τ-Joule
The τ-Joule is the natural unit of energy in the τ-framework: a structural energy scale derived from the master constant ι_τ and the dimensional bookkeeping of the calibration cascade. SI joules are recovered by multiplying the τ-Joule by a dimensionless ι_τ-chain factor and the m_n-anchored energy scale m_n c_τ².
τ-Definition
The τ-Joule is the natural unit of energy in the τ-framework: a structural energy scale derived from the master constant ι_τ and the dimensional bookkeeping of the calibration cascade. SI joules are recovered by multiplying the τ-Joule by a dimensionless ι_τ-chain factor and the m_n-anchored energy scale m_n c_τ².
Categorical invariant. Natural-unit energy J_τ = m_n c_τ²; mass-energy equivalence applied to the calibration anchor.
Primary registry anchor:
IV.D255
τ-Derivation Chain
-
I.K0— Universe Postulate establishes τ -
I.D34— Master constant ι_τ ≈ 0.341304 emerges from the categorical kernel -
IV.D255— ι_τ at the E₁ physics layer governs the dimensional cascade -
V.D231— The ι_τ-chain assembles c_τ and ℏ_τ from ι_τ -
V.T157— Calibration Sufficiency: m_n c_τ² fixes the SI energy scale
Lean modules referenced:
TauLib.BookV.Coda.CalibrationChain
SI Translation
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- c_τ via ι_τ chain (Established tier; algebraic identity)
- natural energy scale E_τ = m_n c_τ²
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex
Lean Coverage
See Also
Related glossary entries
Referenced by
Cross-domain bridges
This glossary term sits on the boundary between domains. The τ-framework's cross-domain pivots are the structural junctions where physics, life, and metaphysics readouts meet.