Preprint and reproducibility archive; not peer reviewed. What this record contains. The full text of the manuscript "Identical Few-Particle Gauge Hamiltonians, Programmable Collective Charge Response" (M. J. Baek), its Supplementary Information with complete proofs, and the archive that certifies every closed-form value the paper states. The result. Few-particle dynamics are routinely used to infer collective response in paired quantum matter. This work constructs finite-range interacting response twins that defeat that inference exactly. For any prescribed finite p, two positive finite-range parents have complete static gauge Hamiltonians that coincide at every Peierls link phase on every sector N ≤ p and first separate at N = p+1; their zero-twist finite-density ground rays are the same Dicke condensate, yet their collective charge curvatures differ extensively. The obstruction has no universal depth, and the paper locates it exactly: the blind depth equals the spectator body order, the algebraic bound is independent of geometric range, and bounded range still bounds depth only through the number of sites a ball can hold — so no arbitrary-depth family of uniformly fixed range is claimed. Conversely, a structurally closed exact-pair tower closes at depth two. What is hidden is designable: with d(d+1)/2 displacement families the whole symmetric response-tensor difference is locally realizable at interior filling, and a triangular-lattice twin pair differs only in shear while both diagonal responses stay equal. A 4×4 hard-core-qubit discriminator gives an exact factor-of-two contrast with an internal null control and a state-preparation certificate in 17 equal-time settings. What is certified, and what is not. Results proved in closed form are stated as theorems and proved in full in the Supplementary Information; results established by exact rational or symbolic computation are labelled computer-assisted and carry the script that produces them; the 16-qubit discriminator is a blueprint with an end-to-end noise simulation, not a hardware demonstration, which is not claimed anywhere. Scope limits, open proof lines and one refuted conjecture are recorded explicitly rather than omitted. The archive. response_twins_unified_v1.0.zip contains the manuscript and Supplementary sources, the proof notes, the complete fail-closed verification harness (31 executed stages in release mode — 27 claim-bearing certificate stages, 1 non-claim diagnostic stage and three fail-closed gates — and 24 in quick mode) with one frozen log per stage, independent reimplementations of the load-bearing calculations, negative controls that must fail, the exact-arithmetic certificates behind every closed-form value in the paper, the figure-generation scripts, the scientific claim and provenance record (79 rows with status and scope notes, 50 of them naming the in-archive script or certificate that checks them, the rest saying in words why not), and a per-file SHA-256 manifest of all 209 payload files. Verifying it. Extract the archive and run python3 REPRODUCIBILITY/run_all.py --mode quick for the fast subset or --mode release for all 31 stages; bash BUILD.sh rebuilds both PDFs from source. The three gates check journal-format limits, the release payload against its manifest, and every number the documentation states about the artefacts. Running the harness does not modify the archive: all runtime output is written outside the immutable tree, so verification cannot invalidate the manifest. README.md separates reproducing the content (TeX Live 2023 or newer) from reproducing the archived PDF bytes, which needs the exact producing build recorded inside the PDFs. Licences. Manuscript, Supplementary Information and documentation CC BY 4.0; source code MIT; certificate data CC0 1.0. LICENSE.md is the authoritative per-file mapping and is included both in the archive and as a separate file on this record.
ECEG V9: the submitted manuscript, editable LaTeX source and computational supplement. This repository deposit was created on 31 October 2026 to preserve a dated, DOI-identified copy. The manuscript and accompanying scientific files are unchanged from the Quantum Information Processing submission of 10 October 2026. This is a preprint, not an accepted or peer-reviewed publication. Full text and supplementary files are restricted; bibliographic metadata are public. AbstractQuantum records can encode different source observables while sharing the same reduced states and energy statistics. We determine the optimal fidelity for converting a family of such records using local diagonal controls on an arbitrary interaction hypergraph. The answer depends only on the branch overlap and the smallest unsupported interaction. A weighted phase inequality proves the optimum and supplies an attaining control. We also derive limits on shared access to records, distinguish equal endpoint marginals from stationary evolution, and extend the fidelity bound to mixed preparation errors and integrated control deviations. All results concern a specified finite-dimensional quantum model. FilesECEG_V9_QIP_Submitted.pdf: submitted English manuscript (18 pages).ECEG_V9_QIP_Source.zip: editable LaTeX source and template files.ESM_1.zip: numerical verification scripts, machine-readable results, reproducibility instructions and file manifest. The statement in the submitted manuscript that no public repository identifier was claimed describes the submission on 10 October 2026; the present DOI identifies this later archival deposit.
# 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.