IndisputableMonolith.Gravity.RAREmergence
The RAREmergence module supplies the ILG weight function that parameterizes the Radial Acceleration Relation via an acceleration-dependent scaling. It defines w(a) = C (a0/a)^{α/2} with α near 0.191 from the RS time-acceleration bridge. Workers deriving BTFR power laws from modified gravity would cite these definitions. The module consists of definitions and direct algebraic statements with no nontrivial proofs.
claimThe ILG weight function is $w(a) = C · (a_0/a)^{α/2}$ for baryonic acceleration $a$, where $a_0$ is the characteristic scale and $α ≈ 0.191$ is the dynamical-time exponent.
background
Recognition Science places gravity modifications inside the forcing chain and J-cost framework. This module imports the fundamental time quantum τ₀ = 1 tick from Constants. The ILG weight arises from the acceleration-time bridge, with the exponent 1/2 reflecting that relation. The module introduces RAR power-law forms, log slopes, and universality statements as sibling definitions.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
These definitions feed the algebraic BTFR setup recorded in BTFREmergence, which relates ILG/RAR scaling to BTFR-style power laws. A fully structural BTFR emergence theorem with mass-independent constant remains in progress. The module supplies the mechanically checkable power-law wrappers needed for that development.
scope and limits
- Does not derive a mass-independent BTFR constant.
- Does not contain a structural BTFR emergence theorem.
- Does not include observational data or numerical fits.
- Does not prove α from the forcing chain inside this file.