w_t_rescale
plain-language theorem explainer
The rescaling lemma establishes invariance of the ILG time function w_t under simultaneous positive scaling of its dynamical time and reference time arguments. Researchers normalizing units in Recognition Science gravitational models would cite it to confirm homogeneity before numerical integration. The proof is a direct one-line application of the general parameterized rescaling result at the default configuration.
Claim. Let $P$ be a parameter structure with components $alpha$, $C_{lag}$, $A$, $r_0$, $p$, and $h_z/R_d$. For any real $T_{dyn}$, $tau_0$ and any $c > 0$, the time function satisfies $w_t(P, c T_{dyn}, c tau_0) = w_t(P, T_{dyn}, tau_0)$.
background
In the ILG module the structure Params assembles the six free parameters of the induced local gravity model: the fine-structure constant alpha, the lag coefficient Clag, amplitude A, reference radius r0, power-law exponent p, and the ratio hz_over_Rd. The function w_t computes the weighted time kernel that enters the gravitational dynamics and potential. This lemma operates inside the defaultConfig which fixes numerical tolerances eps_r, eps_v, eps_t, eps_a together with upsilonStar = 1.
proof idea
The proof is a one-line wrapper that applies the parameterized rescaling lemma w_t_rescale_with instantiated at defaultConfig.
why it matters
The lemma secures dimensional homogeneity of the time kernel inside ILG, a prerequisite for consistent unit choices in cosmological and astrophysical applications of Recognition Science gravity. It closes a basic scaling property required by the ParamProps interface and the broader forcing chain (T5 J-uniqueness through T8 D=3). No downstream uses are recorded yet, leaving open whether it will be invoked inside BaryonCurves or vbar_with derivations.
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