The Inevitable Framework of Reality
Independent Researcher
Summary
This paper presents a deductive, parameter‑free framework for fundamental physics built from a single logical tautology (the impossibility of self‑referential non‑existence). From this starting point it derives \(3{+}1\) spacetime, the constants \((c,\hbar,G)\), a universal coherence quantum \(E_{\text{coh}}=\varphi^{-5}\,\text{eV}\), and a particle‑mass spectrum closely matching PDG‑2025. It predicts a dark‑matter fraction \(\Omega_{\mathrm{dm}}=\sin(\pi/12)+\delta\approx 0.2649\) and shifts the Planck‑inferred Hubble rate to \(70.6\,\mathrm{km\,s^{-1}Mpc^{-1}}\) without tunable fields. Portions are formalized in Lean 4.
Abstract
We present a complete framework for fundamental physics derived deductively from a single principle of logical consistency: the impossibility of self-referential non-existence. From that tautology we obtain spacetime dimensionality (3+1), the constants $(c,\hbar,G)$, the universal energy quantum $E_{\text{coh}}=\varphi^{-5}\;\text{eV}$, and a particle-mass spectrum that matches PDG-2025 values to $\le 0.03\,\%$.
The framework closes outstanding cosmological tensions: it predicts the dark-matter fraction as $\Omega_{\mathrm{dm}}=\sin(\tfrac{\pi}{12}) + \delta \approx 0.2649$, and shifts the Planck-inferred Hubble rate from $67.4$ to $70.6\;\text{km\,s}^{-1}\text{Mpc}^{-1}$—the value the model itself calls "local"—without introducing any tunable field. Additional parameter-free derivations cover the DNA helical pitch, the black-hole entropy $S=A/4$, and the Riemann-zero spectrum. Roughly half of the chain is already formalised in Lean 4.
Key Points
- Deductive, parameter‑free framework: Built from a single logical tautology; no tuned fields.
- Derived structure and constants: \(3{+}1\) spacetime, $(c,\hbar,G)$, and $E_{\text{coh}}=\varphi^{-5}\,\text{eV}$.
- Quantitative predictions: $\Omega_{\mathrm{dm}}\approx 0.2649$ from $\sin(\pi/12)+\delta$; local $H_0\approx 70.6$.
- Empirical alignments: Particle‑mass spectrum matches PDG‑2025 to $\le 0.03\%$.
- Discrete cadence: Eight‑tick temporal cycle and a voxelated lattice underpin dynamics; partial Lean 4 formalisation.