Boltzmann constant k_B
The Boltzmann constant k_B is, in the τ-framework, a Layer-3 SI unit-conversion entry — exact by 2019 SI definition (k_B fixes the kelvin) and adopted verbatim by the τ-cascade. It carries no τ-prediction beyond consistency: it is a thermodynamic unit-conversion, not a sector readout.
τ-Definition
The Boltzmann constant k_B is, in the τ-framework, a Layer-3 SI unit-conversion entry — exact by 2019 SI definition (k_B fixes the kelvin) and adopted verbatim by the τ-cascade. It carries no τ-prediction beyond consistency: it is a thermodynamic unit-conversion, not a sector readout.
Categorical invariant. k_B = (M L² H² / Θ) — the dimensional unit-conversion that defines the kelvin in the (M, L, ℏ, Θ) projection.
Primary registry anchor:
IV.P139
τ-Derivation Chain
-
I.K0— Universe Postulate -
IV.D255— Master constant ι_τ -
IV.P139— Status of Boltzmann constant — k_B as thermodynamic unit conversion -
V.T142— E₁ Completeness — k_B is a Tier-I unit conversion that the cascade exhausts at Layer 3
Lean modules referenced:
TauLib.BookIV.Calibration.SIReference,
TauLib.BookV.Coda.ConstantsLedger
SI Translation
Numerical value: 1.380649e-23 ± 0 J K⁻¹
Calibration anchor: PG-P01-neutron
Calibration chain:
- Layer 0: ι_τ = 2/(π + e_math)
- Layer 3: k_B = 1.380 649 × 10⁻²³ J K⁻¹ — exact by 2019 SI definition (fixes the kelvin)
- k_B carries no τ-prediction; it is a thermodynamic unit conversion adopted verbatim from SI
- k_B enters Stefan-Boltzmann, ideal gas R, and BH entropy S_BH = k_B A / (4 ι_τ²) (entry #25)
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex