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This record contains the complete development of a two-mode Jaynes–Cummings model of endogenous and exogenous phase coherence, organized in two independent tracks. TRACK A — FORMAL AND FALSIFIABLE A two-mode quantum model in which an analytic sequential mode (a qubit) interacts with a non-analytic substrate mode (a truncated harmonic oscillator) through a time-dependent Jaynes–Cummings coupling with Lindblad dissipation. The coupling is modulated by an empirically accessible signal identified with Default Mode Network (DMN) activity. The model contains no speculative constants: all parameters are free and listed in the main paper. Numerical integration with an implicit BDF solver produces a two-dimensional phase diagram in the plane (α = g/δ, γφ), where the boundary between analytic-dominated and substrate-dominated steady states is a curve rather than a single threshold. The paper states four falsifiable predictions testable with current EEG/fMRI techniques. Track A documents: • track_A_formal.pdf — main paper, 7 pages • track_A_field_equations.pdf — technical appendix, 15 pages • track_A_Extended_version_full_derivation.pdf — extended appendix, 20 pages, supersedes the previous one and adds full derivations of the mean-field closure, the dressed-state expansion, and the linear stability of the Liouvillian superoperator TRACK B — SPECULATIVE RESEARCH PROGRAM An ontological interpretation of the same two-mode structure in terms of the Binary Universe Ontology: Bit 1 = analytic qubit (baryonic, finite, sequential), Bit 0 = substrate oscillator (non-baryonic, infinite, superposed); Jaynes–Cummings exchange = causal friction; Lindblad dissipation = entropic homeostasis; DMN = baryonic filter. The document presents the geometric constants Φ_UAT = π²/8, kUAT ≈ 10.90677, and κcrit ≈ 10⁻⁷⁸ explicitly as speculative hypotheses, not as derived results. Track B documents: • track_B_speculative.pdf — 6 pages INDEPENDENCE OF THE TWO TRACKS Track A does not use any constant from Track B. Track B does not modify the numerical results of Track A. Track A remains valid even if Track B is refuted. RECORD CONTENTS • 4 PDF documents (main paper, two technical appendices, speculative interpretation) • 4 LaTeX sources, compilable with pdflatex • 3 standalone figures in PNG format (Rabi oscillation, 2D phase diagram, 1D cuts) • 6 code archives (trackA_v2 through trackA_v6) documenting the full historical development, with v5 and v6 being the versions that generated the published results NOTES The 20 fMRI sessions of Agustina Vélez Picatto (led by Pablo Barttfeld, IIPsi — CONICET / Universidad Nacional de Córdoba) are cited as compatibility, not validation, as of 22 September 2026. No peer-reviewed DOI has been issued yet. Reproducibility: all results can be regenerated from trackA_v6.zip using standard Python scientific libraries (numpy, scipy, pandas, matplotlib) and the BDF implicit solver with rtol = 1e-7, atol = 1e-9. Compilation of the LaTeX sources requires two pdflatex passes for cross-references. License: CC BY 4.0 for manuscripts, MIT for code.
Percudani M. A. 2026. Two-Mode Jaynes–Cummings Model of Endogenous and Exogenous Phase Coherence: Formal Model, Field Equations, and Speculative Binary-Ontology Interpretation. PREPRINTS.RU. https://doi.org/10.24108/preprints-3116456
