z) X) and "proved" finite-dimensional consistency with the standard Petz map; that identity is false in general (the printed proof contains an invalid cyclicity step; numerically the identity fails at order 1e-1 on random faithful states, holding only in commuting/product situations). The correct statement, proved and machine-verified here, is that the standard Petz map is the trace-predual of the generalized (Accardi-Cecchini) conditional expectation; accordingly, v2 defines the recovery channel in Schrodinger picture as precomposition with the conditional expectation. This also repairs a type/direction error in v1's recovered-state definition, whose corrected form (omega restricted to AB, composed with the normal extension of id_A tensor eps) reproduces the standard Petz reconstruction exactly in finite dimensions. We further relabel v1's finite-dimensional map as the generalized conditional expectation (its Takesaki module property fails generically -- verified), record that for a true state-preserving conditional expectation the recovery is the CE-pullback, and add series positioning: this note is the AQFT capstone announced by the companions, its split-implemented CMI is one of three compatible regularizations in the series, and the numerical program deferred by v1 has since been executed. The main theorem is unchanged: a conditional framework statement isolating the missing bridge assumptions.
Research paperHistorical importARR-2026-0MHWPSFFX696C8KW · v1
Lluis Eriksson
We study finite-size scaling of an operational recovery length extracted from Petz-map recovery in the transverse-field Ising chain. For a tripartition A-B-C with a collar B of width w, we define E_Petz(w) = -log F (squared Uhlmann fidelity), E_best(w) = min over w' <= w of E_Petz(w'), and the effective recovery distance d_eff(epsilon), with log-linear interpolation. Using exact diagonalization at hz = 0, beta = 12, |A| = 2 for N in {9, 10, 11, 12}, we analyze the peak height d_max(epsilon; N) = max over hx of d_eff in a censoring-free threshold regime, finding that the finite-window data are well summarized by descriptive power-law fits d_max(epsilon; N) ~ N^kappa(epsilon) with, e.g., kappa(3e-3) of about 0.44 and kappa(5e-3) of about 0.26, and a pseudocritical drift of the peak location with a threshold-dependent effective exponent nu_eff -- reported as operational quantities, not universal estimates. v2 adds (no v1 number is changed) two mandatory caveats, both quantified by a regenerable suite that reproduces v1's Table 1 exactly: (i) a |C|-shrinkage/growth confound -- the off-critical baseline d_eff(hx = 0.80; N) also grows with N at fixed thresholds, so the raw peak growth conflates critical physics with tripartition geometry; the cleaner object is the critical enhancement Delta(N) = peak - baseline, which still grows with N (e.g. 0.42 to 0.74 over N = 9, 10 at epsilon = 3e-3), so the critical signal survives baseline subtraction while kappa(epsilon) from raw peaks must be read as geometry-contaminated; (ii) functional-form indistinguishability -- over the accessible sub-octave in N, power-law, logarithmic and linear fits of the peak height have R^2 spreads below 0.01, and kappa itself shifts strongly with the fit window; the correct reading of kappa(epsilon) is a descriptive summary, not an established power law. Series positioning and a verification suite are included.
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-2026-1HR3DENYAZ9S8VCR · 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-2025-2AQXS44H6Z8GQAG2 · 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.
