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[25] ai.viXra.org:2601.0115 [pdf] replaced on 2026-07-31 23:16:43
Authors: Lluis Eriksson
Comments: 9 pages. v3: layout-only replacement. Table 1 on p.6 was clipped in v2; page 6 was uniformly scaled/repositioned. No text, data, figures, claims, or references changed.
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).
Category: Quantum Physics
[24] ai.viXra.org:2601.0111 [pdf] replaced on 2026-07-05 21:44:34
Authors: Lluis Eriksson
Comments: 6 Pages. v2 (no v1 number changed): Gauss stars corrected to prod Z (printed prod X anticommuted with H); Table 1 replicated from the manifest alone; complement-shrinkage and saturation remarks added; w=1 Petz-over-CMI excess traced to the delta floor.
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.
Category: Quantum Physics
[23] ai.viXra.org:2601.0099 [pdf] replaced on 2026-07-05 21:05:26
Authors: Lluis Eriksson
Comments: 6 Pages. v2 (no v1 number changed): Appendix A repaired (filenames garbled, near-critical entry missing); Table 1 re-typeset; Colab scripts shipped as runnable files; independent free-fermion suite reproduces the gapped point digit for digit.
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.
Category: Quantum Physics
[22] ai.viXra.org:2601.0097 [pdf] submitted on 2026-01-24 01:13:50
Authors: Vel Tomanovic
Comments: 11 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references in a standard manner such as APA style)
We propose a phenomenological, testable objective-collapse framework—the Beable Theory—for electron spin measurements. An electron excitation carries a real internal orientation (a 'beable' field on the spinor bundle S³ → S²) that generates coherent spinor precession, while stochastic collapse localizes a physically instantiated pointer variable encoding measurement records or environmental imprinting. Spin-state definiteness emerges when the spin entangles with distinct pointer configurations, enforcing single-run outcome selection via pointer localization, with ensemble dynamics reducing to pure dephasing in the measurement basis. We derive the reduced spin master equation, identifying the measurement-induced dephasing rate κ_meas with pointer-branch separation and parameterizing an always-on background channel κ_bg. Using published trapped-electron spectroscopy data (Fan et al., Phys. Rev. Lett. 130, 071801 (2023)), we translate the anomaly linewidth budget into an upper bound κ_bg ≲ 5×10^{-2} s^{-1} (order-of-magnitude), with a conservative bound κ_bg ≲ 2×10^{-1} s^{-1} from the full linewidth. The functional scaling in the strong-measurement (quantum Zeno) regime of circuit QED (Slichter et al., New J. Phys. 18, 053031 (2016)) is consistent with the model's dephasing structure. We provide a microscopic derivation of pointer-record noise statistics using continuous-measurement theory, establishing the Born rule via the martingale property of branch weights under diffusive unraveling. The beable modulates the effective measurement axis â_eff(t) in a gauge-invariant way depending only on the Bloch vector ru20d7(t), yielding testable signatures in trajectory-level pointer-record observables (e.g., variance, dwell times). Compatibility with Diósi—Penrose-type gravitational collapse is discussed, identifying κ_bg with a gravity-related rate κ_DP ~ ΔE_G/ħ acting on pointer branches, suppressing macroscopic superpositions while preserving isolated spin coherence. A unified stochastic model and simulation program are outlined for bounding the basis-modulation parameter ε using public data.
Category: Quantum Physics
[21] ai.viXra.org:2601.0080 [pdf] submitted on 2026-01-20 17:15:02
Authors: Kelly Sonderegger
Comments: 36 Pages. Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0)
Quantum Field Theory (QFT) successfully describes the evolution of probability amplitudes but remains formally agnostic about the physical process by which definite events, causal ordering, and classical experience emerge. We propose the Anchored Causality Interpretation (ACI), which identifies measurement as progressive thermalization through quantum Brownian motion in the omnipresent Higgs field bath. ACI elevates Einstein's result that massless particles experience τ=0 to an ontological principle: quantum fields exist atemporally as pure waves until Higgs-mediated interactions progressively anchor specific observables into temporal existence. The anchoring mechanism applies well-established quantum Brownian motion theory (Caldeira-Leggett, Feynman-Vernon, Hu-Paz-Zhang) to the unique Higgs bath, making anchoring calculable rather than conceptual. Energy conservation is automatic via the fluctuation-dissipation theorem. This framework provides a unified explanation for a diverse body of existing experimental results—weak measurements, variable which-path detection, quantum erasers with partial erasure, and detector-mass-dependent decoherence—all of which demonstrate continuous partial quantum-classical transitions scaling with measurement coupling strength. While other interpretations treat these as distinct phenomena requiring separate explanations, ACI recognizes them as manifestations of a single physical process: incomplete thermalization with the Higgs bath. We further derive distinguishing predictions including a 17.4% mass-dependent difference in decoherence times between carbon-12 and carbon-13 in matter-wave interferometry. ACI resolves the quantum measurement problem without modifying QFT dynamics or introducing hidden variables, treating wave-particle duality as an ontological phase transition driven by Higgs-mediated quantum Brownian motion.
Category: Quantum Physics
[20] ai.viXra.org:2601.0066 [pdf] replaced on 2026-07-05 20:13:04
Authors: Lluis Eriksson
Comments: 7 Pages. v2 (no v1 number changed): cross-references and Tables 1-2 repaired; c_FR = 1 alignment executed in the locked conventions; deferred interfaces now cite 2601.0064/0065 and the series suites; verification suite instantiates the closed recoverability lane.
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.
Category: Quantum Physics
[19] ai.viXra.org:2601.0065 [pdf] replaced on 2026-07-05 19:47:43
Authors: Lluis Eriksson
Comments: 8 Pages. v2 (no v1 number changed): cross-references and Table 1 repaired; recovery-candidate direction corrected (E^# is the inclusion; recovery is the CE predual); Type I reduction and constructive CE instance proved; verification suite added.
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).
Category: Quantum Physics
[18] ai.viXra.org:2601.0064 [pdf] replaced on 2026-07-05 19:25:29
Authors: Lluis Eriksson
Comments: 7 Pages. v2 (no v1 number changed): cross-references and Table 1 repaired; Delta-MONO proved for the energy pinching; sufficient bridge with explicit constant proved; omega=0 identity placed in the 2601.0023 decomposition; verification suite added.
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.
Category: Quantum Physics
[17] ai.viXra.org:2601.0051 [pdf] replaced on 2026-07-05 18:33:10
Authors: Lluis Eriksson
Comments: 4 Pages. v2 (no v1 number changed): broken Appendix A.1 repaired; working-title leaks removed; MPS-contiguous proxy quantified (DMRG replication reproduces v1's buffer inversion).
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,
Category: Quantum Physics
[16] ai.viXra.org:2601.0050 [pdf] replaced on 2026-07-05 18:08:54
Authors: Lluis Eriksson
Comments: 4 Pages. v2 (no v1 number changed): saturation lemma explains Table 1's exact I(w=2)=I(w=0) coincidence (informative range w in {0,1}); collar monotonicity shown geometry-dependent; CMI benchmark cross-linked to the Petz twin.
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
Category: Quantum Physics
[15] ai.viXra.org:2601.0049 [pdf] submitted on 2026-01-13 23:34:37
Authors: Natasha Zink
Comments: 8 Pages. (Note by ai.viXra.org Admin: For the last time, author name is required in the article after article title, the abstract should be labled as such, and please cite listed scientific references)
The emergence of Heptagonal Unitary Field Theory (HUFT), as articulated in the foundational documents provided and the research profile of Natasha Zink, represents a radical departure from traditional particle-based ontologies in theoretical physics. By reconceptualizing the universe as an emergent submanifold M^{4} embedded within a seven-dimensional toroidal manifold T^{7}, HUFT attempts to provide a unified geometric framework that accounts for gravity, quantum information preservation, and non-local transport. This report provides an exhaustive verification of the scientific bases of HUFT and the Zero-Time Transport (ZTT) protocol, tracing their mathematical lineage through G_{2} holonomy, spectral signal processing, and high-dimensional lattice theory.
Category: Quantum Physics
[14] ai.viXra.org:2601.0047 [pdf] replaced on 2026-08-01 08:40:56
Authors: Lluis Eriksson
Comments: 7 pages. v3 adds a two-page supersession and scope note, then preserves the five-page v2. Consolidated ED-plus-ladder source: ai.viXra:2601.0051v2.
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.
Category: Quantum Physics
[13] ai.viXra.org:2601.0046 [pdf] replaced on 2026-07-05 17:09:22
Authors: Lluis Eriksson
Comments: 5 Pages. v2 corrects the operational core: v1's Petz-dual pairing refuted (invalid cyclicity step); correct duality is the trace-predual identity; recovered state redefined as CE-pullback (type error fixed), reproducing standard Petz in finite dimensions.
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.
Category: Quantum Physics
[12] ai.viXra.org:2601.0044 [pdf] replaced on 2026-07-05 16:44:35
Authors: Lluis Eriksson
Comments: 4 Pages. v2 executes the Z2 testbed v1 only specified: exact Gauss sector, xi_rec vs Wilson decay across five couplings -- no tracking at ladder level (inconclusive: area/perimeter degeneracy declared). Shared TFIM control row flagged; verification suite included.
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,
Category: Quantum Physics
[11] ai.viXra.org:2601.0043 [pdf] replaced on 2026-07-05 16:21:06
Authors: Lluis Eriksson
Comments: 5 Pages. v2 (definitions unchanged): control table regenerated (unstable g=0.5 row flagged), first in-model test of the tracking conjecture, first end-to-end embedding demo, separation-condition lesson, regularized-Petz caveat, verification suite included.
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.
Category: Quantum Physics
[10] ai.viXra.org:2601.0042 [pdf] replaced on 2026-07-05 15:57:50
Authors: Lluis Eriksson
Comments: 5 Pages. v2 (no v1 number changed): corrupted reproducibility paragraph replaced by a regenerable verification suite (reproduces the beta-sweep to two decimals at N=9), mild |C| caveat, series positioning added.
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.
Category: Quantum Physics
[9] ai.viXra.org:2601.0040 [pdf] replaced on 2026-07-05 15:18:12
Authors: Lluis Eriksson
Comments: 4 Pages. v2 (no v1 number changed; suite reproduces Table 1 exactly): |C|/baseline confound quantified (critical enhancement survives), functional-form/window dependence of kappa made explicit, regenerable verification suite included.
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.
Category: Quantum Physics
[8] ai.viXra.org:2601.0038 [pdf] replaced on 2026-07-05 14:43:48
Authors: Lluis Eriksson
Comments: 4 Pages. v2 (no v1 result changed): |C|-shrinkage caveat on the absolute length scale, window-relativity remark, CMI companion diagnostic showing the same signature, regenerable verification suite included.
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.
Category: Quantum Physics
[7] ai.viXra.org:2601.0035 [pdf] replaced on 2026-07-05 13:44:55
Authors: Lluis Eriksson
Comments: 5 Pages. v2: FR factor corrected (-log F <= I); v1's Petz overshoot/gap withdrawn as half-scale artifact (dataset-wide r_max 0.62); regenerable verification suite included.
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.
Category: Quantum Physics
[6] ai.viXra.org:2601.0034 [pdf] replaced on 2026-07-05 13:15:01
Authors: Lluis Eriksson
Comments: 5 Pages. Type III capstone of the clustering-recovery program (2512.0060/0101, 2601.0007/0020/0031). v2: FR-type assumption restated in importable squared-fidelity form (v1 half-form refuted as anchor, 40/40), compatibility with 2601.0020, N-dependence demo.
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.
Category: Quantum Physics
[5] ai.viXra.org:2601.0031 [pdf] replaced on 2026-07-05 12:40:49
Authors: Lluis Eriksson
Comments: 6 Pages. Integrative closure of the 2601 block. v2: work-cost sign corrected (v1 one-step lemma false as printed; downstream theorem survives), Petz relabeled as conditional reattachment, GNS/KMS bridge, series positioning, verification suite included.
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.
Category: Quantum Physics
[4] ai.viXra.org:2601.0026 [pdf] submitted on 2026-01-09 16:10:41
Authors: Alexander Mats
Comments: 6 Pages. Developed with AI assistance for calculations, formatting, and figures. All results independently verified. Code available upon request.
This work presents a topological framework for quark confinement in which gluons emerge as induced flow fields between vortex rings rather than as fundamental particles. Quarks are modeled as quantized vortex rings with specific (p,q) torus knot winding numbers, and hadrons arise from topologically linked configurations: Hopf fibrations for mesons (linking number Lk=1) and Borromean rings for baryons (triple linking L3=1). The model predicts hadron masses with sub-1% accuracy using zero adjustable parameters, with confinement arising purely from topological linking energy. Key results include: proton mass predicted to 938.27 MeV (measured 938.27 MeV, error <0.001%); pion mass 139.6 MeV (measured 139.6 MeV, error <0.01%); confinement string tension σ≈0.18 GeV2 consistent with lattice QCD. The framework makes four testable predictions: (1) glueballs do not exist as distinct particles; (2) jet fragmentation exhibits vortex-cascade signatures distinct from gluon splitting; (3) confinement potential is purely linear V(r)=σr with no Coulombic term; (4) pentaquark lifetimes determined by topological barriers. This work was developed by an independent researcher Alexander Mats (registered nurse by profession) with AI assistance (Claude by Anthropic, ChatGPT by OpenAI) for mathematical calculations, LaTeX formatting, and figure generation. All results have been independently verified against experimental data from the Particle Data Group (2024).
Category: Quantum Physics
[3] ai.viXra.org:2601.0022 [pdf] replaced on 2026-07-05 10:46:14
Authors: Lluis Eriksson
Comments: 7 Pages. v2: power analysis (no-floor null design-limited), declared regenerable witness ED benchmark, S=X null case, series cross-refs. TEBD figures unchanged (data not shipped); witness reproducible from scratch.
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.
Category: Quantum Physics
[2] ai.viXra.org:2601.0020 [pdf] replaced on 2026-07-05 09:50:00
Authors: Lluis Eriksson
Comments: 10 Pages. Bridge note CMI→RIP of the series. v2: Fawzi-Renner factor corrected (-log F, squared fidelity); v1 diagonal bulk-collar comparison refuted and replaced by proved B^(+2r) version; exact-enumeration verification suite included.
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.
Category: Quantum Physics
[1] ai.viXra.org:2601.0007 [pdf] replaced on 2026-07-05 08:56:03
Authors: Lluis Eriksson
Comments: 16 Pages. Finite-mode Gaussian core of the clustering—recovery program (companions 2512.0060, 2512.0101). v2: collar-suppressed recovery corollary; Petz-identification corrected to conditional reattachment (aligned with 2512.0060 v2) with explicit admissibility hyp
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.
Category: Quantum Physics