Dark Geometry
Hugo Hertault
Dark Geometry derives approximately 170 quantitative predictions, coupling constants, particle masses, cosmological parameters, from a single axiom and zero free parameters. Average agreement with experiment: less than 2%.
The Hertault Axiom: the conformal mode of spacetime equals the local information saturation ratio. From this, combined with d = 3 spatial dimensions, the entire framework follows.
d = 3 → θH = 35.26° → β, α*, ξ → ~170 predictions
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Book Zero — Behind The Horizon
Self-contained introduction for readers without technical background.
Covers all five volumes in plain language, with step-by-step derivations of β = 2/3, the Dark Boson mass function, the critical density, α* = 0.075, and the coupling constants. Includes accessible treatments of the Yang–Mills mass gap and the Riemann Hypothesis.
Book I — Informational Relativity
Cosmological framework.
Hubble tension resolved: H0(SH0ES)/H0(Planck) = 11/10 exactly (Tier A). σ8 tension: 0.0σ vs KiDS-1000 (Tier B). Dark energy fraction Ω_Λ = 2/3. Three equivalent formulations: IDG, QGU, HDG. Celestial holography: c = 24β = 16.
Book II — Informational Geometry
Complete particle mass spectrum from the Rosen–Morse potential.
Gauge couplings: α_em = sin(θH)/(8π²), α_s = sin(2θH)/8, sin²θW = 3/13. Higgs mass: 125.07 GeV (0.10%). Proton/electron mass ratio: 6π⁵ (19 ppm). Neutrino mass ratio: 1/34. Zero free parameters.
Book III — Quantum Geometry
Spacetime as a MERA tensor network of qutrits, bond dimension χ = d = 3.
Big Bang as quantum bounce. Black hole entropy correction: −(1/3) ln S_BH. CMB hemispherical asymmetry A = 1/17 ≈ 6%, single cascade axis testable by CMB-S4/LiteBIRD. 18 new falsifiable predictions.
Book IV — The Holographic Fibration
Rigorous mathematical theory of the information fibre F = (0,1] as a multiplicative monoid.
Yang–Mills mass gap: Δ² ≥ 0.18003 GeV² (Tier A/B, 8-step proof). Spectral identity: ζ_F(s;π) = ζ_R(2s) — the Riemann zeta function is the spectral zeta of spacetime. Five equivalent formulations of the Riemann Hypothesis. GUE universality of Riemann zeros from holographic irreversibility.
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Falsifiable predictions currently under experimental test
DESI/Euclid — dark energy equation of state w_a ≈ 0.10
JUNO (2030) — neutrino mass ratio → 1/34
CMB-S4/LiteBIRD — single cascade axis for all four CMB anomalies
Hyper-Kamiokande — proton lifetime ~10⁴⁰ yr
Einstein Telescope — gravitational wave echoes
Laboratory (YbB₁₂) — surface/bulk conductivity ratio → 2, Fibonacci frequency ratios, transport exponent β = 2/3
This community welcomes contributions that directly engage with the Dark Geometry framework. Proposals based on independent theoretical frameworks not connected to the Hertault Axiom or the holographic fibration are outside the scope of this community.