pi0_prediction_within_2_percent
plain-language theorem explainer
The theorem establishes that the Recognition Science prediction for neutral pion lifetime deviates from the observed value by less than 2 percent. Particle physicists comparing discrete-time models to chiral anomaly data would cite this bound when validating 8-tick phase predictions. The proof substitutes the precomputed rational error via rewriting and confirms the inequality by direct numerical reduction.
Claim. The relative error between the predicted and observed neutral pion lifetime satisfies $|8.4 - 8.52| / 8.52 < 2/100$.
background
The module derives quantum anomalies from 8-tick phase mismatches in Recognition Science. A chiral anomaly appears when axial current conservation fails under quantum effects, with the neutral pion decay to two photons serving as the canonical example. The local setting treats anomalies as mismatches between continuous classical phases and the discrete eight-tick octave structure. pi0_relative_error_rational is defined as the absolute difference between predicted (8.4) and observed (8.52) lifetimes divided by the observed value. The upstream lemma pi0_error_computation supplies the exact rational form 12/852 for this difference.
proof idea
The proof is a one-line wrapper that rewrites the target inequality using the pi0_error_computation lemma to insert the rational 12/852, then applies norm_num to verify that 12/852 lies strictly below 2/100.
why it matters
This theorem supplies the pi0_accurate field inside the anomalyProofs summary, confirming that the 8-tick mechanism reproduces the chiral anomaly for π⁰ → γγ to the stated precision. It directly supports the paper proposition on quantum anomalies from discrete time structure and instantiates the eight-tick octave landmark (T7) within the QFT anomalies module. No open scaffolding remains for this specific numerical check.
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