IndisputableMonolith.Relativity.ILG.ClusterLensing
The ClusterLensing module supplies RS-locked definitions for gravitational lensing parameters in cluster contexts, centered on the power-law exponent α_RS. Physicists modeling modified gravity or RS cosmology cite these for scale-consistent predictions. It is a pure definition module importing only Constants and Mathlib, with no proofs.
claim$α_{RS} = (1 - φ^{-1})/2 ≈ 0.191$, together with lag correction $C_{lag,RS}$, weight functions $w_{RS}$, κ ratios, and first-order bounded lensing corrections.
background
This module sits in the Relativity domain and imports the fundamental RS time quantum τ₀ = 1 tick from IndisputableMonolith.Constants. It introduces cluster-lensing quantities built on the J-cost function, phi-ladder scaling, and the Recognition Composition Law. The local setting assumes self-similar fixed-point behavior for φ and the eight-tick octave structure.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The definitions supply the RS-locked inputs required by parent lensing theorems in the ILG framework. They ensure consistency with the alpha band (137.030, 137.039) and the mass formula on the phi-ladder, closing the parameter gap for cluster-scale predictions.
scope and limits
- Does not derive α_RS from the forcing chain T0-T8.
- Does not include numerical lensing simulations or data fits.
- Does not prove positivity or boundedness of the weight functions.
- Does not address higher-order or strong-lensing regimes.