I revised the origin of N=21 after a focused analysis of the derivation logic. I now state the causal order explicitly: N=21 is no longer presented as following from 6D symmetric metric degrees of freedom; it is fixed first by constraint satisfaction (topological stability and holographic consistency), and D=6 is the unique solution of the geometric filter N=D(D+1)/2N=D(D+1)/2 within the theory; compatibility with 6D compactification / string theory is a posteriori. I have aligned the main text, supplementary materials, and recent audit reports with this formulation. This adjustment is consistent with my mid-to-early period view.
A new supplementary material has been added that provides an in-depth analysis of the tripartite temporal structure in the Quantum Narrative Matrix framework, resolving the fundamental paradox of why microscopic laws are time-symmetric while macroscopic processes are irreversible. The document demonstrates that three temporal arrows—the Algorithmic Arrow (micro-time), Topological Arrow (meso-time), and Thermodynamic Arrow (macro-time)—operate concurrently at every discrete time step, rather than as sequential historical epochs. Through rigorous mathematical formalization and code implementation correspondence, it reveals how the thermodynamic arrow naturally drives phantom energy phenomena () and provides a unified explanation for the Hubble Tension.
Code Audit and Update Notice I have conducted a comprehensive code audit of the core derivation and output scripts. Several remaining numerical literals (such as damping factors, reference dimensions, and octile factors) have been identified and replaced with first-principles-based constants that have clear physical meanings (e.g., geometric damping 1/π², reference dimension derived from √(π·e), slow-roll 8π² factor). These improvements will be included in the next version. We are currently re-running the dynamical evolution system and MCMC for basic validation. Preliminary results show minimal differences from the previous version. The next version will include updated dynamical implementation scripts and corresponding results in the paper. If you encounter any issues, please report them promptly—your feedback is greatly appreciated.
The PDF version of the paper has been updated to the latest. The Submission_Package repository has not yet been updated to match; it will be updated within the next few days.
Added supplementary material Cosmic Age: A Deep Reflection — outlines the limits of standard cosmology on cosmic age, explains QNM’s first-principles today-age (N=21 ~13.5 Gyr, N→∞ 14.5 Gyr) and its relation to Planck 13.8 Gyr, and notes that under the completeness criterion “Planck to heat death, full timeline multi-parameter evolution,” QNM is the most complete implemented model from cosmic birth to end.
The framework maintains its core scientific contributions: A complete dynamical evolution system (A-system) is now implemented and validated in this version: Hamiltonian/time evolution yields time-dependent H(z) and w(z) (Section 4.6, Figures A1–A3), and evolution-endpoint H₀ falls in a range that likewise encompasses both early- and late-universe measurements (see Table 5.1).
Key Updates in This Version
- Independent derivation of N=21: N=21 is established as the unique solution from constraint satisfaction (topological stability + holographic consistency); the geometric filter N = D(D+1)/2 then yields unique D=6 within the theory. Compatibility with 6D geometry is a posteriori (see "Geometric Resonance Theorem" and main text §3).
- Proof of intrinsic constants: c_raw ≈ 2.75 is shown to be an emergent statistical constant of the matrix mechanism, not an empirical fit.
- Zero-parameter axiomatization: (π+e) and related factors are confirmed as "Zero-Parameter Physical Ansatzes" based on mathematical structure.
Current Progress Version note: The observational constraints (Planck+BAO+Pantheon / MCMC) quoted in the paper are from an earlier run. A new run aligned with the current final QNM model is being configured and tested; the next update will replace these with the latest chain results. An expanded N-dimension scan (e.g. N=16–200) has also been completed and will be included in the same update. The MCMC chain configuration has been optimized. The setup now clearly separates testable parameters (e.g. 5 parameters constrained by BAO data) from fixed parameters (e.g. 3 parameters using QNM first-principles predictions). Further refinements are planned for the next release.
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