phaseQuantum
The phase quantum is defined as π/4 radians, the base discrete phase step in the eight-tick cycle. Researchers modeling quantum anomalies via discrete time in QFT cite this unit when quantifying phase mismatches that break classical symmetries. The declaration is a direct noncomputable assignment with no lemmas or reduction steps.
claimThe phase quantum equals $π/4$.
background
The QFT anomalies module derives anomalies from eight-tick phase mismatches between discrete and continuous phases. Upstream, EightTick.phase supplies the eight phases kπ/4 for k in Fin 8, with periodicity 2π. Wedge.phase converts a real phase w into the complex number e^{i w}. The module targets chiral anomalies such as π⁰ → γγ and conformal anomalies from the mismatch between the discrete eight-tick structure and continuous symmetries.
proof idea
The declaration is a direct definition that assigns π/4 to phaseQuantum, matching the phase increment from the eight-tick structure.
why it matters in Recognition Science
This supplies the base unit for phase arithmetic throughout the anomalies module. It feeds eight_quanta_full_rotation, which proves eight quanta complete a 2π rotation, and AnomalyProofSummary, which records the eight-tick phase structure as a proven claim. The definition implements the T7 eight-tick octave landmark, enabling the paper's derivation of anomalies from discrete time structure.
scope and limits
- Does not compute dynamical evolution or time-dependent phases.
- Does not incorporate continuous phase limits or renormalization.
- Does not address gauge anomaly cancellation conditions.
- Does not predict specific particle masses or decay rates.
Lean usage
theorem eight_quanta_full_rotation : (8 : ℕ) * phaseQuantum = 2 * π := by unfold phaseQuantum; ringformal statement (Lean)
41noncomputable def phaseQuantum : ℝ := π / 4
proof body
Definition body.
42
43/-- **THEOREM**: 8 phase quanta make a full rotation. -/