pi0_error_computation
The theorem establishes that the relative error between the Recognition Science predicted π⁰ lifetime (8.4 units) and observed value (8.52 units) equals exactly 12/852. Physicists modeling chiral anomalies via 8-tick phase quantization would cite this to quantify the discrepancy at 1.41%. The proof is a one-line native_decide that evaluates the rational equality directly from the upstream definition.
claimThe relative error satisfies $|8.4 - 8.52| / 8.52 = 12/852$.
background
The QFT.Anomalies module derives quantum anomalies from 8-tick phase mismatches in Recognition Science, where discrete time breaks classical symmetries such as chiral invariance in π⁰ → γγ. The upstream definition pi0_relative_error_rational computes |predicted lifetime - observed lifetime| / observed lifetime using the values 8.4 and 8.52 in RS-native units. This computation sits inside the local setting of T7 eight-tick octave discreteness inducing measurable phase quantization effects.
proof idea
The term proof applies native_decide directly to the equality pi0_relative_error_rational = 12/852, reducing the rational arithmetic to a decidable ground computation with no additional lemmas.
why it matters in Recognition Science
This result is invoked by the downstream theorem pi0_prediction_within_2_percent to establish that the error is less than 2/100. It supplies the exact rational needed for the QFT-014 paper claim that anomalies arise from discrete time structure, connecting to the eight-tick octave and phase mismatch mechanism in the Recognition framework.
scope and limits
- Does not derive the input lifetime values 8.4 and 8.52.
- Does not treat gauge or conformal anomalies.
- Does not prove the underlying lifetime prediction formula.
- Does not generalize beyond the π⁰ case.
Lean usage
rw [pi0_error_computation]formal statement (Lean)
78theorem pi0_error_computation :
79 pi0_relative_error_rational = 12 / 852 := by
proof body
Term-mode proof.
80 native_decide
81
82/-- Simplify: 12/852 = 1/71 -/