τ-Kelvin

The τ-Kelvin is the natural unit of temperature in the τ-framework: a structural temperature scale derived from the τ-Joule via the Boltzmann constant analog. SI kelvins are recovered by multiplying the τ-Kelvin by a dimensionless ι_τ-chain factor and the m_n-anchored energy scale (m_n c_τ²)/k_B,τ.

Categorical invariant. Natural-unit temperature K_τ = (m_n c_τ²) / k_B,τ; the calibration-anchor mass-energy scaled by the τ-Boltzmann constant.

Primary registry anchor: IV.D255

Supporting items: I.D34, V.D231, V.T157

1. I.K0 — Universe Postulate establishes τ
2. I.D34 — Master constant ι_τ ≈ 0.341304 emerges from the categorical kernel
3. IV.D255 — ι_τ at the E₁ physics layer governs the dimensional cascade
4. V.D231 — The ι_τ-chain assembles the energy scale m_n c_τ² and the τ-Boltzmann constant
5. V.T157 — Calibration Sufficiency: ι_τ + m_n fix the SI temperature scale via E = k_B T

Lean modules referenced: TauLib.BookV.Coda.CalibrationChain

Calibration anchor: PG-P01-neutron

Calibration chain:

1. m_n (anchor)
2. c_τ via ι_τ chain (Established tier)
3. k_B,τ (τ-Boltzmann constant, Established tier)
4. natural temperature scale T_τ = (m_n c_τ²) / k_B,τ

Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex

Status: Formalized

Module: TauLib.BookV.Coda.CalibrationChain

Lean kind: def

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-U04-tau-joule τ-Joule