mass_gap_bounds
The theorem establishes the numerical interval 0.118 < massGap < 0.119. Unification researchers would cite it to confirm the Recognition Science mass gap prediction sits at the QCD scale. The proof is a one-line wrapper that applies the massGap_numerical_bound lemma.
claim$0.118 < Δ < 0.119$, where $Δ$ is the mass gap.
background
The module shows that 4D Lorentzian spacetime with signature (−,+,+,+) emerges from the J-cost functional and the T0–T8 forcing chain. J-cost is the non-negative cost of a recognition event, obtained as the derived cost of the comparator on positive ratios from the multiplicative recognizer. Upstream structures supply nuclear densities on φ-tiers and ledger factorization for J calibration.
proof idea
The proof is a one-line wrapper that applies the massGap_numerical_bound lemma.
why it matters in Recognition Science
This declaration supplies the numerical anchor for the mass gap inside the spacetime emergence certificate, which verifies the full 4D Lorentzian structure forced by J-cost and the T0–T8 chain. It completes the Yang-Mills mass gap step in the unification without introducing free parameters. No downstream theorems depend on it yet.
scope and limits
- Does not derive the mass gap value analytically from the J-cost equation.
- Does not include uncertainty propagation or parameter sensitivity.
- Does not connect the interval to specific collider data or measurements.
formal statement (Lean)
344theorem mass_gap_bounds : (0.118 : ℝ) < massGap ∧ massGap < (0.119 : ℝ) :=
proof body
Tactic-mode proof.
345 massGap_numerical_bound
346
347/-! ## §12 The Complete Spacetime Emergence Certificate -/
348
349/-- **THE SPACETIME EMERGENCE CERTIFICATE**
350
351 Verifies the full structure of 4D Lorentzian spacetime is forced
352 by the J-cost functional and the RS forcing chain T0–T8. -/