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Configuration Space Temporality: A Reformulation of Time as State Identity in Configuration Space

Frederic David Blum

Published Feb 22, 2026• 0 citations
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Abstract

Configuration Space Temporality — Complete Research Archive v33Corrections, a Resolution Law, and the foundations of CST among timeless formulations Frédéric David Blum · Catalyst AI Research · Haifa, Israel · DOI: 10.5281/zenodo.18859602 · October 2026Computations and drafting assisted by Claude (Anthropic). What is CST?Configuration Space Temporality (CST) is a framework in which time is not a background parameter: it emerges as the accumulated cost of energy-driven transitions between configurations of a physical system. Three axioms (configuration uniqueness, energy-driven transition, bounded transition rate) define a tensor of transition G on configuration space (the Bures metric on quantum configurations, with the Umegaki relative entropy as potential), a transport distance d_CST satisfying the Carlen–Maas axioms of a quantum Wasserstein distance, the Witten Laplacian H_W whose thermodynamic limit is a Lindblad generator, and the cascade number κ = ΔE·Δτ/(ħ ln 2). STATUS — October 2026Every claim in this archive that the Riemann Hypothesis has been proved, reduced to a single assumption, or approached through the Bost–Connes Hamiltonian, the Fisher–Rao action functional, the rigidity matrix or the confinement constant α is WITHDRAWN. The physical framework is kept, placed on its exact foundations, and given one law. What's new in v33 Corrections. A re-audit with every number recomputed found four errors. (i) The Fisher pole identity |I(s)|·|s−ρ|² = 1 holds at every simple zero of every analytic function, on or off the critical line; it is not a quantization condition and carries no information about RH. (ii) The rigidity matrix R has an exact zero eigenvalue (its rows sum to zero), so α = μ₁/μ₀ is undefined; the collinear configuration is a transverse maximum of the log-gas energy, not a minimum; and R is built from ordinates already on the line, so no property of R can be equivalent to RH. (iii) Exponential dominance fails: μ₁/μ₀ grows only from 10^6.4 (N = 45) to 10^7.8 (N = 200), α(N) → 0, and GUE, Poisson and evenly spaced control points give the same values as the zeros (the tiny eigenvalues come from the cosine basis, not from arithmetic). (iv) The Bost–Connes Hamiltonian has spectrum {log n}; Assumption A, Assumption B and the "zeros as resolvent poles" claim are withdrawn, and the CMP v25–v27 "complete proof chain" is withdrawn in full. Of 17 RH-related results: 3 hold as stated, 3 hold but are trivial or known, 1 is falsified numerically, 1 stays open (Li positivity, equivalent to RH), 9 are withdrawn. The full audit, with the status of every claim and the superseded files listed, is the document "CST/FDBC Archive v33 — Corrections and a Non-Circular Weil-Form Test". Foundations. CST is placed explicitly on the three established timeless formulations of physics: Jacobi geometry and Barbour's relational dynamics (G is a Jacobi metric, CST time is the Jacobi arc length, i.e. the Maupertuis action, and κ_cl = S₀/(ħ ln 2)); Wheeler–DeWitt and the Page–Wootters mechanism (time as clock correlation); and the thermal time of Connes–Rovelli (time as the modular flow of the state — the correct use of the KMS machinery in CST). These formulations are empirically equivalent to their timed counterparts; a new law must therefore live where state-based and timed descriptions differ. The Resolution Law (new). For a quantum trajectory ψ(t) = e^{−iHt/ħ}ψ of duration Δτ whose energy distribution is flat on a band of width Ω_E, the number of modes of the trajectory distinguishable at level ε isd_ε = Ω_E Δτ/h + (1/π²) ln(Ω_E Δτ/4ħ) · ln((1−ε)/ε) + o(ln c),and no mode beyond twice the Slepian parameter c = Ω_EΔτ/4ħ is distinguishable above e^{−1.5c}. The leading term is the Landau count (the action budget in units of h), of the same kind as the Margolus–Levitin and Mandelstam–Tamm speed limits and identifying the cascade number (κ = (2π/ln 2) × Landau count); the second term is a universal logarithmic "soft horizon" (Landau–Widom plunge); the cutoff is a rigorous non-asymptotic bound. The law is proved as a theorem of time–band limiting — the Gram operator of a quantum trajectory is Slepian's time–band limiting operator with the energy distribution as symbol — with two-sided bounds for bounded energy densities, verified numerically (prolate eigenvalue counts at c = 10, 30, 100), and given a falsification protocol on a many-level system (cavity mode or quantum simulator) through the survival amplitude. It replaces the earlier prediction P2 of a sharp reversibility threshold at κ = 1, and it is the first prediction of CST stated with a theorem behind it. A tested negative. The conjecture that the cascade number is tied to Barbour–Koslowski–Mercati shape complexity by a universal power law was tested on E = 0 three-body solutions: the Janus structure is reproduced, but the exponent is not universal (0.8–1.9); the CST clock is the ephemeris time of the bound pair. Recorded so that it is not tried again. Companion workScale-Resolved Weil Positivity (preprint, DOI 10.5281/zenodo.23229271; code: github.com/davidangularme/scale-resolved-weil-positivity): the positive mathematics that came out of the audit — a prime-side study of the truncated Weil form, with certified positivity on the window [1/2, 2] (margin enclosed between 1.38×10⁻¹³ and 7.6×10⁻¹³; an independent certification, at L = log 2, of a theorem of X. Zhu, arXiv:2608.24827, valid for L ≤ 0.8), certified rigidity of the prime data, the detection and reconstruction laws, and the structure of the minimiser as Riemann's Φ times a window. Nothing there bears on RH beyond the finite scales treated. Validated and untestedValidated: the H_W spectral diagnostic on 768 qubit pairs of six IBM Eagle r3 processors, r = 0.365 after projecting out calibration parameters (a diagnostic correlation; it does not test the Resolution Law). Untested: P6 (no dark-matter particle), P9 (gravity as collective mode), P16, and the Resolution Law itself. Withdrawn: P2 (cascade criticality at κ = 1), IG-P1 to IG-P5. Files added in v33CST_v33_Corrections_and_a_Resolution_Law.pdf (the single document of this version) · cst-fdbc-archive-v33-corrections.pdf (the full audit) · v33_cst_code.zip (prolate.py, lw_check.py, janus.py and results). Earlier files remain for the record; those superseded are listed in the audit document: CMP_Paper_FDBC_v25–v27, FDBC_v2_CMP_Submission, FDBC_v2_Complete_Proof_Chain, FDBC_v2_Proof_Chain_CORRECTED, FDBC_v2_Assumption_B_PROVED (both), FDBC_v2_Spectral_Gap_PROVED, FDBC_v2_No_Gap_Final, Information_Geometric_Confinement_Riemann_Zeros_Blum_2026, blum-claude-weil-minimiser-2026 (its table stands, its conclusions do not). The submission CIMP-D-26-00460 is being withdrawn. Previous versionsv33 (current): corrections and withdrawals; foundations; the Resolution Law; tested negative on complexity. v32: information-geometric confinement (withdrawn in v33). v31: exponential isolation of the Weil minimiser (table stands, conclusions withdrawn). v30: Fourier-side ΨDO identification. v29.1–v25: see the archive. CitationBlum, F. D. (2026). Configuration Space Temporality: Complete Research Archive v33 — Corrections, a Resolution Law, and the foundations of CST among timeless formulations. Zenodo. https://doi.org/10.5281/zenodo.18859602 Keywordsemergent time · configuration space temporality · Jacobi metric · relational dynamics · Page–Wootters · thermal time · quantum optimal transport · Bures metric · Witten Laplacian · cascade number · quantum speed limit · Margolus–Levitin · time–band limiting · prolate spheroidal functions · Landau–Widom · resolution law · transmon qubits · Weil positivity · corrections · retraction

DOI
10.5281/zenodo.18733669

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•May 1, 2026•0 citations

Integral quantization in the quantum configuration space

ANDRZEJ GÓŹDŹ, Marek Góźdź, Aleksandra Pȩdrak

Abstract Quantum spacetime in which time is considered on the same footing as other observables is a part of the quantum configuration space. In such space a natural geometry is generated by the transition amplitudes among quantum configuration space points. It is shown, that a good candidate for quantization of extended (plus time) classical configuration spaces is integral quantization. This quantization is compatible with the notion of quantum time. The most basic features of this quantization are presented.

Journal of Physics Conference Series•Dec 1, 2024•1 citation
Configuration Space Temporality — Complete Research Archive v33Corrections, a Resolution Law, and the foundations of CST among timeless formulations Frédéric David Blum · Catalyst AI Research · Haifa, Israel · DOI: 10.5281/zenodo.18859602 · October 2026Computations and drafting assisted by Claude (Anthropic). What is CST?Configuration Space Temporality (CST) is a framework in which time is not a background parameter: it emerges as the accumulated cost of energy-driven transitions between configurations of a physical system. Three axioms (configuration uniqueness, energy-driven transition, bounded transition rate) define a tensor of transition G on configuration space (the Bures metric on quantum configurations, with the Umegaki relative entropy as potential), a transport distance d_CST satisfying the Carlen–Maas axioms of a quantum Wasserstein distance, the Witten Laplacian H_W whose thermodynamic limit is a Lindblad generator, and the cascade number κ = ΔE·Δτ/(ħ ln 2). STATUS — October 2026Every claim in this archive that the Riemann Hypothesis has been proved, reduced to a single assumption, or approached through the Bost–Connes Hamiltonian, the Fisher–Rao action functional, the rigidity matrix or the confinement constant α is WITHDRAWN. The physical framework is kept, placed on its exact foundations, and given one law. What's new in v33 Corrections. A re-audit with every number recomputed found four errors. (i) The Fisher pole identity |I(s)|·|s−ρ|² = 1 holds at every simple zero of every analytic function, on or off the critical line; it is not a quantization condition and carries no information about RH. (ii) The rigidity matrix R has an exact zero eigenvalue (its rows sum to zero), so α = μ₁/μ₀ is undefined; the collinear configuration is a transverse maximum of the log-gas energy, not a minimum; and R is built from ordinates already on the line, so no property of R can be equivalent to RH. (iii) Exponential dominance fails: μ₁/μ₀ grows only from 10^6.4 (N = 45) to 10^7.8 (N = 200), α(N) → 0, and GUE, Poisson and evenly spaced control points give the same values as the zeros (the tiny eigenvalues come from the cosine basis, not from arithmetic). (iv) The Bost–Connes Hamiltonian has spectrum {log n}; Assumption A, Assumption B and the "zeros as resolvent poles" claim are withdrawn, and the CMP v25–v27 "complete proof chain" is withdrawn in full. Of 17 RH-related results: 3 hold as stated, 3 hold but are trivial or known, 1 is falsified numerically, 1 stays open (Li positivity, equivalent to RH), 9 are withdrawn. The full audit, with the status of every claim and the superseded files listed, is the document "CST/FDBC Archive v33 — Corrections and a Non-Circular Weil-Form Test". Foundations. CST is placed explicitly on the three established timeless formulations of physics: Jacobi geometry and Barbour's relational dynamics (G is a Jacobi metric, CST time is the Jacobi arc length, i.e. the Maupertuis action, and κ_cl = S₀/(ħ ln 2)); Wheeler–DeWitt and the Page–Wootters mechanism (time as clock correlation); and the thermal time of Connes–Rovelli (time as the modular flow of the state — the correct use of the KMS machinery in CST). These formulations are empirically equivalent to their timed counterparts; a new law must therefore live where state-based and timed descriptions differ. The Resolution Law (new). For a quantum trajectory ψ(t) = e^{−iHt/ħ}ψ of duration Δτ whose energy distribution is flat on a band of width Ω_E, the number of modes of the trajectory distinguishable at level ε isd_ε = Ω_E Δτ/h + (1/π²) ln(Ω_E Δτ/4ħ) · ln((1−ε)/ε) + o(ln c),and no mode beyond twice the Slepian parameter c = Ω_EΔτ/4ħ is distinguishable above e^{−1.5c}. The leading term is the Landau count (the action budget in units of h), of the same kind as the Margolus–Levitin and Mandelstam–Tamm speed limits and identifying the cascade number (κ = (2π/ln 2) × Landau count); the second term is a universal logarithmic "soft horizon" (Landau–Widom plunge); the cutoff is a rigorous non-asymptotic bound. The law is proved as a theorem of time–band limiting — the Gram operator of a quantum trajectory is Slepian's time–band limiting operator with the energy distribution as symbol — with two-sided bounds for bounded energy densities, verified numerically (prolate eigenvalue counts at c = 10, 30, 100), and given a falsification protocol on a many-level system (cavity mode or quantum simulator) through the survival amplitude. It replaces the earlier prediction P2 of a sharp reversibility threshold at κ = 1, and it is the first prediction of CST stated with a theorem behind it. A tested negative. The conjecture that the cascade number is tied to Barbour–Koslowski–Mercati shape complexity by a universal power law was tested on E = 0 three-body solutions: the Janus structure is reproduced, but the exponent is not universal (0.8–1.9); the CST clock is the ephemeris time of the bound pair. Recorded so that it is not tried again. Companion workScale-Resolved Weil Positivity (preprint, DOI 10.5281/zenodo.23229271; code: github.com/davidangularme/scale-resolved-weil-positivity): the positive mathematics that came out of the audit — a prime-side study of the truncated Weil form, with certified positivity on the window [1/2, 2] (margin enclosed between 1.38×10⁻¹³ and 7.6×10⁻¹³; an independent certification, at L = log 2, of a theorem of X. Zhu, arXiv:2608.24827, valid for L ≤ 0.8), certified rigidity of the prime data, the detection and reconstruction laws, and the structure of the minimiser as Riemann's Φ times a window. Nothing there bears on RH beyond the finite scales treated. Validated and untestedValidated: the H_W spectral diagnostic on 768 qubit pairs of six IBM Eagle r3 processors, r = 0.365 after projecting out calibration parameters (a diagnostic correlation; it does not test the Resolution Law). Untested: P6 (no dark-matter particle), P9 (gravity as collective mode), P16, and the Resolution Law itself. Withdrawn: P2 (cascade criticality at κ = 1), IG-P1 to IG-P5. Files added in v33CST_v33_Corrections_and_a_Resolution_Law.pdf (the single document of this version) · cst-fdbc-archive-v33-corrections.pdf (the full audit) · v33_cst_code.zip (prolate.py, lw_check.py, janus.py and results). Earlier files remain for the record; those superseded are listed in the audit document: CMP_Paper_FDBC_v25–v27, FDBC_v2_CMP_Submission, FDBC_v2_Complete_Proof_Chain, FDBC_v2_Proof_Chain_CORRECTED, FDBC_v2_Assumption_B_PROVED (both), FDBC_v2_Spectral_Gap_PROVED, FDBC_v2_No_Gap_Final, Information_Geometric_Confinement_Riemann_Zeros_Blum_2026, blum-claude-weil-minimiser-2026 (its table stands, its conclusions do not). The submission CIMP-D-26-00460 is being withdrawn. Previous versionsv33 (current): corrections and withdrawals; foundations; the Resolution Law; tested negative on complexity. v32: information-geometric confinement (withdrawn in v33). v31: exponential isolation of the Weil minimiser (table stands, conclusions withdrawn). v30: Fourier-side ΨDO identification. v29.1–v25: see the archive. CitationBlum, F. D. (2026). Configuration Space Temporality: Complete Research Archive v33 — Corrections, a Resolution Law, and the foundations of CST among timeless formulations. Zenodo. https://doi.org/10.5281/zenodo.18859602 Keywordsemergent time · configuration space temporality · Jacobi metric · relational dynamics · Page–Wootters · thermal time · quantum optimal transport · Bures metric · Witten Laplacian · cascade number · quantum speed limit · Margolus–Levitin · time–band limiting · prolate spheroidal functions · Landau–Widom · resolution law · transmon qubits · Weil positivity · corrections · retraction
The author proposes two postulates for the foundation of time and spacetime in open quantum systems. Postulate P1 (Time): the proper time of an open quantum system is generated by the integral of its boundary structural-persistence functional Φ on the variationally selected autonomous boundary. Postulate P2 (Spacetime): spacetime is the synchronisation pattern of a network of open-system boundary Φ-clocks coupled through shared baths. From P1 the author derives (i) a thermodynamic clock τ_∂ = ∫ Φ ds, whose sign and magnitude classify structure-building, structure-maintaining, and structure-dissolving regimes; and (ii) two channels of local arrow-inversion windows (monitored feedback Φ_fb > 1; non-Markovian backflow Φ_NM > 1), bounded in duration by the local entropy budget and consistent with the global second law (Sagawa-Ueda for feedback; memory-induced negative σ_irr for backflow). From P2 the author derives (iii) a synchronisation functional Σ_ij between two Φ-clocks coupled through a shared bath, with the Connes-Rovelli thermal time hypothesis recovered in a triple limit (joint KMS state + Σ → 1 + Spohn-modular reduction); and (iv) an induced graph distance d_ij = -log|<X_i X_j>|/N that satisfies the triangle inequality on a metric-compatibility regime operationally characterised by joint CP-divisibility and absence of BLP non-Markovianity witnesses on the relevant triangles. The two witness conditions are jointly necessary for the triangle inequality on this regime; their sufficiency is conjectured under qualifications stated in the manuscript and listed as an open problem. The author provides a complete epistemic-status audit of every quantitative claim and an explicit comparison with the principal existing programmes on time and emergent spacetime: Connes-Rovelli thermal time hypothesis, Page-Wootters conditional time, Van Raamsdonk / AdS-CFT entanglement-based emergence, causal set theory (Sorkin), Verlinde / Padmanabhan thermal gravity, and Wolfram hypergraph rewriting. The audit of falsifiable predictions, the experimental discriminators (3-qubit feedforward, directional asymmetry, triangle inequality), and the worked-case reanalysis of Micadei et al. (2019) are the subject of the companion Preprint II.
Configuration Realism (CR) is a physical ontology consisting of a finite, timeless configuration space. Each configuration is a complete arrangement of fundamental degrees of freedom; none evolves; phase attaches additively to degrees of freedom and is defined relationally, relative to a stage of an observer chain. Information exists only as finite, lossy physical records. Each record defines a compatibility class, the configurations it cannot distinguish, and probability is defined as counting over these classes. The framework's derived core is proved and computed in three companion papers under named structural assumptions. The population of an outcome class equals N|α|²: the Born rule as a theorem, with the frequency reading consuming exactly one typicality principle. The CHSH quantity assembled from integer counts reaches 2√2 to O(1/N), the ontology giving up counterfactual definiteness in the plain Bell scenario—and the absoluteness of outcomes where Wigner's-friend extensions demand it—rather than locality or free settings. And equipped with a local move set, counted populations propagate as wavepackets: the effective mass is the inverse hopping rate of elementary refinement, the potential is a cell-dependent phase cost, and the counted dynamics reproduces Schrödinger phenomenology with the number of configurations conserved exactly at every stage. Around this core, closure laws order records by refinement. Observers are chains of record-bearing stages; change is difference read along a refinement chain; time is the emergent coordinate that labels it; and closure distance, accumulating in discrete quanta, measures the restructuring refinement requires. Direct consequences follow for entropy and the arrow of time, for the classical limit, and for objectivity as redundancy. The remainder is a labeled research program: causal structure, Lorentzian geometry, geodesic dynamics, and horizon thermodynamics as conjectured continuum limits of closure geometry, with the constructions that would establish them stated as open problems. A dedicated section collects the framework's distinctive predictions—the O(1/N) family separating a counting world from continuum quantum mechanics—each with its mechanism and in-principle test. Every claim in the paper is tabulated with its status: postulate, theorem, verified, argument, conjecture, or open.
We provide a mathematically rigorous derivation of the quantum mechanicalformalism — Hilbert space, Schrödinger equation, and Born rule — from thecondensate dynamics of Temporal Emergence Theory (TET), assuming Postulate P4of TET as the sole non-derived input at the level of stochastic dynamics. Starting from the Langevin equation for the condensate fluctuation δφ on thetemporal manifold H_τ = H^{3,1}, we apply stochastic differential geometry onRiemannian manifolds to extend Nelson's stochastic equivalence theorem to thecurved emergent spatial sections H^3 = SO(3,1)/SO(3). Three rigorous results are established: - Theorem A: the emergent Hilbert space H = L^2(H^3, dμ_{H^3}) is a separable complex Hilbert space with Plancherel orthonormal basis. - Theorem B: under Postulate P4 and a Nelson-type condition, the condensate diffusion on H^3 is unitarily equivalent to quantum mechanics with the identification ℏ = 2 m_φ D obtained as a definitional consequence of the Nelson formalism (an explicit dimensional analysis distinguishes what is derived from what is definitional); the Born rule follows from the polar decomposition of the diffusion density. - Theorem C (flat-space limit): the quantum evolution operator on H^3 converges to the standard QM evolution on R^3 with corrections bounded by C(l/R_τ)^2 t, reproducing all of standard quantum mechanics at laboratory scales with relative precision ≤ 4×10^{-53}. A conditional reduction of Postulate P4 to a single geometric assumption isalso presented. Under Assumption EQ — quantum ergodicity of the geodesic flowon H^{3,1}, proven for compact hyperbolic manifolds and conjectured for thenon-compact case — P4 follows from mode independence, a functional CLT onSO(3,1) (with explicit caveats on UV renormalization, since |c(s)|^{-2} growspolynomially at infinity), and the Lévy–Khintchine theorem on symmetric spaces.We do not claim that P4 is hereby derived; we claim that the problem is reducedto Assumption EQ. We do not claim a derivation of canonical commutation relations on H^3: this isexplicitly recorded as an open problem in the quantization of constrainedsystems on curved manifolds. Two consistency statements and one quantitative prediction follow from theframework:(i) an effective UV length cutoff l_UV = ℏc/μ_EW ≈ 8×10^{-19} m from the inter-sheet kink thickness of TET, presented as an internal consistency statement (degenerate with standard EW physics at present phenomenology);(ii) a pointwise suppression of the primordial scalar power spectrum of ~5.6% at k ≈ 2H_0 from the Plancherel spectral gap of H_τ, with the integrated effect on C_2^{TT} recorded as an open problem requiring a full Boltzmann calculation;(iii) a modified primordial spectral tilt δn_s ≈ -2.8×10^{-5} at the pivot scale, a geometric correction distinct from inflationary dynamics, potentially accessible to CMB-S4. This version (v4) supersedes earlier drafts (v1, v2, v3) and includes:- explicit retraction of the v1 "Theorem C" on canonical commutation relations (algebraically incorrect, foundationally ill-posed);- retraction of the v1 GUP framing of the inter-sheet UV scale;- corrected dimensional analysis of ℏ in TET vs laboratory units;- explicit UV/renormalization caveats in the P4 conditional reduction;- alignment of the abstract with the body (the v2/v3 numerical claim of 15–25% C_2^{TT} suppression is corrected to the pointwise ~5.6% at k ≈ 2H_0). Companion paper to: Temporal Emergence Theory (TET), Zenodo preprintdoi:10.5281/zenodo.19410988 Keywords: stochastic differential geometry, Nelson stochastic mechanics,emergent quantum mechanics, hyperbolic manifold, Plancherel decomposition,quantum ergodicity, CMB low-quadrupole anomaly. AI-assisted research: mathematical derivations and document elaboration weredeveloped with the assistance of online LLMs. The physical ideas andtheoretical framework are the author's original work.
Title: Spectral Diagnostics of Superconducting Quantum Circuits via the Witten Laplacian on Configuration Space Authors: Frédéric David Blum (Catalyst AI); Claude (Anthropic) continue work : https://zenodo.org/records/18776120 email : dvid75113@gmail.com We construct the Witten Laplacian on the configuration torus T² of coupled transmon qubits and compute it for 772 qubit pairs across six IBM Quantum processors (Sherbrooke, Brisbane, Osaka, Kawasaki, Kyiv, Quebec — real calibration snapshots via Qiskit FakeProvider). Three principal findings: 1. Spectral Universality (CV = 1.4%) — Rescaled eigenvalue ratios collapse across all processors with sub-percent coefficient of variation. The Witten spectrum possesses a universal structure independent of fabrication and noise environment. 2. Orthogonal Information Content (r = 0.205, p < 10⁻³) — After removing all variance explained by 10 raw calibration parameters, Witten spectral features still predict gate-length residuals with r = 0.205. The spectral transform extracts information invisible to standard characterization. In a rigorous 5-fold cross-validated benchmark, Witten features (R² = 0.134) outperform raw features (R² = 0.097), PCA, and polynomial Koopman lifting. 3. Inter-Processor Coherence Sensing (ρ = −0.76) — The relative Witten index ν_ij correlates with T₁ relaxation-time differences between processors at Spearman ρ = −0.76, sensing intrinsic hardware coherence rather than calibrated gate parameters. Additional finding: A semiclassical phase boundary at ℏ_eff ≈ 0.42 where Z(β) diverges, consistent with a phase transition in the Witten Laplacian observable on real IBM Kawasaki hardware. This deposit includes the theoretical framework (CST v13/v14), the PRX Quantum manuscript draft, all analysis code (reproducible in ~60 seconds with pip install qiskit-ibm-runtime), and complete numerical results. Code repository: https://github.com/davidangularme/cst Keywords: Witten Laplacian, superconducting qubits, transmon, spectral universality, quantum computing, IBM Quantum, configuration space, spectral diagnostics, heat kernel, decoherence License: CC BY 4.0 Files to upload: prx_quantum_draft.docx (manuscript) Configuration_Space_Temporality_v13.pdf Configuration_Space_Temporality_v14.pdf witten_transmon_paper.pdf nu_ij_witten.py phase2_benchmark.py phase2_results.json nu_ij_results.json spectral_collapse.png phase2_results.png Response to Methodological Review Document: Response to Methodological Review — Algebraic Coherence, Discretization Artifacts, and Interventional Diagnostics Authors: Frédéric David Blum, Claude (Anthropic), Catalyst AI Date: February 26, 2026 Target manuscript: Spectral Diagnostics of Superconducting Quantum Circuits via the Witten Laplacian on Configuration Space (Draft PRX Quantum) Summary This document responds to a structured methodological review identifying four revision requirements (R1–R4) for the PRX Quantum draft. The review's central thesis — that a discretization producing λ₀ < 0 constitutes a category error, not a numerical imperfection — is accepted in full. The companion paper Spectral Fidelity of the Discrete Witten Laplacian on S¹ (v3) independently establishes the diagnosis (96/96 violation rate under standard stencil) and the remedy (factored dW†dW / FEEC schemes). Response to Revision Requirements Req. Reviewer Demand Response Status R1 λ₀ ≥ 0 as identity test Adopt factored scheme as primary pipeline COMMITTED R2 Inter-scheme replication Full 772-pair recomputation; 2×2 outcome matrix COMMITTED R3 Suspend Z(β) interpretation All claims conditional until λ₀ ≥ 0 guaranteed ACCEPTED R4 Break E_{J,c} circularity Phase IV fingerprinting elevated; sensitivity sweep ACCEPTED The 2×2 Outcome Matrix The recomputation (R2) tests spectral universality (U) and orthogonal information content (O) independently: (O) r ≈ 0.205 SURVIVES (O) r ≈ 0.205 FAILS (U) CV ≈ 0.014 SURVIVES Quadrant A: Full validation. Microscope works. Quadrant B: Universal structure, no ML surplus. (U) CV ≈ 0.014 FAILS Quadrant C: No universality, but useful tool. Quadrant D: Full falsification of PRX claims. We commit to publishing whichever quadrant materializes. Post-Review Dialogue Refinements "Indécidable" → "Non tranché": The Z(β) interpretation is not fundamentally undecidable — it is unresolved pending recomputation under a structure-preserving scheme. Separate (U) from (O): Spectral universality and orthogonal information content are vulnerable to different artifact mechanisms and must be tested independently. Files response_to_methodological_review_prx_quantum.docx — Full formatted response document RESPONSE_REVIEW.md — This summary Related PRX Quantum draft: DOI 10.5281/zenodo.18779189 CST v14: DOI 10.5281/zenodo.18776120 Code: github.com/davidangularme/sdsq
Version 2.8 — submission manuscript. Preprint prepared for submission to Foundations of Physics. Supersedes v2.6, v2.5, v2.3, v2.2 and v1. A gravitational collapse model in which spacetime geometry is postulated to be irreducibly classical and superpositions of massive systems decay under a stochastic dynamics driven by a physical temporal medium: one stationary noise field combining the Diósi–Penrose spatial kernel with a coloured temporal kernel of finite universal bandwidth ω_u — the single new parameter of the primary model. The decoherence envelope is derived exactly (Gaussian onset, DP exponential tail), and two universality propositions are proved: the DP tail is fixed by the kernel's zero-frequency weight alone, and a Gaussian onset is generic for any finite-bandwidth medium — making the crossover, not any particular kernel, the experimental signature. A selectivity theorem shows each configuration draws its collapse dominantly from noise modes near its own gravitational frequency ΔE_g/ℏ. The parameter-free tuning of earlier versions is retained as named Conjecture C1, with a proof that no single stationary spectrum realises it for all configurations at once. The coloured kernel suppresses collapse-induced spontaneous radiation, reconciling the model with underground null results; heating bounds survive at full strength. Predictions include a closed-form optimal measurement window (separation 0.330 at t = 0.837 τ_dec under C1) and a mass-and-time ceiling on Bell violations, with five falsification conditions. The BMV/GIE treatment is current with the 2024–2026 literature. Changes in v2.8 (Appendix B, B11–B13): universal-bandwidth primary model with derived (ω_u, R_0) window; C1 demoted to conjecture with proved obstruction; no-signalling corrected and branch-conditioned; non-Markovian trajectory literature engaged, Born-rule theorem declared open; one prediction and the "present moment" identification withdrawn with reasons; GIE dispute disentangled; references verified. This paper builds on v1 of the companion collapse-model work (10.5281/zenodo.19960071). The lowest-energy principle assumed here was withdrawn in v2.2 of that paper and does not appear in the current version (v2.8); the framework presented here has not been revised accordingly. Retained as a record of the earlier line of enquiry All revisions, withdrawn claims, and corrected errors are documented in Appendix B; open problems in Section 8. AI tools (Claude, Anthropic) assisted with formalisation and editing; the conceptual framework originated with the author, who takes full responsibility. Full declaration in the manuscript.
Abstract Quantum spacetime in which time is considered on the same footing as other observables is a part of the quantum configuration space. In such space a natural geometry is generated by the transition amplitudes among quantum configuration space points. It is shown, that a good candidate for quantization of extended (plus time) classical configuration spaces is integral quantization. This quantization is compatible with the notion of quantum time. The most basic features of this quantization are presented.