module module high

`IndisputableMonolith.RRF.Foundation.Gravity`

The Gravity module defines ledger-based structures for gravitational modeling inside the RRF Foundation. It introduces SpatialLedger as local density at a point, derives LocalStrain and ScalarCurvature, and states that gravity equals ledger curvature. Researchers building ledger alternatives to Einstein gravity cite these constructions. The module consists of definitions plus elementary non-negativity and vacuum-zero theorems proved with real arithmetic and linarith.

claimA local ledger is the density function $L(x)$ at spatial point $x$. Strain is obtained via strainFromLedger$(L)$, curvature via curvatureFromStrain, and gravity_is_ledger_curvature asserts gravity equals the resulting scalar curvature.

background

This module belongs to the foundational layer of the Reality Recognition Framework. The parent module IndisputableMonolith.RRF.Foundation states it contains the single foundational axiom (MP), physical constants derived from φ, and double-entry bookkeeping and conservation for the Ledger. The Gravity submodule specializes the ledger concept to spatial points for gravity, defining density, strain, and curvature while proving basic ledger properties such as non-negative mass and zero vacuum strain.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module feeds the parent RRF.Foundation, which houses the MetaPrinciple, φ-derived constants, and Ledger conservation. Its ledger-to-curvature identification supplies the gravity-specific bookkeeping needed to embed gravitational effects inside the double-entry framework.

scope and limits

Does not derive the Newtonian limit or geodesic motion.
Does not produce numerical values for G or the alpha band.
Does not address time-dependent or cosmological solutions.
Does not connect to the phi-ladder mass formula or T5-T8 forcing chain.

used by (1)

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

IndisputableMonolith.RRF.Foundation module_import

declarations in this module (22)

structure SpatialLedger L26
def vacuumLedger L37
def massiveLedger L45
def massFromSpatialLedger L55
theorem mass_nonneg L58
theorem vacuum_has_zero_mass L61
structure LocalStrain L66
def strainFromLedger L73
theorem vacuum_has_zero_strain L79
structure ScalarCurvature L87
def curvatureFromStrain L92
theorem gravity_is_ledger_curvature L97
def G_Newton L107
def newtonGravity L110
def ledgerGravity L113
theorem ledger_equals_newton L117
structure LedgerDeadlock L123
def schwarzschildRadius L132
structure InsideSchwarzschild L135
structure GravityLedgerCorrespondence L144
def gravity_ledger_consistent L154
theorem gravity_interpretation_valid L161