IndisputableMonolith.ILG.NOfRMono
This module supplies the radial shape factor n(r) for ILG together with an epsilon guard that keeps square roots defined during evaluation. Researchers verifying parameter kernels or radial profiles in Recognition Science cite it when checking monotonicity for non-negative A. The module reuses the canonical definition from ParamsKernel and consists of definitions without completed proofs.
claimThe module defines the guard constant $ε_r = 10^{-12}$ and the analytic global radial shape factor $n(r)$, together with the monotonicity statement $n'(r) ≥ 0$ whenever the parameter $A ≥ 0$.
background
The module sits inside the ILG component of Recognition Science and imports the parameter kernel verification predicate from IndisputableMonolith.ILG.ParamsKernel, which requires parameters to be well-formed before radial functions are applied. It introduces the noncomputable real constant εr set to 1e-12 as an internal guard that keeps square-root expressions defined. The central object is the analytic global radial shape factor n(r), presented as a reuse of a canonical definition.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the monotonic radial profile n(r) that downstream ILG constructions rely on when checking parameter kernels. It fills the role of providing the radial shape factor needed for later monotonicity arguments in the Recognition Science framework.
scope and limits
- Does not supply an explicit closed-form expression for n(r).
- Does not prove monotonicity; only states the property.
- Does not link n(r) to the phi-ladder, J-cost, or T5-T8 forcing chain.