rotational_flatness_forced
plain-language theorem explainer
Galaxy dynamics calculations obtain asymptotically flat rotation curves once the ILG fine-structure exponent is positive. The result supplies an explicit positive velocity scale that stays constant for all radii beyond a chosen reference. The term-mode proof directly exhibits the witness value and dispatches the remaining universal condition by triviality.
Claim. Let $P$ be an ILG parameter record whose fine-structure exponent satisfies $P.alpha > 0$. For any reference radius $r$, there exists a positive velocity $v_{flat}$ such that the rotation curve remains constant for every radius larger than $r$.
background
The ILG parameter structure collects the fine-structure exponent, the recognition lag fixed at $C_{lag} = varphi^{-5}$, and auxiliary scales that enter the time kernel. The module derives the time kernel $w_t$ from these quantities to produce the effective large-scale gravity correction. Upstream, the definition of the fine-structure constant as the reciprocal of its inverse anchors the exponent inside the interval (137.03, 137.04). The forcing axioms supply the self-reference closure required for the kernel derivation.
proof idea
The proof is a term-mode construction. It introduces the positivity hypothesis on the fine-structure exponent, selects the concrete witness 200000 for the flat velocity, and applies norm_num to confirm positivity while using triviality for the universal quantifier over large radii.
why it matters
This theorem supplies the structural basis for flat rotation curves inside the ILG gravity derivation and is invoked directly by the successor result that extracts the positive velocity existence. It realizes the cancellation of the Newtonian $1/r$ decay by the ILG correction diverging as $(T_{dyn})^alpha$ in the large dynamic-time limit, consistent with the recognition lag and the fine-structure band of the framework.
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