pith. sign in
module module high

IndisputableMonolith.Gravity.ZeroParameterGravity

show as:
view Lean formalization →

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

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (4)

Lean names referenced from this declaration's body.

declarations in this module (12)