IndisputableMonolith.Gravity.ZeroParameterGravity
This module derives the Einstein gravitational coupling as κ = 8φ⁵ from Recognition Science without free parameters. Physicists studying unification or quantum gravity would cite it for replacing G with a forced constant. The argument assembles results on J-cost defects, existence via zero defect, and D = 3 to obtain gravitational potential from the phi-ladder.
claimThe Einstein gravitational coupling in RS units satisfies $\kappa = 8\phi^5$.
background
The module sits in the Gravity domain and imports Constants (τ₀ = 1 tick), Cost (J-cost and Recognition Composition Law), LawOfExistence (x exists iff defect(x) = 0), and DimensionForcing (D = 3 forced by four arguments). These supply the ledger defects and phi-ladder on which gravitational potential is built. The module doc-comment states the RS prediction for the Einstein gravitational coupling: κ = 8φ⁵, derived not assumed.
proof idea
The module consists of a sequence of theorems (kappa_rs, gravitational_potential, gravity_from_ledger, etc.). Each applies upstream lemmas from LawOfExistence and DimensionForcing via short algebraic reductions or one-line wrappers that invoke the Recognition Composition Law to express the coupling in terms of φ.
why it matters in Recognition Science
This module supplies the gravitational sector required by the downstream SpacetimeEmergence module, which forces the full Lorentzian geometry from J-cost. It realizes the T8 step (D = 3) in the forcing chain and supplies the derived coupling that enters the Einstein equations, closing a free parameter in the RS framework.
scope and limits
- Does not assume a value for G or κ.
- Does not extend beyond classical gravity.
- Does not incorporate matter fields or sources.
- Does not prove stability of the derived κ under perturbations.
used by (1)
depends on (4)
declarations in this module (12)
-
def
kappa_rs -
theorem
kappa_pos -
theorem
kappa_rs_closed_form -
theorem
kappa_ne_zero -
theorem
equivalence_principle_automatic -
def
gravitational_potential -
theorem
potential_negative -
theorem
gravity_from_ledger -
theorem
gravity_from_ledger_implies_eight_tick -
theorem
gravity_from_ledger_implies_kappa_pos -
theorem
gravity_from_ledger_implies_kappa_ne_zero -
theorem
kappa_bounds