IndisputableMonolith.Relativity.GRLimit
The Relativity.GRLimit module establishes the parameter regime in which the Recognition Science functional equation recovers the Einstein field equations of general relativity. Cosmologists and quantum-gravity researchers would cite it when mapping the discrete phi-ladder onto classical spacetime. The module organizes its content as a sequence of limiting statements on J-cost and defect distributions that collapse to the Einstein-Hilbert action.
claimIn the limit where the rung index $r$ and gap parameter satisfy $r - 8 + g(Z) >> 1$, the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$ reduces to the Einstein equations $G_{ab} = 8pi T_{ab}$ with $c=1$, $G=phi^5/pi$.
background
Recognition Science starts from the single functional equation whose solutions are built on the J-cost $J(x)=(x+x^{-1})/2-1$ and the self-similar fixed point phi. The GRLimit module sits inside the relativity domain and supplies the classical limit of the eight-tick octave and the phi-ladder mass formula. It assumes the upstream forcing chain (T0-T8) has already fixed D=3 and the Berry threshold phi^{-1}.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the classical endpoint required by the UnifiedForcingChain, allowing the discrete mass formula yardstick * phi^(rung-8+gap(Z)) to pass to the continuum Einstein-Hilbert action. It therefore closes the loop from the Recognition Composition Law to observable general-relativistic dynamics.
scope and limits
- Does not compute explicit numerical values inside the alpha band.
- Does not address quantum corrections or the Berry creation threshold.
- Does not derive the eight-tick octave period from first principles.