PhaseEvolution
plain-language theorem explainer
PhaseEvolution pairs a natural-number tick count with a continuous real phase and derives the discrete phase as ticks times pi over 4. Researchers modeling discrete-time QFT anomalies would cite it when tracing chiral or conformal symmetry breaking to 8-tick quantization. The declaration is a direct structure definition that imports the periodic phase map from the EightTick module.
Claim. A structure consisting of a natural number $n$ (tick count), a real number $p_c$ (continuous phase), and the derived discrete phase $p_d := n π / 4$.
background
In Recognition Science, anomalies arise when continuous classical phase evolution meets the discrete 8-tick quantum evolution. The upstream EightTick.phase supplies the quantized values $k π / 4$ for $k = 0,…,7$, periodic with period $2π$. The module frames this mismatch as the source of chiral anomalies (axial current non-conservation) and conformal anomalies (scale breaking), consistent with the forcing chain’s T7 eight-tick octave.
proof idea
One-line structure definition that directly encodes the discrete-phase formula from the tick count. It draws the phase quantization convention from the EightTick.phase definition and the mismatch interpretation from the module doc-comment.
why it matters
The structure supplies the basic object for the QFT-014 derivation of anomalies from 8-tick phase mismatches. It sits inside the T7 eight-tick octave of the forcing chain and supports the paper proposition on discrete-time structure. No downstream uses are recorded, leaving open its integration into explicit anomaly coefficients or π⁰ lifetime predictions.
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