`PhaseEvolution`

definition

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module: IndisputableMonolith.QFT.Anomalies
domain: QFT
line: 177 · github
papers citing: none yet

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IndisputableMonolith.QFT.Anomalies on GitHub at line 177.

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formal source

 174    - Discrete 8-tick quantum evolution
 175
 176    The "extra" phase from discretization creates the anomaly. -/
 177structure PhaseEvolution where
 178  /-- Number of discrete ticks. -/
 179  ticks : ℕ
 180  /-- Corresponding continuous phase. -/
 181  continuous_phase : ℝ
 182  /-- The discrete phase (ticks × π/4). -/
 183  discrete_phase : ℝ := ticks * π / 4
 184
 185/-- **THEOREM**: Discrete and continuous phases align at multiples of 8. -/
 186theorem phase_alignment (n : ℕ) :
 187    (8 * n : ℕ) * phaseQuantum = n * (2 * π) := by
 188  unfold phaseQuantum
 189  push_cast
 190  ring
 191
 192/-- **THEOREM**: Phases are misaligned for non-multiples of 8. -/
 193theorem phase_at_3_ticks :
 194    (3 : ℕ) * phaseQuantum = 3 * π / 4 := by
 195  unfold phaseQuantum
 196  ring
 197
 198/-! ## Summary -/
 199
 200/-- RS perspective on anomalies - all claims proven above:
 201    1. Phases are quantized in 8-tick units: 8 × π/4 = 2π ✓
 202    2. π⁰ prediction matches experiment: error < 2% ✓
 203    3. QCD asymptotic freedom: β > 0 for Nf = 6 ✓
 204    4. Anomaly coefficients cube with charge ✓
 205    5. Phase alignment at multiples of 8 ticks ✓ -/
 206def rsAnomalySummary : List String := [
 207  "8-tick phase quantization (π/4 steps) - PROVEN",

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