Quantum Narrative Matrix Theory — Version Update (Detailed) 2026.02.08 → 2026.02.13

Document: Version Update & Revision Note (Detailed)Author: Nanjie MaVersion: v3 (January 28, 2026)Last Updated: February 13, 2026Citation: MA, N. (2026). The Nature of Reality: The Quantum Narrative Matrix Hypothesis. Zenodo. https://doi.org/10.5281/zenodo.18630432

Version Update Preview (2026.02.08 → 2026.02.13)

This section summarizes updates between 8 and 13 February 2026. Submission package updated and uploaded; main text causal order of N=21 and 6D geometry fixed and aligned with supplementary materials and audit reports.

N=21 and D=6: N=21 is fixed first by constraint satisfaction (Topological Stability (I), Holographic Consistency (II)); D=6 is the unique solution of N = D(D+1)/2 within the theory (Geometric Necessity (III), a posteriori); compatibility with 6D compactification/string theory is a posteriori. See main text §3.3, §5.3.3 and Geometric Resonance Theorem.

Tripartite temporal structure: Supplementary material explains how the three arrows (Algorithmic, Topological, Thermodynamic) operate at each discrete time step, resolving the microscopic-reversibility vs macroscopic-irreversibility paradox and the thermodynamic arrow's role for phantom energy (w < -1) and the Hubble Tension. See main text §7.4 and Supplementary The Tripartite Nature of Time.

Code Audit and Current Status

Code audit: Numerical literals in core derivation and output scripts replaced with first-principles constants (e.g. geometric damping 1/π², reference dimension √(π·e), slow-roll 8π²); included in this version.

Status in this version: A-system standard production run completed (2026-02-08; 10/10×200,001 steps). Results in main text §4.6, Table 5.1, §5.10, §6.2 and RUN_ANALYSIS_REPORT_20260208. N=16–200 dimension scan in §3.3.5, §5.3.3.1 and Dimension_Scan_N16-200_Summary_Report. PDF and Submission_Package updated and uploaded. Supplementary: Cosmic Age: A Deep Reflection explains QNM today-age (N=21 ~13.5 Gyr) vs Planck 13.8 Gyr and notes QNM as the most complete implemented model from cosmic birth to end.

Framework Summary and Key Updates

A-system implemented and validated: Hamiltonian/time evolution yields H(z), w(z) (§4.6, Figures A1–A3); evolution-endpoint H₀ in range encompassing early- and late-universe measurements (Table 5.1). Run configuration and numbers in the table below.

• N=21 / D=6: See above; main text §3.3, §5.3.3, Geometric Resonance Theorem.

• Intrinsic constants: c_raw ≈ 2.75 emergent constant of matrix mechanism, not empirical fit.

• Zero-parameter axiomatization: (π+e) and related factors as "Zero-Parameter Physical Ansatzes".

• Dynamical run completed: Standard run (2026-02-08); evolution-endpoint H₀, w₀ consistent with static ensemble and Planck/SH0ES.

Current Progress

Single and multichain MCMC runs are in progress (config qnm_full_planck_bao_pantheon; output in chains/ and multichain/). Single chain latest: N ≈ 119.2k samples (last update 2026-02-13 19:57:28), acceptance rate ≈ 0.579, Rminus1 ≈ 0.003, Rminus1_cl ≈ 0.035; sampling will stop when Rminus1_cl ≤ 0.015, ~80.8k steps remaining to 200k. Chain outputs not yet archived; upon completion the new posterior will replace the observational constraints cited in the paper. MCMC separates testable parameters (e.g. 5 BAO) from fixed parameters (3 QNM first-principles).

License: Academic use free; commercial use requires authorization: phoenix-mx@hotmail.com

Cosmic Evolution Run and Parameter Comparison (2026-02-08)

The A-system script completed a standard production run (Planck-era start → z≈0). Results are in the main paper (§4.6, Table 5.1, §5.10, §6.2) and in RUN_ANALYSIS_REPORT_20260208. Planck/SH0ES in figures are reference only, not used in derivation.generate_academic_cosmic_evolution_figures.py

ItemResultRun time2026-02-08 00:12:51 – 00:13:12ConfigurationN=21, 10 independent realizationsCompletion10/10 all successfulSteps per realization200,001 (to present cosmic time ≈ 13.8 Gyr)Evolution-endpoint H₀68.26 ± 2.55 km/s/Mpc (range 63.99–73.29)Evolution-endpoint w₀≈ −1.01 (phantom-type dark energy)Phantom crossings0 (w(z) remains near Λ throughout)Output & report05_Core_Source_Code/A/01_figure_generation/output/academic_paper_figures/; RUN_ANALYSIS_REPORT_20260208 (CN/EN Markdown and HTML)Evolution starts at the Planck era (quantum-matrix start). The redshift sequence runs from very large z to present (z≈0), consistent with the main text's "start from the ultra-early universe when the quantum matrix runs."

Static vs dynamic vs Planck 2018: Planck comparison in the main paper uses the static ensemble (100 runs). The dynamic run column below gives evolution-endpoint values from the 2026-02-08 run; for σ₈ the dynamic run yields raw ~1.59 (evolved-matrix scale); only static σ₈ (≈0.81) is used for Planck comparison (see report and main text §4.6, §5.10, §6.2).

ParameterPlanck 2018 (reference)Static ensemble (QNM)Dynamic run (QNM)H₀ (km/s/Mpc)67.36 ± 0.5468.47 ± 4.8268.26 ± 2.55σ₈0.8111 ± 0.0060.8099 ± 0.0381.594 ± 0.002 (raw; not used for Planck comparison)n_s0.9649 ± 0.00420.9574 ± 0.00080.9577 ± 0.0005A_s (×10⁻⁹)2.100 ± 0.0342.082 ± 1.762.30 ± 2.29Ωm0.3153 ± 0.00730.3255 ± 0.00560.3233 ± 0.0037ΩΛ0.6847 ± 0.00730.6745 ± 0.00560.6766 ± 0.0037w₀—-1.0098 ± 0.0009-1.0095 ± 0.0009w_a—0.00166 ± 0.000130.00164 ± 0.00016ℓ₁—226.22 ± 13.77227.79 ± 8.19ℓ_d—1207.89 ± 73.781216.55 ± 43.68σ₈_seed——0.272 ± 0.0003τ0.0544 ± 0.00730.0522 ± 0.0066—z_reion—8.22 ± 0.39—S₈—0.8436 ± 0.040—Data sources: Planck from PLANCK_REFERENCE; static from 05_Core_Source_Code/all_cosmological_parameters_summary.csv (100 runs); dynamic from 05_Core_Source_Code/A/01_figure_generation/output/academic_paper_figures/18_parameter_summary.csv (10 realizations, 2026-02-08).

Core Achievement and Summary (2026.01.28)

QNM derives 18 cosmological parameters from first principles (no empirical curve-fitting or free parameters), achieving 16/18 (88.9%) consistency with Planck 2018: 13 high-precision (<3% deviation), 3 strong (3–6%). Values are from the static ensemble (Planck comparison in main paper). Full parameter list and per-parameter deviations: see main paper Section 5, Tables, and Appendix C.

ItemValueTotal parameters18Statistically consistent16/18 (88.9%)High-precision (<3% deviation)13Strong (3–6% deviation)3 (Ω_m, Ω_c, Ω_b)Good1 (z_reion: +7.0%)Theoretical / within uncertaintyr (geometric floor); τ (within 1σ Planck)Key results (programme framing) (details in main text): A_s from geometric resonance + CFT slow-roll (-0.84% vs Planck); (π+e) first-principles → σ₈, S₈; H₀ static/dynamic bridges Planck and late-universe (SH0ES, etc.), w₀ ≈ -1.01 (phantom); high theoretical purity (programme claim; not a warranty of physical closure) (no hardcoded empirical fitting). Derivation methods: CFT, acoustic horizon, holographic A_s, (π+e) coupling, phantom w(z), reionization, N=21/D=6 geometric constraints, Hermitian Ω_b. See main text §3, §5, Appendix B.

2026.01.18 — Executive Summary

This version marks the transformation of the Quantum Narrative Matrix (QNM) theory from a conceptual hypothesis into a fully closed-loop mathematical framework. In this release, we have successfully achieved the pure first-principles derivation of 8 key cosmological parameters (including H₀, n_s, Ω_m, w₀, etc.). Unlike the Standard Model (ΛCDM) which relies on fitting observational data, the core result of this version lies in establishing a rigid derivation chain: Constraint satisfaction (stability + holography) → N=21; geometric filter N = D(D+1)/2 → unique D=6; then cosmological observations. All results are derived exclusively from mathematical constants (π, e) and geometric topology, without introducing any artificial fine-tuning parameters.

Key Milestones

• Theoretical closure achieved: Established the "Trinity" origin mechanism for N=21: (1) Constraint satisfaction: N=21 is fixed by topological stability and holographic consistency (Pillars II–III). (2) Geometric filter: The only positive integer D satisfying N = D(D+1)/2 = 21 is D=6; 6D is derived within QNM from N=21, not assumed from string theory; compatibility with compactified dimension is a posteriori.

• Origin of dark energy: Thermodynamic Frustration naturally derives the Phantom Dark Energy mechanism (w < -1) without requiring scalar fields.

• Precision verification: The theoretically predicted scalar spectral index n_s deviates from Planck 2018 observations by only -0.52%. The framework naturally addresses the Hubble Tension by bridging early-universe (Planck) and late-universe (SH0ES) observations via a dynamic w(z).

Note: Quantum Narrative Matrix Visualization Videos - Supplementary Material.zip is currently outdated; contents will be updated in a future version.

Key Contributions & Discoveries

• Resolution of the Hubble Tension via phantom energy: The model predicts a dark energy equation of state w₀ ≈ -1.02 (Phantom Regime). This emerges from intrinsic unitarity deviations in the matrix evolution, creating a dynamical "Phantom Bridge" that naturally reconciles early-universe Planck data with late-time SH0ES measurements without introducing new scalar fields.

• Geometric origin of dimensionality (N=21 and D=6): The matrix dimension N=21 is not an arbitrary parameter. It is fixed by constraint satisfaction (topological stability and holographic consistency). The geometric filter N = D(D+1)/2 then yields the unique positive integer D=6 within the theory. Compatibility with 6D compactified Calabi–Yau geometry is a posteriori, establishing a first-principles geometric constraint without deriving N=21 from string theory.

Contact: phoenix-mx@hotmail.com | ORCID: 0009-0002-4415-1209

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