Informational Relativity (IR)

Informational Relativity is Book I of the Dark Geometry series. It develops a framework in which dark matter and dark energy are not substances but two regimes of a single geometric field — the conformal mode of spacetime, the Dark Boson φDG = √6 MPl σ. Everything follows from a single axiom — the Hertault Axiom, e4σ = Sent/SBek (spacetime volume equals information content) — together with one empirical input: that space has three dimensions. The dimension d = 3 fixes the Hertault angle θH = arccos√(2/3) ≈ 35.26°, whose two beam-splitter channels — surface (cos²θH = 2/3) and bulk (sin²θH = 1/3) — organise every result. Key results (zero free parameters): Mass function unifying the dark sector: m²eff(ρ) = (α*MPl)²[1 − (ρ/ρc)2/3], changing sign at ρ = ρc. Dark-sector ratio ΩΛ/Ωm = 2, i.e. ΩΛ = 2/3 and Ωm = 1/3 (cosmic coincidence resolved). Hubble tension: H0(SH0ES)/H0(Planck) = 1 + ξ = 11/10, exact; geometric value H0 ≈ 70.3 km/s/Mpc. σ8 tension relieved to ≲1σ: σ8 ≈ 0.77–0.79, from a scale-dependent Geff. Coupling identity locking both tensions: Δn/ξ = 20/(27π²) ≈ 0.07503. Newton's constant derived: G4 = sin²θH/(8πM5³). Neutrino mass-squared ratio Δm²21/Δm²31 = 1/34 (Fibonacci F9). Cored halo profiles (no cusp), reduced satellite counts, and no gravitational slip (η = Ψ/Φ = 1). Conformal-mode ghost eliminated structurally: the Goroff–Sagnotti two-loop divergence is absent. Every result carries an epistemological tier (A: exact/proven; B: derived with stated approximations; C: conjectural). The framework is falsifiable through DESI, Euclid, Rubin/LSST, JUNO, CMB-S4, LIGO/LISA, and laboratory tests. Simulations and reproducible code: github.com/hugohertault Author: Hugo Hertault (Tahiti, French Polynesia).