IndisputableMonolith.Gravity.Gravity
Gravity layer that packages the Recognition cost on spatial domains, a positive canonical threshold, and a 3D tidal-deformation certificate. Relativists and RS auditors cite it when tying the J-cost to weak-field gravity and multipole response. The module is mostly definitions plus nonnegativity and positivity lemmas, closed by an inhabited certificate bundle.
claimOn a spatial domain one has a cost $C(\Omega)\ge 0$ built from the Recognition $J$-functional, a canonical threshold $\tau_*>0$, and a certificate that the tidal deformation response in $D=3$ is well-defined and inhabited.
background
Recognition Science forces $D=3$ spatial dimensions (T8) and a unique cost $J(x)=(x+x^{-1})/2-1$. Gravity is read off as the continuum limit of that cost on spatial domains, with $G=\phi^5/\pi$ in RS-native units.
This module sits on Constants (tick quantum $\tau_0$) and Cost (the $J$-calculus). It introduces a domain cost $C(\Omega)$, its evaluation identity and nonnegativity, a strictly positive canonical threshold, and a tidal-deformation certificate in three dimensions. The certificate is the Lean stand-in for the claim that the multipole/tidal response of the RS cost is under control in $D=3$.
proof idea
Definition-heavy module, not a single deep theorem. Domain cost is defined from the imported $J$-cost; equality-at-point and nonnegativity are short algebraic lemmas. Canonical threshold is a positive constant with a positivity proof. The tidal package is a structure TidalDeform3Cert plus an inhabited instance cert, so downstream code can assume a 3D tidal certificate without rebuilding the data.
why it matters in Recognition Science
Supplies the gravity-side cost and threshold primitives that later RS gravity and phenomenology modules expect. The $D=3$ tidal certificate aligns with the forcing-chain step T8 (three spatial dimensions) and with the continuum reading of $J$ as the seed of Newtonian and post-Newtonian response. No downstream edges are recorded on this page; the module is a local gravity foundation rather than a leaf theorem.
scope and limits
- Does not derive Einstein equations or full GR field dynamics.
- Does not compute numerical Love numbers or observational tidal constraints.
- Does not prove uniqueness of the domain cost beyond the imported $J$-calculus.
- Does not treat $D\neq 3$ or higher-dimensional tidal response.
- Does not fix cosmological constant or strong-field horizons.