module module high

`IndisputableMonolith.QFT.Anomalies`

The QFT.Anomalies module defines the discrete phase structure for rotations inside the Recognition Science QFT setting. It supplies the count of discrete phases together with phase quanta and cycle identities that feed anomaly calculations. All content rests on the RS time quantum imported from Constants. The module contains only definitions and supporting identities with no theorems.

claimLet $N_{ m phases}$ be the number of discrete phases in a full rotation. The module also introduces the phase quantum $ heta_q$ and the identities eight_quanta_full_rotation, full_cycle_identity, and half_cycle_phase.

background

The module sits in the QFT domain of Recognition Science and imports only Mathlib and IndisputableMonolith.Constants. The upstream Constants module supplies the fundamental RS time quantum $ au_0 = 1$ tick. Within this setting the module introduces the discrete phase count, phase quanta, and rotation identities that discretize the eight-tick octave structure for anomaly work.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the phase discretization primitives required for QFT anomaly resolutions. It supports sibling declarations that compute pi0 lifetime predictions and relative errors, thereby connecting the eight-tick octave (T7) to concrete particle-physics observables inside the Recognition framework.

scope and limits

Does not derive the discrete phase count from the forcing chain.
Does not perform numerical anomaly integrals.
Does not address continuous phase or non-RS models.
Does not contain any theorem linking phases to specific gauge anomalies.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import

declarations in this module (31)

def numDiscretePhases L38
def phaseQuantum L41
theorem eight_quanta_full_rotation L44
theorem phase_at_step L50
theorem full_cycle_identity L56
theorem half_cycle_phase L60
def pi0_lifetime_predicted_units L68
def pi0_lifetime_observed_units L71
def pi0_relative_error_rational L74
theorem pi0_error_computation L78
theorem pi0_error_simplified L83
theorem pi0_prediction_within_2_percent L88
theorem pi0_error_bound L94
def qcdBetaCoeff L101
theorem qcd_beta_nf6 L104
theorem qcd_asymptotic_freedom_nf6 L109
theorem qcd_beta_nf17 L115
theorem qcd_no_af_nf17 L120
theorem qcd_critical_flavors L126
def u1CubeCoeff L135
theorem anomaly_cubes L138
theorem anomaly_antisymmetric L144
theorem anomaly_zero L150
def chiralAnomalyEquation L159
def chiralAnomalyConsequences L163
structure PhaseEvolution L177
theorem phase_alignment L186
theorem phase_at_3_ticks L193
def rsAnomalySummary L206
structure AnomalyProofSummary L217
def anomalyProofs L228