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κ-Theoretic Quantum Optimization as an Upper-Governance Principle

Masaki Okada

Published Mar 27, 2026• 0 citations
Publisher

Abstract

This record contains the Japanese and English v1 releases of the paper“κ-Theoretic Quantum Optimization as an Upper-Governance Principle,” togetherwith curated supplementary materials for reproduction. The paper positions κ-theory not as a stand-alone optimization trick but as anupper-governance principle that regulates when and how existing quantum-optimization levers should be activated. The empirical study is organized intothree directions: (A) whether the same performance can be reached with lowercost-to-target, (B) whether higher performance can be obtained under the sameoperational burden, and (C) whether one can construct a governed stack thatsurpasses existing stand-alone baselines in both performance and efficiency. Within the benchmark suite studied in the paper, the κ-governed optimizer showsa substantial advantage in Directions A and B, and the governed stack alsooutperforms stand-alone vendor-like baselines in Direction C for the includedsemi-real and hold-out cases. The paper further studies exploratory real-timeswitching among A/B/C modes and separates replay-based main evidence fromsynthetic operating-map supplementary evidence through an explicit provenancemap. This Zenodo record includes:- Japanese paper PDF/TeX (v1)- English paper PDF/TeX (v1)- Replay reproduction package (curated v2)- Synthetic operating-map package (curated v2)- Combined convenience bundle of the supplementary materials Supplementary bundle note:The “v2” suffix in the supplementary ZIP files denotes the curation version ofthe supplementary bundles and is independent of the paper version, which remainsv1. Related κ-theory background volumes:- Volume I of κ-Theory: A Local Comparison Framework for Gateway Anomaly and Higher-Family Law. DOI: 10.5281/zenodo.19254863- Volume II of κ-Theory: Structural Readings and Application-Side Interpretations Through Reduced Local-Form Matching. DOI: 10.5281/zenodo.19255089

DOI
10.5281/zenodo.19255843

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Camino 1 — Extended Analysis: Regime Classification, Two-Exponential Structure, and Proxy Comparison in the Two-Mode Jaynes-Cummings Model

Miguel Percudani

# 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** ($\Phi_{\text{UAT}}$, $k_{\text{UAT}}$, $\kappa_{\text{crit}}$). The coupling strength $g_0$ 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 $(\alpha = g/\delta,\ \gamma_\phi)$ 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 $\Delta$ 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 $\Phi_{\text{UAT}} = \pi^2/8$, $k_{\text{UAT}} \approx 10.90677$, $\kappa_{\text{crit}} \approx 10^{-78}$ **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 $k_{\text{UAT}}$ 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: $\langle \sigma_z \rangle$, $\langle n_0 \rangle$, $S_{vN}$, purity for $g = 17$ Hz, 10 periods- **`v6_scan2D.png`** (150 kB) — Phase diagram in $(\alpha = g/\delta,\ \gamma_\phi)$ plane, four steady-state observables- **`v6_cortes1D.png`** (173 kB) — One-dimensional cuts at $\gamma_\phi \in \{0.09, 0.44, 2.26, 11.60\}$ 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 $|0,0\rangle$ bug, crashes for $\gamma_\phi \gtrsim 10$ 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 $(\alpha, \gamma_\phi)$ 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 $\alpha_{\text{cruce}}(\gamma_\phi)$, empirical scaling $g_{\text{cruce}} \cdot \gamma_\phi^{0.62} \approx 3.95$. **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.

•Sep 23, 2026•0 citations
This record contains the Japanese and English v1 releases of the paper“κ-Theoretic Quantum Optimization as an Upper-Governance Principle,” togetherwith curated supplementary materials for reproduction. The paper positions κ-theory not as a stand-alone optimization trick but as anupper-governance principle that regulates when and how existing quantum-optimization levers should be activated. The empirical study is organized intothree directions: (A) whether the same performance can be reached with lowercost-to-target, (B) whether higher performance can be obtained under the sameoperational burden, and (C) whether one can construct a governed stack thatsurpasses existing stand-alone baselines in both performance and efficiency. Within the benchmark suite studied in the paper, the κ-governed optimizer showsa substantial advantage in Directions A and B, and the governed stack alsooutperforms stand-alone vendor-like baselines in Direction C for the includedsemi-real and hold-out cases. The paper further studies exploratory real-timeswitching among A/B/C modes and separates replay-based main evidence fromsynthetic operating-map supplementary evidence through an explicit provenancemap. This Zenodo record includes:- Japanese paper PDF/TeX (v1)- English paper PDF/TeX (v1)- Replay reproduction package (curated v2)- Synthetic operating-map package (curated v2)- Combined convenience bundle of the supplementary materials Supplementary bundle note:The “v2” suffix in the supplementary ZIP files denotes the curation version ofthe supplementary bundles and is independent of the paper version, which remainsv1. Related κ-theory background volumes:- Volume I of κ-Theory: A Local Comparison Framework for Gateway Anomaly and Higher-Family Law. DOI: 10.5281/zenodo.19254863- Volume II of κ-Theory: Structural Readings and Application-Side Interpretations Through Reduced Local-Form Matching. DOI: 10.5281/zenodo.19255089
NOTE: This paper is part of a 4-part research series (tetralogy) on database systems: structural trade-offs in modern data architectures and quantum-augmented techniques for robust query optimization and OLAP execution. Other parts (Zenodo DOIs):- 10.5281/zenodo.17797344- 10.5281/zenodo.17797276- 10.5281/zenodo.17796162 Research positioning:- This is an unpublished research manuscript intended for open dissemination and community feedback.- The work emphasizes explicit assumptions/limitations and model- or simulation-based evidence where applicable. Reproducibility (current status):- The current release focuses on the manuscript and experimental description.- Code/data packaging will be added in subsequent releases (new versions) as a reproducibility bundle. License:- Please see the license field of this Zenodo record for reuse terms. We analyze key-only offloading for OLAP bottlenecks (Top-K and join-related primitives) and derive break-even conditions under an explicit hybrid latency/cost model.
This paper rewrites a quantum-optimization selector note originally framed in the language of kappa-theory as a paper on the visualization of bridge grammar in Okada Theory and its translation into diagnosis-driven governance. Its purpose is not to redefine quantum optimization from the top down by introducing one uniquely privileged hidden object. Instead, it separates within an existing optimization stack what had previously been bundled into one opaque decision layer: the dominant route that is currently carrying improvement, the retained load carried forward as switching, recalibration, queueing, hysteresis, or search history, and the competitor pressure entering from alternative or misaligned routes. The first visible handles of this bridge grammar are tracked operationally by diagnostic scores, pure/mixed classification, and the selector quantity gap_to_plain. The empirical study proceeds in three directions: reducing arrival burden at fixed quality, improving quality under fixed burden, and constructing a balanced stack that dominates existing single-method baselines in both quality and efficiency. The main evidence lies in replay-based A/B/C comparisons, while synthetic operating-map experiments are used only as auxiliary evidence for controller standardization. The core claim is that Okada Theory does not merely visualize a previously hidden bridge grammar; it translates that visibility into diagnosis, lever restriction, mode selection, and auditable failure boundaries.
This Zenodo record contains the main preprint and supplementary information for a shared-parameter closure analysis of Continuous Spontaneous Localization (CSL) using public upper-bound evidence and direct astrophysical inequalities. Over the reporting domain x = log10(r_C / m) in [-10, 0] and y = log10(λ / s^-1) in [-20, -5], the study reconstructs admissible upper envelopes for XENONnT, a GW/LISA composite constraint, radiation-channel searches, cold-atom and bulk-heating constraints, cantilever-related bounds, and direct astrophysical heating inequalities. The principal result is a quantified compression of the shared admissible CSL region under the current public evidence stack, together with an evidence-class limit: when each channel is represented only by one-sided admissible upper envelopes or direct inequalities, the shared-envelope admissible set is exactly the intersection of the individual admissible sets. Under this evidence class alone, positive-measure closure-failure regions cannot be established. Accordingly, the record supports a bounded claim: current public single-channel summaries overstate the shared admissible CSL volume, whereas decisive inconsistency testing requires richer, likelihood-aware evidence. Files included in this record:1. Main preprint PDF.2. Supplementary PDF containing source/provenance notes, formulas, exact reported metrics, and reproducibility notes.
# 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\Phi_{\text{UAT}}ΦUAT​, kUATk_{\text{UAT}}kUAT​, κcrit\kappa_{\text{crit}}κcrit​). The coupling strength g0g_0g0​ 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)(\alpha = g/\delta,\ \gamma_\phi)(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\DeltaΔ 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\Phi_{\text{UAT}} = \pi^2/8ΦUAT​=π2/8, kUAT≈10.90677k_{\text{UAT}} \approx 10.90677kUAT​≈10.90677, κcrit≈10−78\kappa_{\text{crit}} \approx 10^{-78}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 kUATk_{\text{UAT}}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⟩\langle \sigma_z \rangle⟨σz​⟩, ⟨n0⟩\langle n_0 \rangle⟨n0​⟩, SvNS_{vN}SvN​, purity for g=17g = 17g=17 Hz, 10 periods- **`v6_scan2D.png`** (150 kB) — Phase diagram in (α=g/δ, γϕ)(\alpha = g/\delta,\ \gamma_\phi)(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}\gamma_\phi \in \{0.09, 0.44, 2.26, 11.60\}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⟩|0,0\rangle∣0,0⟩ bug, crashes for γϕ≳10\gamma_\phi \gtrsim 10γϕ​≳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)(\alpha, \gamma_\phi)(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)\alpha_{\text{cruce}}(\gamma_\phi)αcruce​(γϕ​), empirical scaling gcruce⋅γϕ0.62≈3.95g_{\text{cruce}} \cdot \gamma_\phi^{0.62} \approx 3.95gcruce​⋅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.