Informational Dark Geometry (IDG)

Informational Dark Geometry (IDG) — The Hertault Axiom and the Four Laws of Informational ThermodynamicsH. Hertault (2026). 30 pages. The informational and thermodynamic face of the programme. The framework rests on the Hertault axiom e4σ(x) = I(x) = Sent(x)/SBek(x), identifying the conformal mode of the metric with the local informational saturation ratio. The paper proves this is the unique continuous section of the holographic fibration satisfying four physical conditions (the Uniqueness Theorem), and develops its algebraic, thermodynamic, dynamical and observational consequences. The principal results The conformal mode carries zero propagating degrees of freedom (Dirac analysis), resolving the conformal-factor problem structurally and eliminating the two-loop Goroff–Sagnotti divergence. Classical thermodynamics is recovered as the I « 1 emergent limit of four informational laws (zeroth, first, second, third), in which the information ratio I plays the role conventionally played by temperature. Each informational law corresponds, at null infinity, to a Bondi–Metzner–Sachs (BMS) Ward identity — the bulk–boundary dictionary. The dark sector emerges as the over/under-saturated regimes of a single field with mass function meff2(ρ) = (α*MPl)2[1 − (ρ/ρc)β] and exponent β = (d−1)/d = 2/3. Black-hole thermodynamics as theorems: the Bekenstein–Hawking entropy law, the Hawking temperature, the Page curve tPage = (1 − 2−3/2)tevap, and the scrambling time tscr = (rs/c)ln SBH. The unified logarithmic correction clogtotal = 11/6, decomposed into the LQG gauge-fixing contribution (3/2) and the conformal-mode contribution (1/3). The Hubble tension resolved algebraically by the monoid identity H0SH0ES/H0Planck = 11/10. The σ8/S8 tension relieved by the non-minimal coupling ξ = 1/10: σ8IDG = 0.766, i.e. S8IDG ≈ 0.78, within ∼1σ of the weak-lensing surveys in the observable they report. Architecture The paper is organised from the axiom and its uniqueness, through the beam-splitter algebra and the four laws, to black-hole thermodynamics, the information paradox, the QFT of the conformal mode, the BMS dictionary, and the “five faces of quantum gravity as projections of θH”. The Dark Boson mass is given in different astrophysical environments (full-Planck convention, α*MPl = 9.2 × 1017 GeV, cross-referenced to the reduced convention of the w(z) companion). Every claim carries its tier (A/B/C); the only empirical input is d = 3.