amati_exponent
Amati exponent evaluates to one half by adding the quarter contribution from Lorentz factor scaling to the quarter from isotropic energy square root. GRB modelers working in Recognition Science cite this for the correlation exponent. Proof applies direct numerical normalization to the arithmetic identity.
claim$1/4 + 1/4 = 1/2$, where the left side combines the exponent from $Γ ∝ E_{iso}^{1/4}$ with the square-root factor from isotropic energy.
background
The module develops gamma-ray burst properties in Recognition Science following the paper RS_Gamma_Ray_Bursts.tex. Energy quantities appear as real numbers via the upstream abbreviation Energy := ℝ. Sibling declarations handle GRB energy scales, accretion efficiency, and Lorentz factors.
proof idea
One-line wrapper that applies norm_num to the arithmetic equality.
why it matters in Recognition Science
Supplies the exponent in the Amati relation for the GRB module. It fills the scaling step that combines Lorentz and energy factors in the Recognition Science treatment of gamma-ray bursts.
scope and limits
- Does not derive the Lorentz factor proportionality.
- Does not compute numerical GRB energies or ranges.
- Does not link to the phi-ladder or J-cost functions.
formal statement (Lean)
60theorem amati_exponent : (1:ℝ)/4 + 1/4 = 1/2 := by norm_num
proof body
Term-mode proof.
61
62/-! ## Key Energy Scale -/
63
64/-- GRB isotropic energy: 10^51 to 10^54 erg. -/