Milgrom MOND acceleration a₀
The Milgrom MOND acceleration a₀ ≈ 1.2 × 10⁻¹⁰ m s⁻² is, in the τ-framework, derived as the gravity-sector readout a₀ = c²/(2 ℓ_τ), where ℓ_τ is the τ-derived horizon length anchored by the κ_τ coupling. It is a Layer-2/3 cascade output and is reframed by the τ-framework as a *capacity proxy* — not a fundamental dynamical scale, but the boundary-holonomy capacity of the dual sector.
τ-Definition
The Milgrom MOND acceleration a₀ ≈ 1.2 × 10⁻¹⁰ m s⁻² is, in the τ-framework, derived as the gravity-sector readout a₀ = c²/(2 ℓ_τ), where ℓ_τ is the τ-derived horizon length anchored by the κ_τ coupling. It is a Layer-2/3 cascade output and is reframed by the τ-framework as a *capacity proxy* — not a fundamental dynamical scale, but the boundary-holonomy capacity of the dual sector.
Categorical invariant. a₀ = c² / (2 ℓ_τ) — gravity-sector readout, with ℓ_τ as the τ-derived horizon length.
Primary registry anchor:
V.D232
τ-Derivation Chain
-
I.K0— Universe Postulate -
IV.D255— Master constant ι_τ -
V.D231— The ι_τ chain — κ_τ and ℓ_τ derived from ι_τ -
V.D232— Milgrom Constant from τ — a₀ = c²/(2ℓ_τ) -
V.T142— E₁ Completeness — a₀ as gravity-sector readout, capacity proxy
Lean modules referenced:
TauLib.BookV.Coda.ConstantsLedger,
TauLib.BookV.GravityField.CalibrationTriangle
SI Translation
Numerical value: 1.2e-10 ± 1e-11 m s⁻²
Calibration anchor: PG-P01-neutron
Calibration chain:
- Layer 0: ι_τ = 2/(π + e_math)
- Layer 1: κ_τ = 1 − ι_τ; ℓ_τ derived from κ_τ via the τ-horizon construction
- Layer 3: a₀ = c²/(2 ℓ_τ) ≈ 1.2 × 10⁻¹⁰ m s⁻²
- Reframed: a₀ is a *capacity proxy* of the dual sector, not a fundamental dynamical constant (V.P32)
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex