UVCutoffFalsifier
The structure encodes the conditions that would falsify the natural ultraviolet cutoff derived from Recognition Science discreteness at the tau_0 scale. A QFT researcher testing regularization mechanisms would cite these criteria to specify empirical failure modes. It packages three propositions on spacetime continuity, trans-cutoff observations, and phi-ladder running into a single inconsistency statement.
claimLet $C$ assert spacetime continuity below the $tau_0$ scale, $T$ assert observation of physics beyond the cutoff, and $P$ assert failure of phi-ladder running of couplings. The structure asserts $C lor T lor P to bot$.
background
The QFT module derives an ultraviolet cutoff from Recognition Science discreteness. Spacetime is discrete at the tau_0 scale, so momenta cannot exceed p_max = hbar / tau_0; this regularizes all loop integrals. The upstream scale definition supplies the phi-ladder via phi^k for natural number k, while the Spacetime definition supplies the standard 4D manifold.
proof idea
This is a structure definition that directly assembles the three falsification propositions and their implication to falsehood. No lemmas are applied; it packages the conditions stated in the module documentation.
why it matters in Recognition Science
The definition supplies the falsification criteria for the UV cutoff claim in QFT-013. It connects the Recognition Science discreteness hypothesis to empirical tests via the phi-ladder and tau_0 scale, supporting the module's target of a first-principles regularization paper. It touches the open question of how continuous-spacetime observations would refute the cutoff.
scope and limits
- Does not derive the numerical value of tau_0 or p_max.
- Does not prove spacetime discreteness.
- Does not specify measurement protocols for the three conditions.
- Does not link to particular collider data or running-coupling measurements.
formal statement (Lean)
237structure UVCutoffFalsifier where
238 /-- Spacetime found to be continuous below τ₀ scale -/
239 continuous_spacetime : Prop
240 /-- Trans-cutoff physics observed -/
241 trans_cutoff_physics : Prop
242 /-- φ-ladder running not confirmed -/
243 phi_ladder_fails : Prop
244 /-- Falsification condition -/
245 falsified : continuous_spacetime ∨ trans_cutoff_physics ∨ phi_ladder_fails → False
246
247end UVCutoff
248end QFT
249end IndisputableMonolith