module module moderate

`IndisputableMonolith.QFT.Anomalies`

The QFT.Anomalies module defines discrete phase structures for quantum field theory anomalies inside Recognition Science. It introduces numDiscretePhases as the count of phases per full rotation together with phaseQuantum, eight_quanta_full_rotation, and cycle identities. These rest on the RS time quantum from Constants and enable sibling computations such as the pi0 lifetime prediction. The module contains only definitions.

claimThe module defines the number of discrete phases in a full rotation $N=8$, the phase quantum step $2π/N$, and supporting identities eight_quanta_full_rotation and full_cycle_identity.

background

Recognition Science fixes an eight-tick octave structure (T7) on top of the fundamental time quantum τ₀ = 1 tick supplied by the Constants module. The QFT.Anomalies module imports Mathlib and Constants, then discretizes phase evolution over that tick lattice. It introduces numDiscretePhases to count phases per rotation, phaseQuantum as the incremental step, phase_at_step and half_cycle_phase to track evolution, and full_cycle_identity to close the loop. Additional definitions compute pi0 lifetime in RS-native units and the associated rational error.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the discrete-phase scaffolding that supports QFT anomaly modeling and feeds the pi0 lifetime predictions listed among its siblings. It realizes the eight-tick octave directly in phase language and closes part of the discrete QFT interface in the Recognition framework.

scope and limits

Does not derive numDiscretePhases from the forcing chain.
Does not invoke the Recognition Composition Law or J-cost.
Does not address continuous-phase limits or full anomaly cancellation.
Does not compute mass-ladder or coupling values.

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