Temporal Locations: Discrete-Time CPTP Dynamics with Testable Spectral Signatures We develop a framework in which physical time advances through discrete synchronization events rather than a fundamental continuum, with inter-event intervals modeled as random variables around a base scale tau_0. Between events the quantum state evolves unitarily; at each event it is updated by a completely positive trace-preserving (CPTP) map that represents dephasing and measurement, giving a consistent open-systems description without changing the standard postulates of quantum mechanics. In the weak-fluctuation limit we derive a diffusion approximation for timing deviations and obtain closed-form expressions for the power spectral density of timing noise, the corresponding fractional-frequency spectrum, and the Allan variance. The continuum limit is recovered when the fluctuations vanish, and leading corrections are quantified. We formulate falsifiable predictions based on cross-spectral and coherence measurements of timing residuals across independent channels, provide a detection statistic with explicit scaling in channel count and averaging time, and outline null tests that separate discrete-time jitter from instrumental artifacts. This enables targeted searches for discrete-time signatures in precision platforms such as optical and atomic clocks and high-rate detector systems, and allows existing data to place quantitative bounds on the fundamental timescale and its fluctuations.
# Two-Mode Jaynes–Cummings Model of Endogenous and Exogenous Phase Coherence **Complete Zenodo record with historical development** **DOI:** [10.5281/zenodo.22904994](https://doi.org/10.5281/zenodo.22904994) **Authors:** Miguel Angel Percudani (corresponding: miguel_percudani@yahoo.com.ar, ORCID [0009-0007-1748-3212](https://orcid.org/0009-0007-1748-3212)) & Jorge Iván Díaz **Affiliation:** Independent Research Collaboration **Publication date:** 22 September 2026 **Related records:**- Binary Universe Ontology: [10.5281/zenodo.18015439](https://doi.org/10.5281/zenodo.18015439) (2025)- UAT framework: [10.5281/zenodo.17886549](https://doi.org/10.5281/zenodo.17886549) (2025)- Antifrequency datasets: [10.5281/zenodo.17861265](https://doi.org/10.5281/zenodo.17861265) (2025) --- ## 1. Central paper — read this first > **`track_A_formal.pdf`** (746 kB, 7 pages) > *A Two-Mode Jaynes–Cummings Model of Endogenous and Exogenous Phase Coherence: Falsifiable Predictions for Neural Dynamics* This is the **formal, falsifiable Track A**. The model contains **no geometric constants** (
ΦUAT,
kUAT,
κcrit). The coupling strength
g0 is a free parameter to be fitted to EEG/fMRI data. **This PDF is the one to cite.** All other files in this record are complementary or supplementary. --- ## 2. Two-track structure The record is organized in two independent tracks: ### Track A — Formal, falsifiable, testable now A two-mode Jaynes–Cummings model with Lindblad dissipation and Default Mode Network modulation. The model produces a two-dimensional phase diagram in the plane
(α=g/δ, γϕ) and four falsifiable predictions for EEG/fMRI experiments. All parameters are free and listed in the paper. **Track A remains valid even if Track B is refuted.** Documents:- **`track_A_formal.pdf`** (7 pages) — main paper, 4 falsifiable predictions, phase diagram- **`track_A_field_equations.pdf`** (15 pages) — technical appendix: complete field equations, Hilbert space, operator algebra, Lindblad dissipator, master equation, reduced dynamics, BDF numerical scheme- **`track_A_Extended_version_full_derivation.pdf`** (20 pages) — extended appendix that **supersedes** the previous one: it contains all the material of `track_A_field_equations.pdf` plus three new sections with full step-by-step derivations: - (i) mean-field closure of the reduced dynamics - (ii) expansion of the density matrix in the Jaynes–Cummings eigenbasis (dressed states) - (iii) linear stability analysis of the Liouvillian superoperator and spectral gap
Δ Both appendix versions are provided for convenience. **The extended version is the recommended reference.** ### Track B — Speculative research program An ontological interpretation of Track A in terms of the Binary Universe Ontology (Bit 1 = analytic qubit, Bit 0 = substrate oscillator, causal friction = Jaynes–Cummings exchange, homeostasis = Lindblad dissipation, DMN = baryonic filter). Contains the constants
ΦUAT=π2/8,
kUAT≈10.90677,
κcrit≈10−78 **explicitly labeled as speculative hypotheses, not derived results.** Document:- **`track_B_speculative.pdf`** (6 pages) — *Binary Universe Ontology as an Interpretation of Two-Mode Coupling: The Geometric Origin of
kUAT as a Speculative Research Program* The two tracks are independent. Track A does not use any of the constants from Track B. Track B does not modify the numerical results of Track A. --- ## 3. Figures (stand-alone PNGs for reuse) - **`v5_run1_rabi.png`** (130 kB) — Rabi oscillation:
⟨σz⟩,
⟨n0⟩,
SvN, purity for
g=17 Hz, 10 periods- **`v6_scan2D.png`** (150 kB) — Phase diagram in
(α=g/δ, γϕ) plane, four steady-state observables- **`v6_cortes1D.png`** (173 kB) — One-dimensional cuts at
γϕ∈{0.09,0.44,2.26,11.60} Hz --- ## 4. LaTeX sources (for reproducibility) - `LaTex_track_A_formal.tex` (16 kB) — source of the central paper- `LaTex_track_A_field_equations.tex` (31 kB) — source of the 15-page field-equations appendix- `LaTex_track_A_Extended_version_full_derivation.tex` (45 kB) — source of the 20-page extended appendix- `LaTex_track_B_speculative.tex` (17 kB) — source of the speculative interpretation All sources compile with `pdflatex` (two passes required for cross-references). No external dependencies beyond the standard TeX Live distribution. --- ## 5. Code archives (historical development) The numerical results were developed over six versions. Each `trackA_vN.zip` contains the scripts and data as they were at that stage. Historical versions are included for transparency; **only v5 and v6 are needed to reproduce the published results.** ### Historical / supplementary - **`trackA_v2.zip`** (326 kB) — v2: manual RK4 integrator, initial dark state
∣0,0⟩ bug, crashes for
γϕ≳10 due to stiffness- **`trackA_v3.zip`** (426 kB) — v3: fix with BDF implicit solver (`scipy.integrate.solve_ivp`), first stable runs- **`trackA_v4.zip`** (630 kB) — v4: first sweep in
(α,γϕ) plane- **`trackA_v4_1.zip`** (643 kB) — v4.1: JC coupling corrected (standard Jaynes–Cummings, not anti-JC) ### Final — use these to reproduce - **`trackA_v5.zip`** (1,626 kB) — **IMPORTANT**: Rabi runs and endogen/exogen contrast at equal Rabi period. Generated `v5_run1_rabi.png`.- **`trackA_v6.zip`** (510 kB) — **IMPORTANT**: Final 2D scan and 1D cuts, phase diagram, boundary
αcruce(γϕ), empirical scaling
gcruce⋅γϕ0.62≈3.95. **This is the version used in `track_A_formal.pdf`.** --- ## 6. How to reproduce the central result ### Numerical ```bash# Main result (phase diagram + Rabi)unzip trackA_v6.zip && cd trackA_v6python -m venv venv && source venv/bin/activatepip install numpy scipy pandas matplotlibpython main.py # BDF solver, rtol=1e-7, atol=1e-9# Outputs: v6_scan2D.png, v6_cortes1D.png ## 12. Update: intrinsic transition measures (v8.1) In September 2026, the numerical exploration was extended with v8.1, which replaces the threshold-based definition of the "coexistence window" used in earlier versions (v7.x) with threshold-free intrinsic measures based on the product P(t) = R(t) · I(t). Key result: two distinct coexistence regimes emerge: - Vigilance: slow, weak, sustained (P_max = 0.006, W_half = 46, eta = 0.87) - Flow / Endogenous / Sleep: fast, intense, brief (P_max ≈ 0.013-0.016, W_half ≈ 8-15, eta ≈ 0.24-0.38) The trade-off between peak intensity and effective duration is quantified. See trackA_v8_1.zip for code, data, and figures. Licencia: CC BY 4.0 para manuscritos, MIT para código.
We analyze the Riemannian geometry of several physically relevant families of qubit quantum channels, using the Hilbert–Schmidt metric induced on their Choi representations. For amplitude-damping channels with additional dephasing, we derive closed-form expressions for the metric tensor and scalar curvature and show that the curvature diverges as the damping probability approaches unity. This geometric singularity corresponds to complete population decay and represents an irreversible limit of open-system dynamics. In contrast, pure dephasing channels and noisy unitary channels form flat manifolds with identically zero curvature, revealing that the Hilbert–Schmidt geometry is highly sensitive to dissipative (energy-relaxing) processes but insensitive to coherence loss without energy exchange. We further study the gradient flow of scalar curvature, which for amplitude damping drives channel parameters toward weaker dissipation, with the identity channel acting as an attractor. These results establish a clear geometric separation between different types of quantum noise and suggest potential applications in noise spectroscopy, device benchmarking, and geometric optimization of quantum control. The logical development of this article can be seen here: https://zenodo.org/records/17952025
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This publication presents operational one-dimensional scaling tests of the Dynamical Information Geometry (DIG) framework using the Twin-Test protocol. Dynamical Information Geometry assigns an effective, state-dependent geometry to quantum many-body dynamics based on the spatial organization of mutual information. Earlier parts of the DIG series established the theoretical framework, provided numerical validation, introduced hardened operational definitions, and clarified regime structure and necessity. The present work, DIG Part VI, does not introduce new theory, new observables, or new numerical modeling. Its role is strictly operational. It documents how the Twin-Test protocol behaves under controlled one-dimensional scaling variations along two independent axes: system-size increase in a simulator implementation and circuit-depth increase in a quantum hardware implementation. Both scaling axes are evaluated within the same operational framework, using the mandatory audit logic defined in DIG Part IV. No attempt is made to relate or map these axes onto one another. The analysis is restricted to structural sign behavior, audit classification (marker-stable versus marker-transfer), and the identification of an operational robustness limit (defect) at increased depth. No universal scaling laws are proposed. No fitting, extrapolation, or cross-platform amplitude matching is performed. All operational definitions and decision rules are stated explicitly in the manuscript. The accompanying dataset implements these rules verbatim and enables deterministic third-party reproduction without interpretation. Related works (for reference and context): DIG Part I (theoretical framework):https://doi.org/10.5281/zenodo.17983399 DIG Part II (numerical validation):https://doi.org/10.5281/zenodo.17982058 DIG Part III (hardware validation):https://doi.org/10.5281/zenodo.18100057 DIG Part IV (regime structure and operational necessity):https://doi.org/10.5281/zenodo.18202656 DIG Part V (multidimensional formulation):https://doi.org/10.5281/zenodo.18210315 DIG Part VI Data Set: https://doi.org/10.5281/zenodo.18226272 DIG Part VII Dynamical Information Geometry:Two-Dimensional Twin-Sign Validation under Fixed Audit and Regime Constraintshttps://doi.org/10.5281/zenodo.18313460 DIG — N1 (definitions, scope, and non-equivalences):https://doi.org/10.5281/zenodo.18001179 Correspondence regarding this work may be directed to:kaya@cab-film.com