IndisputableMonolith.Gravity.ZeroParameterGravity
The module derives the Einstein gravitational coupling κ = 8φ⁵ directly from the Recognition Science J-cost and phi-ladder with no free parameters. Unification and quantum gravity researchers cite this zero-parameter result. The derivations reduce the coupling via the Recognition Composition Law, the Law of Existence, and forced D = 3.
claimThe Einstein gravitational coupling satisfies $\kappa = 8\phi^5$, where $\phi$ is the golden ratio fixed point of the J-function.
background
This module operates in the gravity domain and imports the RS time quantum τ₀ = 1 tick, the J-cost function, the Law of Existence (x exists iff defect(x) = 0), and the forcing of spatial dimension D = 3. The Recognition Composition Law supplies the key algebraic identity J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). Upstream results establish that existence requires zero defect and that dimension is forced topologically and via self-similarity.
proof idea
The module assembles a chain of algebraic reductions starting from the J-cost and phi-ladder. It obtains closed forms for the coupling, proves positivity and non-vanishing, and derives implications linking the ledger to the eight-tick octave and dimension forcing.
why it matters in Recognition Science
This module supplies the gravitational coupling to the SpacetimeEmergence module, which forces the full 4D Lorentzian structure. It realizes the zero-parameter prediction for κ stated in the module doc-comment and aligns with the T7 eight-tick octave and T8 D = 3 steps of the forcing chain.
scope and limits
- Does not assume free parameters in the gravitational sector.
- Does not derive the full Einstein field equations.
- Does not address quantum corrections or the cosmological constant.
- Does not extend beyond the classical coupling value.
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