Newton's gravitational constant G

Newton's gravitational constant G is, in the τ-framework, a derived structural ratio that emerges from the gravity-sector embedding of ι_τ in the categorical bridge. It is not a fundamental free parameter but a τ-categorical invariant fixed by the structural cascade.

Categorical invariant. G = (gravity-sector embedding of ι_τ-chain) · (dimensional factor from m_n anchor and c, ℏ derivations).

Primary registry anchor: V.D45

Supporting items: IV.D05, V.R69, V.P58

1. I.K0 — Universe Postulate
2. I.D34 — Master constant ι_τ
3. IV.D05 — Gravity Sector at E₁ — gravity emerges as a categorical sector
4. V.R69 — Newton's gravitation derived from τ-categorical structure
5. V.P58 — Newton's First Law as categorical limit
6. V.D45 — Gravitational constant G as derived structural ratio

Lean modules referenced: TauLib.BookV.GravityField.CalibrationTriangle

Numerical value: 6.67430e-11 ± 1.5e-15 m³ kg⁻¹ s⁻²

Calibration anchor: PG-P01-neutron

Calibration chain:

1. m_n (anchor)
2. ι_τ-derived gravity-sector coupling
3. (M, L, ℏ) cascade via ι_τ-chain
4. G = (gravity-sector ratio) × (kg^{-1} m^3 s^{-2} from cascade)

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

Status: Formalized

Module: TauLib.BookV.GravityField.CalibrationTriangle

Lean kind: def

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-Q01-mass Mass

Referenced by

• PG-C02-iota-tau Master constant ι_τ
• PG-C03-speed-of-light Speed of light c
• PG-C04-planck-hbar Planck's reduced constant ℏ
• PG-C05-fine-structure-alpha Fine-structure constant α
• PG-C13-planck-mass Planck mass m_P
• PG-C14-gravitational-fine-structure Gravitational fine-structure constant α_G
• PG-C18-kappa-tau Gravity-sector coupling κ_τ
• PG-C19-milgrom-acceleration Milgrom MOND acceleration a₀
• PG-O01-hydrogen-atom Hydrogen Atom
• PG-O11-black-hole Black Hole
• PG-O12-neutron-star Neutron Star