IndisputableMonolith.ILG.ISWSign
The ISWSign module defines the ISW driver B(a,k) = -1 + f + dlnw/dlna in the ILG framework. It assembles the expression from the imported kernel w(k,a) and the growth prefactor B derived in GrowthODE. Cosmologists working on modified gravity corrections to large-scale structure would cite this module for the first-order EdS growth term. The module consists of definitions and basic sign properties for the driver and its components.
claim$B(a,k) = -1 + f + dlnw/dln a$, where $w(k,a) = 1 + C (a/(k τ_0))^α$ is the ILG kernel and $f$ is the growth rate.
background
ILG formalizes Infra-Luminous Gravity through the kernel module, where w(k,a) = 1 + C · (a / (k τ₀))^α with k the wave number. The GrowthODE module supplies the prefactor for the first-order growth correction in an EdS background, obtained by substituting D = a(1 + B a^α) into the growth ODE. The present module introduces the ISW driver B(a,k) = -1 + f + dlnw/dlna that links the logarithmic derivative of the kernel to the growth rate f.
proof idea
This is a definition module, no proofs. It organizes the driver expression together with auxiliary definitions (isw_driver, f_growth_gt_one, dlnw_pos, isw_driver_positive) that follow directly from the imported kernel and growth ODE.
why it matters in Recognition Science
The module supplies the ISW driver that feeds first-order ILG growth corrections in the EdS background. It connects the kernel derivative to the growth ODE prefactor, enabling subsequent analysis of the integrated Sachs-Wolfe effect within the Recognition Science ILG setting.
scope and limits
- Does not derive the kernel form or the growth ODE.
- Does not prove higher-order corrections beyond the linear B term.
- Does not address non-EdS backgrounds.