Vacuum permeability μ₀
Vacuum permeability μ₀ is, in the τ-framework, a Tier-I (Established) unit-conversion entry of the constants ledger — the dimensional factor M L / Q² that, together with ε₀ and c, satisfies c² = 1/(ε₀ μ₀). It is exact in the τ-cascade at Layer 3.
τ-Definition
Vacuum permeability μ₀ is, in the τ-framework, a Tier-I (Established) unit-conversion entry of the constants ledger — the dimensional factor M L / Q² that, together with ε₀ and c, satisfies c² = 1/(ε₀ μ₀). It is exact in the τ-cascade at Layer 3.
Categorical invariant. μ₀ = M L / Q² — the magnetic-sector dimensional readout that closes the EM projection at E₁.
Primary registry anchor:
IV.D37
τ-Derivation Chain
SI Translation
Numerical value: 1.25663706212e-6 ± 1.9e-16 N A⁻²
Calibration anchor: PG-P01-neutron
Calibration chain:
- Layer 0: ι_τ = 2/(π + e_math)
- Layer 1: α = (11/15)² ι_τ⁴
- Layer 3: μ₀ = 1/(ε₀ c²) — exact within the cascade
- Pre-2019 SI: μ₀ = 4π × 10⁻⁷ N A⁻² exact; post-2019 SI: μ₀ inherits tiny uncertainty from α
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex