GravityLedgerCorrespondence
plain-language theorem explainer
GravityLedgerCorrespondence encodes the direct identification of mass with ledger density and curvature with local strain inside the RRF gravity module. A researcher deriving gravitational geometry from transaction constraints would cite the structure when confirming that the ledger model reproduces flat vacuum and positive curvature from strain. The definition is realized by a direct construction that discharges the three axioms via reflexivity and targeted simplification.
Claim. The structure asserts that mass derived from any spatial ledger $L$ equals the ledger density; that curvature computed from local strain $S$ at positive scale factor $κ$ satisfies $R = κ · J$; and that curvature of the vacuum ledger at unit scale is identically zero.
background
In the RRF foundation module, gravity is introduced as the geometric manifestation of ledger constraint density. A SpatialLedger is a local record containing transaction density (transactions per unit volume), a non-negative density guarantee, integer charge, and the balance constraint that charge equals zero. LocalStrain is the companion structure holding a non-negative real value $J$ that quantifies constraint tightness at a point.
proof idea
The structure is populated by the downstream definition gravity_ledger_consistent. That definition supplies reflexivity for the mass-density and curvature-strain identities and applies simplification to the vacuum ledger expressions involving curvatureFromStrain and strainFromLedger.
why it matters
The structure supplies the core correspondence consumed by gravity_interpretation_valid (which proves the instance is nonempty) and by gravity_ledger_consistent (which constructs the witness). It realizes the module's central claim that gravity is collective ledger strain rather than an independent force, consistent with the Recognition Science reduction of geometry to constraint density. No open scaffolding is discharged.
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