rsCutoffGeV
The declaration assigns the Recognition Science ultraviolet cutoff energy scale the rational value 3.2 × 10^11 GeV. QFT researchers examining natural regularization from discrete spacetime would cite this constant when comparing the cutoff to collider energies. The definition is a direct numerical assignment that supplies the scale for the downstream ratio comparison to LHC energies.
claimThe Recognition Science ultraviolet cutoff energy scale equals $3.2 × 10^{11}$ GeV.
background
The QFT.UVCutoff module derives the ultraviolet cutoff from spacetime discreteness at the τ₀ scale in Recognition Science. Momenta cannot exceed p_max = ℏ/τ₀, which supplies a natural regulator for all UV divergences in loop integrals. This numerical definition supplies the concrete energy value in GeV for that cutoff, calibrated to sit well above current collider reach.
proof idea
The definition is a direct numerical assignment of the rational 3.2e11. No lemmas or tactics are invoked; it functions as a one-line constant definition for use in ratio comparisons.
why it matters in Recognition Science
This definition supplies the energy scale that feeds the cutoff_above_lhc theorem establishing the cutoff exceeds LHC energies by more than 10^7. It realizes the QFT-013 module goal of natural UV regularization from information-theoretic discreteness, consistent with the forcing chain and eight-tick octave in the Recognition framework. The value supports the proposed major paper on first-principles regularization.
scope and limits
- Does not derive the numerical value from the phi-ladder or τ₀ within this declaration.
- Does not specify renormalization procedures or particle-specific interactions.
- Does not include error bounds or variation under changes to fundamental constants.
formal statement (Lean)
72def rsCutoffGeV : ℚ := 3.2e11 -- ~320 billion GeV
proof body
Definition body.
73
74/-- **THEOREM**: The RS UV cutoff is ~10⁷ times higher than LHC energies. -/