τ-Coulomb
The τ-Coulomb is the natural unit of electric charge in the τ-framework: a structural charge scale derived from the master constant ι_τ via the fine-structure cascade α = (11/15)² ι_τ⁴. SI coulombs are recovered through the elementary charge e = √(4π ε₀ α ℏ c) once α and ℏ are fixed by ι_τ and m_n.
τ-Definition
The τ-Coulomb is the natural unit of electric charge in the τ-framework: a structural charge scale derived from the master constant ι_τ via the fine-structure cascade α = (11/15)² ι_τ⁴. SI coulombs are recovered through the elementary charge e = √(4π ε₀ α ℏ c) once α and ℏ are fixed by ι_τ and m_n.
Categorical invariant. Natural-unit charge C_τ defined via the ι_τ-cascade: e_τ² = 4π ε₀,τ α_τ ℏ_τ c_τ with α_τ = (11/15)² ι_τ⁴.
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 produces α = (11/15)² ι_τ⁴ via the boundary holonomy algebra -
V.T157— Calibration Sufficiency: ι_τ + m_n fix the SI charge scale via e = √(4π ε₀ α ℏ c)
Lean modules referenced:
TauLib.BookIV.Calibration.DimensionlessAlpha,
TauLib.BookV.Coda.CalibrationChain
SI Translation
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- ι_τ ≈ 0.341304 (master constant)
- α = (11/15)² ι_τ⁴ ≈ 0.0072974 (9.8 ppm against CODATA)
- ε₀,τ via Established-tier algebraic identity
- e = √(4π ε₀ α ℏ c)
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex
Lean Coverage
See Also
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.