lorentz_range
The declaration asserts the inequality 100 < 1000 in the real numbers. Researchers modeling gamma-ray bursts under Recognition Science would reference this bound to delimit Lorentz factor ranges in typical events. The proof proceeds as a direct application of the norm_num tactic that confirms the numerical relation without additional lemmas.
claimThe real numbers satisfy the strict inequality $100 < 1000$.
background
This result sits inside the Gamma-Ray Bursts module of Recognition Science, whose overall development follows the paper RS_Gamma_Ray_Bursts.tex. The module imports JcostCore for handling recognition costs and defect distances, yet the present theorem uses none of those structures. It functions as an elementary numerical anchor for subsequent statements on Lorentz factors and GRB energies listed among the sibling declarations.
proof idea
The proof is a one-line wrapper that invokes the norm_num tactic to reduce the inequality to a decidable arithmetic statement and discharge it automatically.
why it matters in Recognition Science
The theorem supplies a fixed numerical interval that supports claims about Lorentz factors in the Recognition Science treatment of gamma-ray bursts. It aligns with the module's goal of deriving GRB properties from the phi-ladder and J-cost framework, even though it itself carries no dependence on those elements. No downstream theorems currently reference it, leaving its integration open for further development in the paper.
scope and limits
- Does not claim physical observability of the bound in actual GRB data.
- Does not invoke any Recognition Science constants or forcing chain steps.
- Does not extend to inequalities involving other parameters such as energies or masses.
formal statement (Lean)
42theorem lorentz_range : (100 : ℝ) < 1000 := by norm_num
proof body
43