IndisputableMonolith.Gravity.ILGDerivation
The ILGDerivation module fixes the time-kernel w_t by the recognition lag equal to phi to the minus five together with the fine-structure exponent alpha. Galaxy-formation and modified-gravity researchers cite the result when modeling rotation curves of low-surface-brightness systems. The module assembles the derivation from the imported time quantum and the base ILG definitions via a chain of grounded formulas.
claimThe time kernel $w_t$ is the unique function of the recognition lag $C_{\rm lag}=\varphi^{-5}$ and the fine-structure exponent $\alpha$ that yields the effective modified-gravity potential at galactic scales.
background
The module sits inside the gravity domain and imports the RS time quantum $\tau_0=1$ tick from Constants together with the base ILG definitions. It works in the setting where the recognition lag is identified with $\varphi^{-5}$ and the RRF gradient cost supplies the kernel that produces large-scale modifications to Newtonian gravity.
The theorem statement records that this construction formalizes the link between the recognition lag and the effective potential, using the fine-structure exponent $\alpha$ to close the expression for $w_t$.
proof idea
The module organizes the argument as a sequence of grounded formulas that fix $w_t$, followed by lemmas establishing rotational flatness and its consequences for nonzero flat velocity. Each step applies the imported constants and the ILG base to enforce uniqueness of the kernel.
why it matters in Recognition Science
The module supplies the time-kernel derivation required by the UltraDiffuseGalaxies analysis of DM-rich and DM-poor systems. It completes the step that connects the RRF gradient cost to the effective modified gravity at large scales, as recorded in the theorem statement.
scope and limits
- Does not derive the full set of ILG field equations.
- Does not compute explicit rotation-curve fits for named galaxies.
- Does not extend the kernel to cluster or cosmological scales.
- Does not incorporate baryonic feedback or star-formation terms.