amati_exponent
plain-language theorem explainer
The identity establishes that one quarter plus one quarter equals one half, arising directly from the product of a Lorentz factor scaling as isotropic energy to the one-quarter power and the square root of that energy in gamma-ray burst models. Researchers working on GRB energetics within Recognition Science would cite this arithmetic step when assembling the Amati relation. The proof reduces to a single numerical normalization tactic that verifies the equality over the reals.
Claim. The Amati exponent satisfies $1/4 + 1/4 = 1/2$, obtained from the combination of the Lorentz factor scaling as $E_{iso}^{1/4}$ with the square-root factor on isotropic energy.
background
The module develops gamma-ray burst phenomenology inside Recognition Science and points to the companion paper RS_Gamma_Ray_Bursts.tex. The sole upstream dependency supplies the type Energy as the real numbers, so all subsequent arithmetic occurs inside ℝ. No further definitions from the J-cost core or the phi-ladder appear in this declaration.
proof idea
The proof is a one-line wrapper that applies norm_num to the arithmetic statement over the reals.
why it matters
This supplies the numerical exponent one half required for the Amati relation inside the GRB module. It completes the exponent combination stated in the module documentation and thereby supports the Recognition Science account of burst energetics. The result sits downstream of the basic Energy abbreviation but does not yet feed any sibling theorems in the current graph.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.