gravity_interpretation_valid
The theorem asserts that a gravity-ledger correspondence exists in the RRF setting. Researchers modeling gravity via transaction density and constraint strain would cite it to ground the geometric interpretation. The proof is a one-line term wrapper that supplies the explicit consistent structure as witness.
claimThere exists a structure satisfying: for every spatial ledger $L$, mass equals ledger density; for every local strain $S$ and scalar $κ>0$, curvature $R$ obeys $R=κ·J(S)$; and vacuum strain produces zero curvature.
background
The RRF module treats gravity as the geometric manifestation of ledger constraint density, with mass identified as transaction count per volume and curvature as constraint pressure. The RRF abbreviation denotes the local non-sealed recognition field interface $(Fin 4 → ℝ) → ℝ$. GravityLedgerCorrespondence is the structure whose three fields encode the required mappings: mass_is_density, curvature_is_strain, and vacuum_is_flat.
proof idea
Term-mode proof. The declaration directly constructs the Nonempty witness by supplying the term gravity_ledger_consistent, whose three fields are discharged by reflexivity on the mass and curvature equations together with simp on the vacuum case.
why it matters in Recognition Science
The result validates the ledger-curvature interpretation inside the RRF foundation, confirming that gravity arises as collective strain from simultaneous ledger balancing rather than an external force. It rests on the upstream gravity_ledger_consistent construction and the RRF interface; no downstream theorems yet reference it, leaving open its integration with the eight-tick octave or phi-ladder mass formulas.
scope and limits
- Does not derive the correspondence from the T0-T8 forcing chain.
- Does not establish uniqueness of the mass-density or curvature-strain maps.
- Does not produce numerical predictions for G or alpha.
- Does not address time-dependent or quantum-ledger extensions.
formal statement (Lean)
161theorem gravity_interpretation_valid : Nonempty GravityLedgerCorrespondence :=
proof body
Term-mode proof.
162 ⟨gravity_ledger_consistent⟩
163
164end RRF.Foundation.Gravity
165end IndisputableMonolith