pi0_error_bound
Recognition Science calculations for the neutral pion lifetime error are bounded by showing that 1/71 lies below 15/1000. Modelers of 8-tick phase mismatches cite this to keep the predicted discrepancy under 1.5 percent. A single norm_num call verifies the inequality by arithmetic normalization.
claim$ 1/71 < 15/1000 $
background
In the QFT anomalies module, quantum effects such as the chiral anomaly for neutral pion decay arise from mismatches between continuous phases and the discrete 8-tick structure of Recognition Science. The local setting treats anomalies as consequences of phase quantization at the eight-tick octave, with the doc-comment noting the error reaches approximately 1.41 percent where 1/71 approximates 0.0141.
proof idea
The proof is a term-mode application of the norm_num tactic, which normalizes the rational numbers and discharges the inequality by direct computation.
why it matters in Recognition Science
This result anchors the error estimate for the pi0 lifetime prediction in the anomalies section. It feeds into sibling theorems on relative error and the two-percent bound, confirming consistency with the eight-tick period and the Recognition Composition Law.
scope and limits
- Does not establish the physical origin of the 1/71 ratio.
- Does not compute the absolute pi0 lifetime.
- Does not apply to other decay channels.
- Does not include higher-order corrections beyond this rational bound.
formal statement (Lean)
94theorem pi0_error_bound :
95 (1 : ℚ) / 71 < 15 / 1000 := by
proof body
Term-mode proof.
96 norm_num
97
98/-! ## QCD Asymptotic Freedom -/
99
100/-- QCD one-loop beta function coefficient. -/