The Torsional Manifold: The Dimensional Origin of Physical Law

// This document is now superseded by: The Torsional Manifold - A Parameter-Free Derivation of Physical Law from the Geometry of S5 / Rossing Öberg, Tor // Version 2 removed an erroneous graph for the energy budget that snuck into the compilation. adresses the observer issue lightly Ninety-five percent of the universe is supposedly missing. Four decades of searches have found nothing. We propose that nothing is missing — the dark sector is a bookkeeping error.The Torsional Origin of Relativity (TOR) rests on two postulates: (1) physical time rate emerges from the balance between locked and free torsional degrees of freedom in spacetime, and (2) observation is restricted to a compatibility surface where stable matter and functioning clocks coexist. These postulates, combined with first-order relaxation mathematics, generate a complete gravitational theory with zero free parameters at galactic and cosmological scales.Every observable follows from one number: ε = 1 − e⁻¹ = 0.632, the fraction of any exponential relaxation that completes in one characteristic time. From it we derive the cosmic energy budget (Ωb = e⁻³, Ωm = e^(−3/e), ΩΛ = e^(−3/e²), summing to unity), the MOND acceleration scale (a₀ = cH₀ε⁴ = 1.05 × 10⁻¹⁰ m/s²), and galaxy rotation curves across 153 SPARC galaxies with zero fitted parameters (mean residual +0.039 dex). The Hubble tension dissolves: geometry and clocks measure different quantities, and their 5σ disagreement is predicted, not anomalous.The Hubble parameter is derived from fundamental constants: H₀ = Gm³_p c/ℏ² × ε¹⁸ = 67.5 km/s/Mpc, matching Planck to 0.1%. The BAO-anchored geometric backbone passes BAO rulers (χ²/dof = 0.92) and Pantheon+ supernovae (Δχ² = −14.6 vs ΛCDM). Every exponent in the theory — 3, 4, 7, 11, 18, 22, 44, 88 — is an integer-coefficient polynomial in the spatial dimensions d = 3 and spacetime dimensions D = 4. The complete theory traces to the dimensionality of the manifold, ℏ, m_p, and e = 2.71828…