Gravitational fine-structure constant α_G
The gravitational fine-structure constant α_G is, in the τ-framework, the dimensionless gravity-sector coupling, derived as α_G = α¹⁸ √3 (1 − (3/π)α). It is the right-hand side of the unique zero-parameter G–α bridge identity (V.T154) — the only known equation in physics that relates G and α with no free parameters.
τ-Definition
The gravitational fine-structure constant α_G is, in the τ-framework, the dimensionless gravity-sector coupling, derived as α_G = α¹⁸ √3 (1 − (3/π)α). It is the right-hand side of the unique zero-parameter G–α bridge identity (V.T154) — the only known equation in physics that relates G and α with no free parameters.
Categorical invariant. α_G = α¹⁸ √3 (1 − (3/π)α) — the gravity-EM crossing readout at the lemniscate boundary.
Primary registry anchor:
IV.P245
τ-Derivation Chain
-
I.K0— Universe Postulate -
IV.D255— Master constant ι_τ -
IV.D407— α = (11/15)² ι_τ⁴ -
IV.P245— Gravitational Fine Structure Constant — α_G as gravity-sector coupling -
V.T154— G–α Bridge — α_G = α¹⁸ √3 (1 − (3/π)α) -
V.P115— Hierarchy as Power Law — α/α_G = 1/[α¹⁷ √3 (1 − (3/π)α)]
Lean modules referenced:
TauLib.BookV.Coda.GAlphaBridge,
TauLib.BookV.Coda.ConstantsLedger
SI Translation
Numerical value: 5.924e-39 ± 1.8e-44 dimensionless
Calibration anchor: PG-P01-neutron
Calibration chain:
- Layer 0: ι_τ = 2/(π + e_math)
- Layer 1: α = (11/15)² ι_τ⁴
- Layer 1: α_G = α¹⁸ √3 (1 − (3/π)α) ≈ 5.924 × 10⁻³⁹
- Hierarchy: α/α_G = α⁻¹⁷ · √3⁻¹ ≈ 10³⁶ — not a fine-tuning, just the seventeenth power of α⁻¹
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex
Lean Coverage
See Also
Related glossary entries
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.