IndisputableMonolith.ILG.Reciprocity
ILG.Reciprocity defines the dimensionless variable X = k τ₀ / a and its reciprocity identities for the Infra-Luminous Gravity kernel. Cosmologists deriving first-order growth corrections cite it when building the prefactor in the GrowthODE module. The module supplies definitions and algebraic identities on top of the imported kernel formalization.
claim\( X = k \tau_0 / a \), with the ILG kernel weight \( w(k,a) = 1 + C (a / (k \tau_0))^\alpha \).
background
The upstream ILG.Kernel module formalizes the weight function as w(k, a) = 1 + C · (a / (k τ₀))^α where k is the wave number. This module introduces the dimensionless variable X = k τ₀ / a, which appears as the reciprocal argument in the kernel term. The theoretical setting is the Infra-Luminous Gravity framework for modified growth in cosmology.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module feeds the GrowthODE module, which derives the prefactor for the first-order ILG growth correction in EdS background by plugging D = a(1 + B a^α) into the growth ODE. It supplies the reciprocity structure for the dimensionless variable X required by that derivation.
scope and limits
- Does not derive the ILG kernel weight function.
- Does not compute the growth prefactor B.
- Does not address reciprocity in other variables.
- Does not extend to non-EdS backgrounds.