IndisputableMonolith.Gravity.ZeroParameterGravity
This module derives the Einstein gravitational coupling as κ = 8φ⁵ directly from the J-cost ledger, Law of Existence, and dimension forcing, with no free parameters introduced. Unified-physics researchers cite it when linking the Recognition framework to classical gravity. The structure proceeds through closed-form lemmas for κ, positivity proofs, and derivations of potential and equivalence principle as ledger consequences.
claimThe Einstein gravitational coupling satisfies $κ = 8φ^5$, where $φ$ is the golden-ratio fixed point of the J-function.
background
The module imports the RS time quantum τ₀ = 1 tick, the J-cost and Recognition Composition Law from Cost, the forcing of spatial dimension D = 3 from DimensionForcing, and the Law of Existence (x exists iff defect(x) = 0) from LawOfExistence. These supply the zero-parameter foundation: gravity emerges as a ledger effect on the phi-ladder once D = 3 is fixed. The local theoretical setting is the gravity sector of Recognition Science, where all couplings are determined by the eight-tick octave and phi^5 scaling.
proof idea
The module first defines kappa_rs via the phi-ladder scaling, proves its closed form and positivity by algebraic reduction from J-uniqueness and the phi fixed point, then derives gravitational potential and automatic equivalence principle as direct consequences of the ledger. Further lemmas establish the eight-tick implication and kappa bounds from the upstream forcing chain.
why it matters in Recognition Science
This module supplies the gravitational sector required by the SpacetimeEmergence module to force the complete 4D Lorentzian geometry. It realizes the T8 step of the UnifiedForcingChain by deriving κ = 8φ⁵ from the phi-ladder and Law of Existence, closing the zero-parameter path from defect-free existence to classical gravity.
scope and limits
- Does not derive the full Einstein field equations from the ledger.
- Does not incorporate quantum corrections or higher-order terms.
- Does not address the cosmological constant or dark-energy contributions.
- Does not extend to modified-gravity or higher-dimensional models.
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