gravitational_potential
plain-language theorem explainer
Gravitational potential is defined as -G M / r in RS-native units with G fixed by the phi-ladder. Researchers deriving zero-parameter gravity from ledger curvature cite this as the explicit Newtonian form emerging from J-cost. The definition is a direct one-line assignment of the standard expression using the RS-derived constant.
Claim. The gravitational potential at distance $r$ from mass $M$ is given by $Φ(M,r) = -G M / r$, where $G$ is the Recognition Science gravitational constant obtained from the forcing chain.
background
The Zero-Parameter Gravity module formalizes gravity as the large-scale curvature of the ledger lattice induced by defect distributions (G-001). It imports the RS-native $G = λ_rec² c³ / (π ℏ)$ from Constants together with LawOfExistence and DimensionForcing to ground the three-dimensional spatial structure and eight-tick octave. The J-cost functional equation supplies the underlying cost measure from which masses and potentials emerge.
proof idea
This is a direct definition that sets gravitational_potential M r to the expression -G * M / r. No lemmas or tactics are applied; it is the base expression for the sibling negativity result.
why it matters
This definition supplies the explicit potential used to prove negativity for positive mass and distance in potential_negative. It realizes G-001 by providing the Newtonian limit from the J-cost framework, with G determined by phi^5 / pi in native units, and supports the automatic equivalence principle since inertial and gravitational mass both trace to the same J-cost.
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