IndisputableMonolith.Relativity.ILG.LensingDerived
This module derives gravitational lensing within the ILG component of Recognition Science relativity. It connects the J-cost functional and phi-ladder mass assignments to light deflection angles. The argument composes the Recognition Composition Law across the eight-tick octave to recover the standard deflection formula in the weak-field limit.
claimThe module defines the derived lensing deflection angle as $4GM/(c^2 b)$ where $M$ is obtained from the phi-ladder yardstick and $b$ is the impact parameter, under the J-cost and RCL composition in three spatial dimensions.
background
The module sits inside the Relativity domain and builds directly on the ILG axioms that encode the J-function $J(x)=(x+x^{-1})/2-1$ together with the Recognition Composition Law. It assumes the forcing chain results T5 through T8 that fix phi as the self-similar point, enforce the eight-tick octave, and set D=3. No new constants are introduced; the module re-uses the RS-native values $c=1$, $G=phi^5/pi$.
proof idea
This is a definition module, no proofs. It organizes the lensing derivation as a sequence of RCL applications to the phi-ladder mass formula followed by the weak-field limit extraction.
why it matters in Recognition Science
The module supplies the explicit lensing map required by downstream relativity theorems that recover observational predictions from the T0-T8 chain. It closes the link between the mass formula yardstick*phi^(rung-8+gap(Z)) and measurable light deflection, feeding directly into any parent result that extracts GR-like limits from Recognition Science.
scope and limits
- Does not treat strong-field lensing or caustics.
- Does not incorporate higher-order phi-ladder corrections beyond the leading term.
- Does not address lensing by extended or time-varying sources.