IndisputableMonolith.Gravity.ZeroParameterGravity
Derives the Einstein gravitational coupling as the closed form κ = 8φ⁵ in RS-native units, with positivity, nonvanishing, and automatic equivalence principle. Gravity theorists citing the zero-parameter RS gravity chain use this module for the fixed κ and ledger-origin implications. Argument packages definitions of κ, potential from defect density, and implication lemmas from gravity-from-ledger to eight-tick structure.
claimIn RS-native units the Einstein coupling is fixed by $\kappa = 8\varphi^5$, with $\kappa > 0$ and $\kappa \neq 0$. Gravity arises from ledger defect structure; that origin implies the eight-tick period and an automatic equivalence principle. The Newtonian potential extracted from defect density is negative.
background
Recognition Science treats gravity as emergent from a discrete recognition ledger rather than a fundamental force. The Einstein coupling $\kappa$ is the constant in $G_{\mu\nu} = \kappa T_{\mu\nu}$. In RS-native units one has $c = 1$ and $G = \varphi^5/\pi$ from the forcing chain, so $\kappa = 8\pi G = 8\varphi^5$ is predicted, not fitted.
The module imports Constants ($\tau_0 = 1$ tick), Cost (the $J$-cost functional), DimensionForcing (spatial $D = 3$ forced), and LawOfExistence ($x$ exists iff $\mathrm{defect}(x) = 0$). Sibling objects introduce $\kappa_{\mathrm{rs}}$, its closed form, positivity and bounds, a gravitational potential built from defect density, and the package gravity-from-ledger with implications for eight-tick structure and $\kappa \neq 0$.
Local setting: zero free parameters in the gravitational sector once $\varphi$ and the ledger axioms are fixed.
proof idea
Definition-first module, not a single theorem. It introduces $\kappa_{\mathrm{rs}}$ as the RS Einstein coupling, proves the closed form $\kappa = 8\varphi^5$ from the native $G$, then records positivity, nonvanishing, and elementary bounds. A gravitational potential is defined from ledger defect density and shown negative. The gravity-from-ledger package packages the discrete origin and discharges three implication lemmas: eight-tick period, $\kappa > 0$, and $\kappa \neq 0$. Equivalence principle is recorded as automatic once inertia and weight both track the same defect structure. No continuum or nonlinear EFE work lives here.
why it matters in Recognition Science
Anchors the zero-parameter gravity claim: $\kappa$ is derived from $\varphi$, matching the primer identity $G = \varphi^5/\pi$. Downstream continuum and field-equation modules import it directly: ContinuumManifoldEmergence (ledger sites to Lorentzian manifold and Einstein equations), FullEFE (nonlinear sourced EFE from the lattice), MetricFromDefect (metric perturbation from $J$-cost defect density), CubicReggeProof and UnifiedLatticeManifoldCorrespondence (Regge convergence on the deformed cubic lattice), NoGraviton (gravity emergent, not force-mediated), ZeroFreeParameters, and SpacetimeEmergence. Without a fixed $\kappa$ and the ledger-origin lemmas, those bridges cannot close the discrete-to-continuum chain or the G-004 graviton resolution.
scope and limits
- Does not derive the full nonlinear Einstein field equations.
- Does not prove continuum or Regge convergence to the Einstein-Hilbert action.
- Does not construct the metric perturbation field $h_{\mu\nu}$.
- Does not address graviton existence beyond supplying $\kappa$ and ledger origin.
- Does not fit or float $\kappa$; the value is fixed by $\varphi$ alone.
used by (8)
-
IndisputableMonolith.Gravity.ContinuumManifoldEmergence -
IndisputableMonolith.Gravity.CubicReggeProof -
IndisputableMonolith.Gravity.FullEFE -
IndisputableMonolith.Gravity.MetricFromDefect -
IndisputableMonolith.Gravity.NoGraviton -
IndisputableMonolith.Gravity.UnifiedLatticeManifoldCorrespondence -
IndisputableMonolith.Gravity.ZeroFreeParameters -
IndisputableMonolith.Unification.SpacetimeEmergence
depends on (4)
declarations in this module (12)
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def
kappa_rs -
theorem
kappa_pos -
theorem
kappa_rs_closed_form -
theorem
kappa_ne_zero -
theorem
equivalence_principle_automatic -
def
gravitational_potential -
theorem
potential_negative -
theorem
gravity_from_ledger -
theorem
gravity_from_ledger_implies_eight_tick -
theorem
gravity_from_ledger_implies_kappa_pos -
theorem
gravity_from_ledger_implies_kappa_ne_zero -
theorem
kappa_bounds