pi0_error_simplified
The rational equality 12/852 = 1/71 is established as an algebraic simplification step inside the neutral-pion lifetime error computation. Researchers verifying the Recognition Science prediction for π⁰ decay would cite it when confirming the match to experiment lies inside 2 %. The proof is a direct one-line normalization of the rationals.
claim$12/852 = 1/71$ holds in the rationals.
background
The module derives quantum anomalies from 8-tick phase mismatches, with the chiral anomaly for π⁰ → γγ arising when discrete phase quantization breaks classical axial symmetry. The upstream lifetime definition supplies the decay rate as phi raised to an integer power in RS-native units. The present equality is invoked inside the relative-error calculation that compares the phi-ladder prediction against the observed π⁰ lifetime.
proof idea
The proof is a one-line wrapper that applies norm_num to reduce the rational equality.
why it matters in Recognition Science
The result closes a computational step in the pi0_prediction_within_2_percent claim, confirming that the 8-tick phase mismatch reproduces the observed π⁰ lifetime to the stated precision. It therefore supports the T7 eight-tick octave as the source of the chiral anomaly in the Recognition Science forcing chain.
scope and limits
- Does not derive the integers 12 or 852 from the underlying phi-ladder or phase model.
- Does not prove that the lifetime formula itself matches experiment.
- Does not extend the error bound to other mesons or decay channels.
formal statement (Lean)
83theorem pi0_error_simplified :
84 (12 : ℚ) / 852 = 1 / 71 := by
proof body
Term-mode proof.
85 norm_num
86
87/-- **THEOREM**: The π⁰ lifetime prediction matches experiment to < 2%. -/