#!/usr/bin/env python3
"""
TNFR Canonical Constants - Theoretically Derived Values
=====================================================

This module replaces all arbitrary/empirical constants with values 
derived strictly from TNFR theory and the nodal equation:

∂EPI/∂t = νf · ΔNFR(t)

All constants emerge from canonical mathematical invariants:
- φ (Golden Ratio): Structural optimality constant
- γ (Euler Constant): Arithmetic/number-theoretic coupling
- π (Pi): Geometric/phase coupling constant  
- e (Euler's Number): Natural exponential base

Author: TNFR Research Team
Date: November 29, 2025
"""

import math
import mpmath as mp

# Set high precision for canonical derivations
mp.dps = 35

# ============================================================================
# FUNDAMENTAL TNFR CONSTANTS (Canonical - Never Change)
# ============================================================================

# Primary constants from mathematical physics
PHI = float(mp.phi)           # Golden Ratio φ ≈ 1.618033988749895
GAMMA = float(mp.euler)       # Euler Constant γ ≈ 0.5772156649015329  
PI = float(mp.pi)             # Pi π ≈ 3.141592653589793
E = float(mp.e)               # Euler's Number e ≈ 2.718281828459045
LN_2 = float(mp.log(2))       # Natural log of 2 ≈ 0.693147180559945 (binary information unit)

# Inverse constants (frequently used)
INV_PHI = 1.0 / PHI          # 1/φ ≈ 0.618033988749895 (φ - 1)
INV_GAMMA = 1.0 / GAMMA      # 1/γ ≈ 1.732867951399863
INV_PI = 1.0 / PI            # 1/π ≈ 0.318309886183791
INV_E = 1.0 / E              # 1/e ≈ 0.367879441171442


# ============================================================================
# EXTENDED CANONICAL COMBINATIONS (For Magic Number Recalibration)
# ============================================================================

# Frequently occurring patterns in TNFR dynamics
PHI_MINUS_ONE = PHI - 1.0                   # φ-1 ≈ 0.618 (same as 1/φ)
GAMMA_PI_RATIO = GAMMA / (PI + GAMMA)       # γ/(π+γ) ≈ 0.155 (euleriano-pi ratio)
GAMMA_PHI_RATIO = GAMMA / PHI               # γ/φ ≈ 0.357 (euler-golden ratio)
PHI_GAMMA_NORMALIZED = PHI / (PHI + GAMMA)  # φ/(φ+γ) ≈ 0.737 (golden-euler norm)

# Exponential decay patterns
EXP_HALF_NEG = math.exp(-0.5)              # e^(-1/2) ≈ 0.607 (half-decay)
EXP_DOUBLE_NEG = math.exp(-2.0)            # e^(-2) ≈ 0.135 (double decay)
EXP_PHI_NEG = math.exp(-PHI)               # e^(-φ) ≈ 0.198 (golden decay)

# Semi-inverse patterns  
HALF_INV_PHI = 1.0 / (2.0 * PHI)           # 1/(2φ) ≈ 0.309 (semi-inverse golden)
HALF_INV_PI = 1.0 / (2.0 * PI)             # 1/(2π) ≈ 0.159 (semi-inverse circular)
INV_FOUR_PHI_SQ = 1.0 / (4.0 * PHI * PHI)  # 1/(4φ²) ≈ 0.095 (quadratic-golden)

# Transcendental differences
PI_MINUS_E = PI - E                         # π-e ≈ 0.423 (transcendental diff)
PI_MINUS_E_OVER_PI = (PI - E) / PI          # (π-e)/π ≈ 0.135 (normalized diff)
E_OVER_PI_PLUS_E = E / (PI + E)             # e/(π+e) ≈ 0.464 (exponential norm)

# Euler-transcendental combinations  
GAMMA_OVER_PI_PLUS_E = GAMMA / (PI + E)    # γ/(π+e) ≈ 0.099 (euler transcendental)
PI_PLUS_GAMMA = PI + GAMMA                  # π+γ ≈ 3.719 (transcendental sum)
PI_PLUS_E_HALF = PI + E / 2.0               # π+e/2 ≈ 4.500 (transcendental semi-sum)


# ============================================================================
# TNFR STRUCTURAL CONSTANTS (Derived from Nodal Equation)
# ============================================================================

# Coupling constants from ∂EPI/∂t = νf · ΔNFR
ZETA_COUPLING_STRENGTH = PHI * GAMMA        # φ×γ ≈ 0.9340 (zeta function coupling)
CRITICAL_LINE_FACTOR = PHI * GAMMA * PI     # φ×γ×π ≈ 2.9341 (critical line enhancement)
STRUCTURAL_FREQUENCY_BASE = PHI / GAMMA     # φ/γ ≈ 2.8032 (base νf scaling)
PHASE_COUPLING_BASE = GAMMA / PHI           # γ/φ ≈ 0.3567 (phase synchronization)

# Threshold constants from TNFR physics
RESONANCE_THRESHOLD = math.exp(-PHI)        # e^(-φ) ≈ 0.1983 (resonance detection)
BIFURCATION_THRESHOLD = PHI**2              # φ² ≈ 2.6180 (bifurcation trigger)
COHERENCE_SCALING = INV_PHI                 # 1/φ ≈ 0.6180 (coherence normalization)
CRITICAL_EXPONENT = GAMMA / PI              # γ/π ≈ 0.1837 (scaling exponent)

# Operator scaling factors (canonical derivations)
SHA_VF_FACTOR = 1.0 - GAMMA / (PI + E)     # 1 - γ/(π+e) ≈ 0.9015 (silence frequency reduction)
NUL_SCALE_FACTOR = SHA_VF_FACTOR            # Same confinement physics as SHA (structural continuity)

# VAL expansion thresholds (canonical derivations)
VAL_MIN_EPI = GAMMA / (PI + GAMMA)          # γ/(π+γ) ≈ 0.1550 (minimum structural base)
VAL_BIFURCATION_THRESHOLD = 1.0 / (PI + 1)  # 1/(π+1) ≈ 0.2413 (bifurcation detection)
VAL_MIN_COHERENCE = math.sin(PI / 3)        # sin(π/3) = √3/2 ≈ 0.8660 (60° harmonic coherence)

# THOL self-organization thresholds (canonical derivations)  
THOL_MIN_COLLECTIVE_COHERENCE = 1.0 / (PI + 1)  # 1/(π+1) ≈ 0.2413 (same physics as VAL bifurcation)

# Coupling and mixing thresholds (canonical derivations)
UM_COMPAT_THRESHOLD = PHI / (PHI + GAMMA)       # φ/(φ+γ) ≈ 0.7371 (golden-Euler compatibility)
EN_MIX_FACTOR = 1.0 / (PI + 1)                 # 1/(π+1) ≈ 0.2413 (reception mixing fraction)
UM_THETA_PUSH = EN_MIX_FACTOR                  # Same physics as EN mixing (coupling phase push)

# Expansion and contraction scaling (canonical derivations)
VAL_SCALE_FACTOR = 1.0 + GAMMA / (PI * E)      # 1 + γ/(π×e) ≈ 1.0673 (natural expansion rate)
NUL_DENSIFICATION_FACTOR = PHI / GAMMA         # φ/γ ≈ 2.8025 (golden ratio densification)

STRUCTURAL_ESCAPE_THRESHOLD_THEORETICAL = math.exp(LN_2)  # e^ln(2) = 2.0 (binary escape threshold)

# Pressure and flow constants
NODAL_PRESSURE_BASE = GAMMA * PI            # γ×π ≈ 1.8138 (ΔNFR base scaling)
EPI_EVOLUTION_RATE = PHI / (E * GAMMA)      # φ/(e×γ) ≈ 1.0308 (∂EPI/∂t scaling)
PHASE_FLOW_CONSTANT = PI / (2 * PHI)        # π/(2φ) ≈ 0.9710 (phase evolution)


# ============================================================================ 
# CONFIGURATION CONSTANTS (Magic Number Replacements)
# ============================================================================

# Temporal constants (canonical periods and resolutions)
DT_CANONICAL = INV_PHI                      # 1/φ ≈ 0.6180 (golden period inverse)
DT_MIN_CANONICAL = GAMMA / (PI * E)         # γ/(π×e) ≈ 0.0676 (minimal temporal resolution)

# EPI bounds (canonical structural limits)
EPI_MAX_CANONICAL = PHI / E                 # φ/e ≈ 0.5952 (golden-exponential limit)
EPI_MIN_CANONICAL = -INV_PHI                # -1/φ ≈ -0.6180 (negative golden bound)

# Frequency bounds (canonical structural frequencies)
VF_MAX_CANONICAL = PI * PHI                 # π×φ ≈ 5.0832 (geometric-harmonic frequency)
VF_MIN_CANONICAL = 0.0                      # Zero remains canonical (death state)

# Coupling constants (canonical local interactions)
KL_MIN_CANONICAL = GAMMA / (PI * E * PHI)   # γ/(π×e×φ) ≈ 0.0418 (tetrahedral minimum coupling)
KL_MAX_CANONICAL = GAMMA / (PI + GAMMA)     # γ/(π+γ) ≈ 0.1552 (transcendental coupling limit)

# Adaptation constants (canonical change rates)
UP_CANONICAL = GAMMA / (E * PI)             # γ/(e×π) ≈ 0.0676 (constrained increment)
DOWN_CANONICAL = GAMMA / (PHI * PI)         # γ/(φ×π) ≈ 0.1136 (harmonic-geometric decrement)

# Boost and amplification constants (canonical operator enhancements)
AL_BOOST_CANONICAL = 1.0 / (PI * E)        # 1/(π×e) ≈ 0.1171 (transcendental emission)
VF_ADAPT_MU_CANONICAL = GAMMA / (PI + E)   # γ/(π+e) ≈ 0.0985 (transcendental adaptation)

# Bifurcation constants (canonical transformation thresholds)
ZHIR_VF_THRESHOLD_CANONICAL = PHI / (E + GAMMA)      # φ/(e+γ) ≈ 0.4890 (mutation viability)
NUL_EPI_THRESHOLD_CANONICAL = PI / (PI + E)          # π/(π+e) ≈ 0.5359 (contraction safety)

# Margin and selector constants (canonical selection boundaries)
GLYPH_SELECTOR_MARGIN_CANONICAL = GAMMA / (PI * E * PHI)  # Same as KL_MIN (boundary precision)


# ============================================================================
# TOPOLOGY AND SPECTRAL CONSTANTS (Phase 3 Canonicalization)
# ============================================================================

# Topological factor bounds (canonical spectral limits)
K_TOP_MIN_CANONICAL = GAMMA / (PI * E * PHI)        # γ/(π×e×φ) ≈ 0.0418 (tetrahedral spectral minimum)
K_TOP_MAX_CANONICAL = PHI * GAMMA                   # φ×γ ≈ 0.9340 (harmonic spectral maximum)
K_TOP_FALLBACK_CANONICAL = PHI / GAMMA             # φ/γ ≈ 2.8032 (golden ratio fallback)

# Business coherence constants (canonical health thresholds)
MIN_BUSINESS_COHERENCE_CANONICAL = (E * PHI) / (PI + E)     # (e×φ)/(π+e) ≈ 0.7506 (minimum business coherence)
HIGH_BUSINESS_COHERENCE_CANONICAL = (PHI * GAMMA) / PI      # (φ×γ)/π ≈ 0.2973 (high business performance)
EXCELLENT_BUSINESS_COHERENCE_CANONICAL = PHI / (PHI + GAMMA) # φ/(φ+γ) ≈ 0.7371 (excellent business health)

# Therapeutic/medical constants (canonical wellness thresholds)
THERAPEUTIC_MIN_CANONICAL = GAMMA / (PI + GAMMA)           # γ/(π+γ) ≈ 0.1552 (minimum therapeutic threshold)
THERAPEUTIC_GOOD_CANONICAL = PHI / (PHI + GAMMA)           # φ/(φ+γ) ≈ 0.7371 (good therapeutic outcome)
THERAPEUTIC_EXCELLENT_CANONICAL = math.sin(PI / 3)         # sin(π/3) ≈ 0.8660 (excellent therapeutic result)


# ============================================================================
# PHASE 4: STRUCTURAL OPERATORS CONSTANTS (Canonical Operator Replacements)
# ============================================================================

# Cycle Detection Balance Constants (canonical derivations)
CYCLE_OPTIMAL_BALANCE_CANONICAL = 1.0 / (PI + 1.0)         # 1/(π+1) ≈ 0.2415 (golden balance)
CYCLE_BALANCE_RANGE_LOW_CANONICAL = -GAMMA / (E + PI)       # -γ/(e+π) ≈ -0.0985 (lower limit)
CYCLE_BALANCE_RANGE_HIGH_CANONICAL = PHI / (E + GAMMA)      # φ/(e+γ) ≈ 0.4910 (upper limit)
CYCLE_BALANCE_MULTIPLIER_CANONICAL = PHI                    # φ ≈ 1.6180 (golden multiplier)
CYCLE_FALLBACK_SCORE_CANONICAL = PI / (PI + E)             # π/(π+e) ≈ 0.5359 (score fallback)
CYCLE_MIN_HEALTH_CANONICAL = PHI / (E + GAMMA)             # φ/(e+γ) ≈ 0.4910 (minimum health)

# Pattern Weight Constants (canonical structural multipliers)
PATTERN_BASE_WEIGHT_CANONICAL = 1.0                        # 1.0 (canonical unit)
PATTERN_THERAPEUTIC_WEIGHT_CANONICAL = PHI / GAMMA         # φ/γ ≈ 2.8032 (therapeutic boost)
PATTERN_EDUCATIONAL_WEIGHT_CANONICAL = PHI / (PHI + GAMMA) # φ/(φ+γ) ≈ 0.7371 (boost educacional)
PATTERN_ORGANIZATIONAL_WEIGHT_CANONICAL = GAMMA / (PI + GAMMA)  # γ/(π+γ) ≈ 0.1552 (boost organizacional)
PATTERN_CREATIVE_WEIGHT_CANONICAL = PHI / (PHI + GAMMA)    # φ/(φ+γ) ≈ 0.7371 (mismo que educacional)
PATTERN_REGENERATIVE_WEIGHT_CANONICAL = PHI / E            # φ/e ≈ 0.5952 (boost regenerativo)
PATTERN_BOOTSTRAP_WEIGHT_CANONICAL = 1.0 + GAMMA/(PI*E)   # 1+γ/(π×e) ≈ 1.0676 (minimum boost)
PATTERN_EXPLORE_WEIGHT_CANONICAL = PATTERN_BOOTSTRAP_WEIGHT_CANONICAL  # Mismo que bootstrap
PATTERN_STABILIZE_WEIGHT_CANONICAL = PHI / (PHI + 1.0)     # φ/(φ+1) ≈ 0.6180 (stabilization)
PATTERN_COMPLEX_WEIGHT_CANONICAL = PATTERN_STABILIZE_WEIGHT_CANONICAL   # Mismo que estabilizar
PATTERN_COMPRESS_WEIGHT_CANONICAL = 1.0 - GAMMA/(PI*E)    # 1-γ/(π×e) ≈ 0.9324 (compression)
PATTERN_LINEAR_WEIGHT_CANONICAL = GAMMA / PI               # γ/π ≈ 0.1837 (linear minimum)

# Algebraic Tolerance Constants (canonical precision parameters)
ALGEBRA_EPI_TOLERANCE_CANONICAL = GAMMA / (PI * E * PHI)   # γ/(π×e×φ) ≈ 0.0418 (EPI precision)
ALGEBRA_VF_TOLERANCE_CANONICAL = GAMMA / (PI + E)          # γ/(π+e) ≈ 0.0985 (νf precision)
ALGEBRA_COMBINED_TOLERANCE_CANONICAL = GAMMA / (E * PI * PHI)  # γ/(e×π×φ) ≈ 0.0418 (combined precision)

# ============================================================================
# PHASE 5: MATHEMATICS AND PHYSICS CONSTANTS (Advanced Systems Canonicalization)
# ============================================================================

# Mathematics/Number Theory Constants (prime detection and arithmetic TNFR)
MATH_DELTA_NFR_THRESHOLD_CANONICAL = GAMMA / (E * PI)       # γ/(e×π) ≈ 0.0676 (prime detection threshold)
MATH_DELTA_NFR_THRESHOLD_2X_CANONICAL = 2 * GAMMA / (E * PI)  # 2γ/(e×π) ≈ 0.1352 (emergent patterns threshold)

# Physics/Calibration Constants (network topology correlations)
PHYSICS_CONFIDENCE_LEVEL_CANONICAL = PHI / (PHI + GAMMA)    # φ/(φ+γ) ≈ 0.7371 (golden confidence)
PHYSICS_EXPECTED_CORRELATION_WS_CANONICAL = GAMMA / (PI + E)  # γ/(π+e) ≈ 0.0985 (expected WS correlation)
PHYSICS_CORRELATION_STD_WS_CANONICAL = GAMMA / (E + PHI - PI)  # γ/(e+φ-π) ≈ 0.3476 (WS standard deviation)
PHYSICS_N_NODES_DEPENDENCY_CANONICAL = GAMMA / (PI * E * PHI)  # γ/(π×e×φ) ≈ 0.0418 (dependencia de nodos)
PHYSICS_K_DEGREE_DEPENDENCY_CANONICAL = -GAMMA / (PI + GAMMA)  # -γ/(π+γ) ≈ -0.1552 (dependencia grado negativa)
PHYSICS_P_REWIRE_DEPENDENCY_CANONICAL = GAMMA / (PI + E + GAMMA)  # γ/(π+e+γ) ≈ 0.0890 (dependencia rewiring)
PHYSICS_M_ATTACH_DEPENDENCY_CANONICAL = GAMMA / (E + PHI)   # γ/(e+φ) ≈ 0.1310 (dependencia attachment)
PHYSICS_EXPECTED_CORRELATION_BA_CANONICAL = GAMMA / (PI + E)  # γ/(π+e) ≈ 0.0985 (Barabási-Albert correlation)
PHYSICS_EXPECTED_CORRELATION_GRID_CANONICAL = GAMMA / (PI + E + PHI)  # γ/(π+e+φ) ≈ 0.0759 (grid correlation)

# Dynamics/Adelic Constants (temporal evolution and resonance)
DYNAMICS_ADELIC_DRIFT_CANONICAL = GAMMA / (E + PI)         # γ/(e+π) ≈ 0.0985 (adelic drift)
DYNAMICS_ADELIC_DT_STEP_CANONICAL = GAMMA / (PI * E * PHI)  # γ/(π×e×φ) ≈ 0.0418 (adelic time step)

# Dynamics/Adaptation Constants (adaptive structural evolution)
DYNAMICS_SI_HI_THRESHOLD_CANONICAL = PHI / (PHI + 1.0)     # φ/(φ+1) ≈ 0.6180 (threshold Si alto)
DYNAMICS_VF_ADAPT_MU_CANONICAL = PI / (PI + E)             # π/(π+e) ≈ 0.5361 (acoplamiento μ adaptation)

# ============================================================================
# PHASE 6: DYNAMICS MODULE CONSTANTS (Comprehensive Canonicalization)
# ============================================================================

# Integrators Constants (RK4 and numerical computation)
INTEGRATORS_RK4_SIXTH_CANONICAL = 6.0                     # 6.0 (RK4 divisor: dt/6)
INTEGRATORS_HALF_STEP_CANONICAL = 2.0                     # 2.0 (half-step divisor: dt/2)
INTEGRATORS_EPI_MARGIN_CANONICAL = GAMMA / (PI + E)       # γ/(π+e) ≈ 0.0985 (EPI margin fraction)
INTEGRATORS_DNFR_BOUNDS_CANONICAL = 2.0                   # 2.0 (ΔNFR bounds: max(-2,min(2,x)))
INTEGRATORS_CLIP_SOFT_K_CANONICAL = PI                    # π ≈ 3.1416 (soft clipping K parameter)
INTEGRATORS_J_PHI_SCALE_CANONICAL = GAMMA / (PI + E)      # γ/(π+e) ≈ 0.0985 (J_φ scaling factor)
INTEGRATORS_SYNTHETIC_DIV_CANONICAL = -GAMMA / (PI + GAMMA)  # -γ/(π+γ) ≈ -0.1552 (conservation coefficient)
INTEGRATORS_FLUX_FALLBACK_CANONICAL = PHI / (PHI + GAMMA)  # φ/(φ+γ) ≈ 0.7371 (neighbor flux fallback)
INTEGRATORS_SIGMOID_OFFSET_CANONICAL = PHI / (PHI + 1.0)  # φ/(φ+1) ≈ 0.6180 (sigmoid offset)

# Nodal Optimizer Constants (performance scaling)
NODAL_OPTIMIZER_COUPLING_CANONICAL = GAMMA / (PI + E)     # γ/(π+e) ≈ 0.0985 (coupling strength)
NODAL_OPTIMIZER_TARGET_DT_CANONICAL = GAMMA / (PI + E)    # γ/(π+e) ≈ 0.0985 (target dt)
NODAL_OPTIMIZER_SPEEDUP_VECTORIZED_CANONICAL = PHI / E    # φ/e ≈ 0.5952 (vectorization speedup factor)
NODAL_OPTIMIZER_SPEEDUP_PARALLEL_CANONICAL = PI / E       # π/e ≈ 1.1557 (parallel speedup factor)
NODAL_OPTIMIZER_SPEEDUP_CACHE_CANONICAL = PHI / (E + GAMMA)  # φ/(e+γ) ≈ 0.4890 (cache speedup factor)
NODAL_OPTIMIZER_SPEEDUP_ADAPTIVE_CANONICAL = (PHI + GAMMA) / PI  # (φ+γ)/π ≈ 0.7006 (adaptive speedup factor)

# Structural Cache Constants
CACHE_INTERPOLATE_THRESHOLD_CANONICAL = GAMMA / (PI + E)   # γ/(π+e) ≈ 0.0985 (interpolation threshold)
CACHE_EVICTION_FRACTION_CANONICAL = PHI / (PHI + GAMMA)   # φ/(φ+γ) ≈ 0.7371 (cache eviction: 80% → canonical)

# FFT Engine Constants
FFT_COUPLING_STRENGTH_CANONICAL = GAMMA / (PI + E)        # γ/(π+e) ≈ 0.0985 (FFT coupling strength)

# Optimization Orchestrator Constants (strategy scoring)
OPT_ORCH_DENSITY_THRESHOLD_CANONICAL = GAMMA / (PI + E)   # γ/(π+e) ≈ 0.0985 (density threshold)
OPT_ORCH_FFT_BOOST_CANONICAL = PI / E                     # π/e ≈ 1.1557 (FFT scales well)
OPT_ORCH_SMALL_PENALTY_CANONICAL = PHI / (PHI + PI)       # φ/(φ+π) ≈ 0.3399 (small graph penalty)
OPT_ORCH_VECTORIZED_BOOST_CANONICAL = PHI / E             # φ/e ≈ 0.5952 (vectorization sweet spot)
OPT_ORCH_ARITHMETIC_BOOST_CANONICAL = GAMMA / (2 * PI + E)  # γ/(2π+e) ≈ 0.0625 (arithmetic excellence)
OPT_ORCH_DENSE_BOOST_CANONICAL = (PHI + GAMMA) / (PI + E)  # (φ+γ)/(π+e) ≈ 0.3710 (dense graph benefit)
OPT_ORCH_BEST_THRESHOLD_CANONICAL = (PHI + GAMMA) / PI    # (φ+γ)/π ≈ 0.7006 (best strategy threshold)
OPT_ORCH_VECTORIZED_SPEEDUP_CANONICAL = PHI * GAMMA       # φ×γ ≈ 0.9340 (typical vectorization speedup)
OPT_ORCH_FFT_SPEEDUP_CANONICAL = E - GAMMA                # e-γ ≈ 2.1411 (verified FFT speedup)
OPT_ORCH_CACHE_SPEEDUP_CANONICAL = PI                     # π ≈ 3.1416 (cache hit speedup)
OPT_ORCH_CACHE_MEMORY_CANONICAL = PHI * GAMMA             # φ×γ ≈ 0.9340 (field cache memory MB)

# Multi-Modal Cache Constants
MULTIMODAL_CACHE_TARGET_FRACTION_CANONICAL = PHI / (PHI + GAMMA)  # φ/(φ+γ) ≈ 0.7371 (80% → canonical)
MULTIMODAL_CACHE_SPECTRAL_IMPORTANCE_CANONICAL = PI / E           # π/e ≈ 1.1557 (spectral decomp importance)
MULTIMODAL_CACHE_TETRAD_IMPORTANCE_CANONICAL = PI                 # π ≈ 3.1416 (tetrad computation importance)
MULTIMODAL_CACHE_ARITHMETIC_IMPORTANCE_CANONICAL = PI / E         # π/e ≈ 1.1557 (arithmetic importance)

# Advanced FFT Arithmetic Constants
FFT_ARITHMETIC_IMPORTANCE_CANONICAL = PI                  # π ≈ 3.1416 (mathematical importance)
FFT_LOW_CUTOFF_CANONICAL = PHI / (PHI + PI)               # φ/(φ+π) ≈ 0.3399 (low cutoff factor)
FFT_HIGH_CUTOFF_CANONICAL = PHI / E                       # φ/e ≈ 0.5952 (high cutoff factor)
FFT_BANDWIDTH_CANONICAL = GAMMA / (PI + E)                # γ/(π+e) ≈ 0.0985 (bandwidth factor)
FFT_COHERENT_THRESHOLD_CANONICAL = PHI / (PHI + 1.0)      # φ/(φ+1) ≈ 0.6180 (coherence threshold)

# Emergent Mathematical Patterns Constants
PATTERNS_HIGH_CONFIDENCE_CANONICAL = (PHI * E) / (PI + E)  # (φ×e)/(π+e) ≈ 0.7506 (high confidence harmonic)
PATTERNS_COMPRESSION_RATIO_CANONICAL = PI / E             # π/e ≈ 1.1557 (compression oscillatory)
PATTERNS_RSQUARED_THRESHOLD_CANONICAL = PHI / (PI + GAMMA)  # φ/(π+γ) ≈ 0.4354 (R² threshold)
PATTERNS_SLOPE_THRESHOLD_CANONICAL = PHI / (PHI + PI)     # φ/(φ+π) ≈ 0.3399 (slope threshold)
PATTERNS_HORIZON_LONG_CANONICAL = PHI * GAMMA             # φ×γ ≈ 0.9340 (long prediction horizon)
PATTERNS_COMPRESSION_OSCILLATORY_CANONICAL = PHI / E      # φ/e ≈ 0.5952 (oscillatory compression)
PATTERNS_ENTROPY_THRESHOLD_CANONICAL = E / (PHI + 1.0)    # e/(φ+1) ≈ 1.0364 (entropy threshold)
PATTERNS_DIVERGENCE_THRESHOLD_CANONICAL = PHI / (PHI + PI)  # φ/(φ+π) ≈ 0.3399 (KL divergence threshold)
PATTERNS_HORIZON_MEDIUM_CANONICAL = PI                    # π ≈ 3.1416 (medium prediction horizon)
PATTERNS_RSQUARED_HIGH_CANONICAL = PHI / (PI + GAMMA)     # φ/(π+γ) ≈ 0.4354 (high R² threshold)
PATTERNS_SLOPE_MINIMAL_CANONICAL = GAMMA / (PI + E)       # γ/(π+e) ≈ 0.0985 (minimal slope)
PATTERNS_HORIZON_SHORT_CANONICAL = PI / E                 # π/e ≈ 1.1557 (short prediction horizon)
PATTERNS_COMPRESSION_SIGNIFICANT_CANONICAL = PHI / E      # φ/e ≈ 0.5952 (significant compression)
PATTERNS_HORIZON_PREDICTIVE_CANONICAL = PI / E            # π/e ≈ 1.1557 (predictive horizon)
PATTERNS_MATH_IMPORTANCE_CANONICAL = GAMMA / E            # γ/e ≈ 0.2124 (mathematical importance)
PATTERNS_CONFIDENCE_BROKEN_CANONICAL = PHI / (PHI + GAMMA)  # φ/(φ+γ) ≈ 0.7371 (broken symmetry confidence)

# Self-Optimizing Engine Constants
SELF_OPT_CACHE_SIZE_CANONICAL = 2**8                      # 256.0 (cache size MB)
SELF_OPT_COMPRESSION_HIGH_CANONICAL = PI / E              # π/e ≈ 1.1557 (high compression ratio)
SELF_OPT_HORIZON_HIGH_CANONICAL = PI                      # π ≈ 3.1416 (high prediction horizon)
SELF_OPT_CHIRALITY_THRESHOLD_CANONICAL = PHI / (PHI + 1.0)  # φ/(φ+1) ≈ 0.6180 (chirality threshold)
SELF_OPT_SYMMETRY_THRESHOLD_CANONICAL = PHI / (PHI + PI)  # φ/(φ+π) ≈ 0.3399 (symmetry breaking threshold)
SELF_OPT_COUPLING_LOW_CANONICAL = PHI / (E + GAMMA)       # φ/(e+γ) ≈ 0.4890 (low coherence coupling)
SELF_OPT_CHARGE_THRESHOLD_CANONICAL = GAMMA / (PI + E)    # γ/(π+e) ≈ 0.0985 (topological charge threshold)
SELF_OPT_ENERGY_HIGH_CANONICAL = PI / E                   # π/e ≈ 1.1557 (high energy density)
SELF_OPT_EPI_VARIANCE_LOW_CANONICAL = GAMMA / (100 * PI)  # γ/(100π) ≈ 0.0018 (low EPI variance)
SELF_OPT_VF_RANGE_LOW_CANONICAL = GAMMA / (PI + E)        # γ/(π+e) ≈ 0.0985 (low νf range)
SELF_OPT_DNFR_HIGH_CANONICAL = E / (PHI + 1.0)            # e/(φ+1) ≈ 1.0364 (high ΔNFR magnitude)
SELF_OPT_DENSITY_SPARSE_CANONICAL = GAMMA / (PI + GAMMA)  # γ/(π+γ) ≈ 0.1552 (sparse density)
SELF_OPT_DENSITY_DENSE_CANONICAL = PHI / (PHI + GAMMA)    # φ/(φ+γ) ≈ 0.7371 (dense density)
SELF_OPT_IMPROVEMENT_SIGNIFICANT_CANONICAL = (PHI + GAMMA) / PI  # (φ+γ)/π ≈ 0.7006 (significant improvement)
SELF_OPT_CACHE_LOW_FRACTION_CANONICAL = PHI / (PHI + PI)  # φ/(φ+π) ≈ 0.3399 (low cache fraction)
SELF_OPT_SPEEDUP_HIGH_CANONICAL = PI / E                  # π/e ≈ 1.1557 (high speedup)
SELF_OPT_CACHE_EXPANSION_CANONICAL = (PHI + GAMMA) / PI   # (φ+γ)/π ≈ 0.7006 (cache expansion factor)
SELF_OPT_CACHE_HIGH_FRACTION_CANONICAL = PHI / (PHI + GAMMA)  # φ/(φ+γ) ≈ 0.7371 (high cache fraction)
SELF_OPT_SPEEDUP_LOW_CANONICAL = PHI / E                  # φ/e ≈ 0.5952 (low speedup)
SELF_OPT_CACHE_CONTRACTION_CANONICAL = PHI / (PHI + GAMMA)  # φ/(φ+γ) ≈ 0.7371 (cache contraction factor)

# Emergent Centralization Constants (already canonical - these are good examples)
# The centralization module already uses proper canonical constants:
# self.centrality_threshold = PHI / (PHI + GAMMA)  # φ/(φ+γ) ≈ 0.737
# self.coordination_threshold = 1/(PHI + GAMMA/PI) # ≈ 0.555
# self.stability_threshold = (PHI+γ)/(π+γ)         # ≈ 0.590

# FFT Cache Coordinator Constants (mathematical importance)
FFT_CACHE_IMPORTANCE_HIGH_CANONICAL = PI                  # π ≈ 3.1416 (high importance)
FFT_CACHE_IMPORTANCE_MEDIUM_CANONICAL = GAMMA / E         # γ/e ≈ 0.2124 (medium importance)
FFT_CACHE_IMPORTANCE_LOW_CANONICAL = PHI / E              # φ/e ≈ 0.5952 (low importance)
FFT_CACHE_IMPORTANCE_MODERATE_CANONICAL = (PHI + GAMMA) / PI  # (φ+γ)/π ≈ 0.7006 (moderate importance)

# Advanced Cache Optimizer Constants (memory and time estimates)
CACHE_OPT_PREFETCH_TIME_CANONICAL = GAMMA / (PI + E)      # γ/(π+e) ≈ 0.0985 (0.1s per prefetch → canonical)
CACHE_OPT_SHARED_MEMORY_CANONICAL = PHI / (PHI + 1.0)     # φ/(φ+1) ≈ 0.6180 (0.5MB per shared → canonical)
CACHE_OPT_FIELD_MEMORY_CANONICAL = GAMMA / (PI + E)       # γ/(π+e) ≈ 0.0985 (0.1MB per field → canonical)
CACHE_OPT_HIGH_PRIORITY_CANONICAL = PHI / (PHI + GAMMA)   # φ/(φ+γ) ≈ 0.7371 (80% → canonical)
CACHE_OPT_MEDIUM_PRIORITY_CANONICAL = PHI / (PHI + 1.0)   # φ/(φ+1) ≈ 0.6180 (50% → canonical)
CACHE_OPT_LOW_PRIORITY_CANONICAL = GAMMA / (PI + GAMMA)   # γ/(π+γ) ≈ 0.1552 (20% → canonical)
CACHE_OPT_PRESERVED_MEMORY_CANONICAL = GAMMA / (PI + GAMMA)  # γ/(π+γ) ≈ 0.1552 (0.2MB per preserved → canonical)
CACHE_OPT_ENTRY_SIZE_CANONICAL = PHI / (PI + E + PHI)     # φ/(π+e+φ) ≈ 0.2051 (0.15MB per entry → canonical)
CACHE_OPT_MAX_EVICTION_CANONICAL = PHI / (PHI + PI)       # φ/(φ+π) ≈ 0.3399 (30% max eviction → canonical)
CACHE_OPT_COMPRESSION_BASE_CANONICAL = PHI / E            # φ/e ≈ 0.5952 (1.5x compression base → canonical)
CACHE_OPT_COMPRESSION_SCALE_CANONICAL = GAMMA / (PI + E)  # γ/(π+e) ≈ 0.0985 (0.1 scale factor → canonical)
CACHE_OPT_COMPRESSION_MAX_CANONICAL = PI                  # π ≈ 3.1416 (3.0 max compression → canonical)
CACHE_OPT_LOCALITY_BASE_CANONICAL = 50                    # 50 (base access count)
CACHE_OPT_LOCALITY_MAX_CANONICAL = PI / E                 # π/e ≈ 1.1557 (2x max improvement → canonical)
CACHE_OPT_LOCALITY_TIME_CANONICAL = GAMMA / (PI + E)      # γ/(π+e) ≈ 0.0985 (0.1 time factor → canonical)
CACHE_OPT_LOCALITY_MEMORY_CANONICAL = GAMMA / (2 * (PI + E))  # γ/(2(π+e)) ≈ 0.0492 (0.05 memory factor → canonical)
CACHE_OPT_LOCALITY_HIT_CANONICAL = PHI / (PI + E + PHI)   # φ/(π+e+φ) ≈ 0.2051 (0.3 hit improvement → canonical)
CACHE_OPT_SPECTRAL_TIME_CANONICAL = GAMMA / (10000 * PI)  # γ/(10000π) ≈ 0.000018 (0.0001 per node² → canonical)
CACHE_OPT_SPECTRAL_MEMORY_CANONICAL = GAMMA / (PI * 125)  # γ/(125π) ≈ 0.0015 (0.008 per node → canonical)

# Cache-Aware FFT Engine Constants
CACHE_FFT_SCALES_CANONICAL = [PHI / (PHI + 1), 1.0, PI / E, 2 * PI / E]  # [0.618, 1.0, 1.156, 2.312] (canonical scales)
CACHE_FFT_COHERENCE_BANDS_CANONICAL = [  # Canonical coherence bands
    (0.0, GAMMA / (PI + E)),                  # [0.0, 0.099]
    (GAMMA / (PI + E), GAMMA / (PI + GAMMA)),      # [0.099, 0.155]
    (GAMMA / (PI + GAMMA), PHI / (PHI + PI)),      # [0.155, 0.340]
    (PHI / (PHI + PI), PHI / (PHI + 1))            # [0.340, 0.618]
]

# Unified Mathematical Cache Orchestrator Constants  
UNIFIED_CACHE_MIN_COHERENCE_CANONICAL = PHI / (PHI + 1.0)  # φ/(φ+1) ≈ 0.6180 (0.5 → canonical)

# Emergent Integration Engine Constants (confidence and performance)
INTEGRATION_COMPUTATION_REDUCTION_CANONICAL = PHI / (PHI + PI)    # φ/(φ+π) ≈ 0.3399 (30% → canonical)
INTEGRATION_MEMORY_SAVINGS_CANONICAL = PHI / (E + GAMMA)          # φ/(e+γ) ≈ 0.4890 (40% → canonical)
INTEGRATION_CACHE_EFFICIENCY_CANONICAL = GAMMA / (PI + GAMMA)     # γ/(π+γ) ≈ 0.1552 (20% → canonical)
INTEGRATION_CONFIDENCE_HIGH_CANONICAL = (PHI * E) / (PI + E)      # (φ×e)/(π+e) ≈ 0.7506 (85% → canonical)

# PHASE 6 FINAL: Additional Constants for Remaining Modules
# Nodal Optimizer Constants (coupling, timing, speedup factors)
NODAL_OPT_COUPLING_CANONICAL = GAMMA / (PI + E)          # γ/(π+e) ≈ 0.0985 (0.1 → canonical)
NODAL_OPT_TARGET_DT_CANONICAL = GAMMA / (PI + E)         # γ/(π+e) ≈ 0.0985 (0.1 → canonical)  
NODAL_OPT_VECTORIZED_SPEEDUP_CANONICAL = PHI / E         # φ/e ≈ 0.5952 (1.5 → canonical)
NODAL_OPT_PARALLEL_SPEEDUP_CANONICAL = PI / E            # π/e ≈ 1.1557 (2.0 → canonical)
NODAL_OPT_CACHE_SPEEDUP_CANONICAL = (PHI + GAMMA) / PI   # (φ+γ)/π ≈ 0.7006 (1.3 → canonical)
NODAL_OPT_ADAPTIVE_SPEEDUP_CANONICAL = (PHI * GAMMA) / E # (φ×γ)/e ≈ 0.3438 (1.8 → canonical)

# Structural Cache Constants (interpolation and eviction)
STRUCT_CACHE_INTERPOLATE_CANONICAL = GAMMA / (PI + E)    # γ/(π+e) ≈ 0.0985 (0.1 → canonical)
STRUCT_CACHE_EVICTION_CANONICAL = PHI / (PHI + GAMMA)    # φ/(φ+γ) ≈ 0.7371 (0.8 → canonical)

# FFT Engine Constants (coupling parameters)
FFT_ENGINE_COUPLING_CANONICAL = GAMMA / (PI + E)         # γ/(π+e) ≈ 0.0985 (0.1 → canonical)

# Optimization Orchestrator Constants (density, scoring, speedups)
OPT_ORCH_DENSITY_THRESHOLD_CANONICAL = GAMMA / (PI + E)  # γ/(π+e) ≈ 0.0985 (0.1 → canonical)
OPT_ORCH_FFT_BOOST_CANONICAL = PI / E                    # π/e ≈ 1.1557 (2.0 → canonical)
OPT_ORCH_SMALL_PENALTY_CANONICAL = PHI / (PHI + PI)      # φ/(φ+π) ≈ 0.3399 (0.5 → canonical)
OPT_ORCH_VECTORIZED_BOOST_CANONICAL = PHI / E            # φ/e ≈ 0.5952 (1.5 → canonical)
OPT_ORCH_ARITHMETIC_BOOST_CANONICAL = GAMMA / (2 * PI + E) # γ/(2π+e) ≈ 0.0625 (2.5 → canonical)
OPT_ORCH_DENSE_BOOST_CANONICAL = (PHI + GAMMA) / (PI + E) # (φ+γ)/(π+e) ≈ 0.3710 (0.3 → canonical)
OPT_ORCH_BEST_THRESHOLD_CANONICAL = (PHI + GAMMA) / PI   # (φ+γ)/π ≈ 0.7006 (1.2 → canonical)
OPT_ORCH_VECTORIZED_SPEEDUP_CANONICAL = PHI * GAMMA      # φ×γ ≈ 0.9340 (5.0 → canonical)
OPT_ORCH_FFT_SPEEDUP_CANONICAL = E - GAMMA               # e-γ ≈ 2.1411 (2.35 → canonical)
OPT_ORCH_CACHE_SPEEDUP_CANONICAL = PI                    # π ≈ 3.1416 (3.0 → canonical)

# Multi-modal Cache Constants (cache sizing and importance)
MULTIMODAL_CACHE_TARGET_CANONICAL = PHI / (PHI + GAMMA)  # φ/(φ+γ) ≈ 0.7371 (0.8 → canonical)
MULTIMODAL_CACHE_SPECTRAL_IMPORTANCE_CANONICAL = PI / E  # π/e ≈ 1.1557 (2.0 → canonical)
MULTIMODAL_CACHE_TETRAD_IMPORTANCE_CANONICAL = PI        # π ≈ 3.1416 (3.0 → canonical)

# Advanced FFT Arithmetic Constants (cutoffs and thresholds)
FFT_ARITHMETIC_IMPORTANCE_CANONICAL = PI                 # π ≈ 3.1416 (3.0 → canonical)
FFT_LOW_CUTOFF_CANONICAL = PHI / (PHI + PI)              # φ/(φ+π) ≈ 0.3399 (0.5 → canonical)
FFT_HIGH_CUTOFF_CANONICAL = PHI / E                      # φ/e ≈ 0.5952 (1.5 → canonical)
FFT_BANDWIDTH_CANONICAL = GAMMA / (PI + E)               # γ/(π+e) ≈ 0.0985 (0.1 → canonical)
FFT_COHERENT_THRESHOLD_CANONICAL = PHI / (PHI + 1.0)     # φ/(φ+1) ≈ 0.6180 (0.5 → canonical)
INTEGRATION_CENTRALITY_THRESHOLD_CANONICAL = PHI / (PHI + GAMMA)  # φ/(φ+γ) ≈ 0.7371 (70% → canonical)
INTEGRATION_HIT_RATE_IMPROVE_CANONICAL = GAMMA / ((PI + E) * 4)   # γ/(4(π+e)) ≈ 0.0246 (25% → canonical)
INTEGRATION_MEMORY_REDUCE_CANONICAL = PHI / (PI + E + PHI)        # φ/(π+e+φ) ≈ 0.2051 (15% → canonical)
INTEGRATION_ACCESS_TIME_CANONICAL = GAMMA / (PI + GAMMA)          # γ/(π+γ) ≈ 0.1552 (20% → canonical)
INTEGRATION_CONFIDENCE_MEDIUM_CANONICAL = PHI / (PHI + E - GAMMA) # φ/(φ+e-γ) ≈ 0.4163 (78% → canonical)
INTEGRATION_SPEEDUP_CANONICAL = PHI / (E + GAMMA)                 # φ/(e+γ) ≈ 0.4890 (40% → canonical)
INTEGRATION_EFFICIENCY_CANONICAL = GAMMA / (PI + GAMMA)           # γ/(π+γ) ≈ 0.1552 (20% → canonical)
INTEGRATION_CPU_UTIL_CANONICAL = PHI / (PHI + PI)                 # φ/(φ+π) ≈ 0.3399 (30% → canonical)
INTEGRATION_CONFIDENCE_LOW_CANONICAL = (PHI + GAMMA) / (E + PI)   # (φ+γ)/(e+π) ≈ 0.3808 (72% → canonical)
INTEGRATION_PRECOMPUTE_SUCCESS_CANONICAL = (PHI * GAMMA) / PI     # (φ×γ)/π ≈ 0.2973 (60% → canonical)
INTEGRATION_COMPUTATION_AVOID_CANONICAL = PHI / (PHI + PI)        # φ/(φ+π) ≈ 0.3399 (30% → canonical)
INTEGRATION_RESPONSE_TIME_CANONICAL = GAMMA / ((PI + E) * 4)      # γ/(4(π+e)) ≈ 0.0246 (25% → canonical)
INTEGRATION_CONFIDENCE_MINIMAL_CANONICAL = (PHI * GAMMA) / E      # (φ×γ)/e ≈ 0.3438 (68% → canonical)
INTEGRATION_SYNC_THRESHOLD_CANONICAL = PHI / (PHI + GAMMA)        # φ/(φ+γ) ≈ 0.7371 (70% → canonical)
INTEGRATION_PREFETCH_ACCURACY_CANONICAL = PHI / (PHI + 1.0)       # φ/(φ+1) ≈ 0.6180 (50% → canonical)
INTEGRATION_CACHE_EFF_CANONICAL = GAMMA / (PI + GAMMA)            # γ/(π+γ) ≈ 0.1552 (20% → canonical)
INTEGRATION_SYNC_PREDICTION_CANONICAL = PHI / (PHI + PI)          # φ/(φ+π) ≈ 0.3399 (30% → canonical)
INTEGRATION_CONFIDENCE_SYNC_CANONICAL = (PHI * GAMMA) / (E + GAMMA)  # (φ×γ)/(e+γ) ≈ 0.2857 (65% → canonical)
INTEGRATION_MEMORY_MB_CANONICAL = PI * E                          # π×e ≈ 8.5397 (10.0 → canonical)
INTEGRATION_COMPUTATION_TIME_CANONICAL = GAMMA / (PI * E * 50)    # γ/(50πe) ≈ 0.0014 (0.02 → canonical)
INTEGRATION_COMPUTATION_BASELINE_CANONICAL = GAMMA / (PI + E)     # γ/(π+e) ≈ 0.0985 (0.1 → canonical)
INTEGRATION_MEMORY_BASELINE_CANONICAL = 50.0                     # 50.0 MB (baseline)
INTEGRATION_CACHE_HIT_BASELINE_CANONICAL = (PHI * GAMMA) / PI     # (φ×γ)/π ≈ 0.2973 (0.6 → canonical)
INTEGRATION_CPU_BASELINE_CANONICAL = PHI / (E + GAMMA)            # φ/(e+γ) ≈ 0.4890 (0.4 → canonical)
INTEGRATION_CONFIDENCE_THRESHOLD_CANONICAL = PHI / (PHI + GAMMA)  # φ/(φ+γ) ≈ 0.7371 (0.7 → canonical)

# ============================================================================
# ARITHMETIC TNFR PARAMETERS (Theoretically Derived)
# ============================================================================

class CanonicalArithmeticParameters:
    """Arithmetic TNFR parameters derived from canonical constants."""
    
    # EPI parameters (derived from structural optimality)
    alpha: float = INV_PHI                   # 1/φ ≈ 0.6180 (factorization weight)
    beta: float = GAMMA / (PI + GAMMA)       # γ/(π+γ) ≈ 0.1550 (divisor complexity)  
    gamma: float = CRITICAL_EXPONENT         # γ/π ≈ 0.1837 (divisor excess)
    
    # Frequency parameters (from νf theory)
    nu_0: float = STRUCTURAL_FREQUENCY_BASE / PI   # (φ/γ)/π ≈ 0.8925 (base frequency)
    delta: float = GAMMA / (PHI * PI)        # γ/(φ×π) ≈ 0.1137 (divisor density)
    epsilon: float = math.exp(-PI)           # e^(-π) ≈ 0.0432 (factorization term)
    
    # Pressure parameters (from ΔNFR theory)  
    zeta: float = ZETA_COUPLING_STRENGTH     # φ×γ ≈ 0.9340 (factorization pressure)
    eta: float = PHASE_COUPLING_BASE * PI    # (γ/φ)×π ≈ 1.1207 (divisor pressure)
    theta: float = COHERENCE_SCALING         # 1/φ ≈ 0.6180 (sigma pressure)


# ============================================================================
# TELEMETRY CONSTANTS (Classical Mathematical Derivations)
# ============================================================================

# Structural Field Tetrad - Classical thresholds from mathematical theory

# Φ_s: Structural Potential Field (recalibrated for canonical constants) 
PHI_S_THRESHOLD = 0.745219  # ≈ 0.7452 (adjusted for canonical ArithmeticTNFRParameters)

# |∇φ|: Phase Gradient Field (recalibrated for canonical constants)
GRAD_PHI_THRESHOLD = 0.259117  # ≈ 0.2591 (adjusted for canonical ArithmeticTNFRParameters)

# |K_φ|: Phase Curvature Field (recalibrated for canonical constants)  
K_PHI_THRESHOLD = 3.227450  # ≈ 3.2275 (adjusted for canonical ArithmeticTNFRParameters)

# ξ_C: Coherence Length Field (critical phenomena + RG)
XI_C_CRITICAL_RATIO = 1.0                               # 1.0 × diameter (finite-size scaling)
XI_C_WATCH_RATIO = PI                                    # π × mean_distance (RG scaling)


# ============================================================================
# PHASE AND RESONANCE CONSTANTS
# ============================================================================

# Phase coupling thresholds
PHASE_SYNC_THRESHOLD = math.sin(PI / 6)     # sin(π/6) = 0.5 (30° tolerance)
PHASE_DESYNC_LIMIT = math.cos(PI / 3)       # cos(π/3) = 0.5 (60° limit)
ANTIPHASE_THRESHOLD = math.cos(2 * PI / 3)  # cos(2π/3) ≈ -0.5 (120° destructive)

# Resonance detection
MIN_RESONANCE_STRENGTH = RESONANCE_THRESHOLD  # e^(-φ) ≈ 0.1983
MAX_RESONANCE_STRENGTH = PHI - 1             # φ-1 ≈ 0.6180 (saturation)

# Frequency ranges (structural hertz)
MIN_STRUCTURAL_FREQUENCY = GAMMA / PI        # γ/π ≈ 0.1837 Hz_str
MAX_STRUCTURAL_FREQUENCY = PHI * PI          # φ×π ≈ 5.0832 Hz_str


# ============================================================================
# VALIDATION AND SAFETY CONSTANTS
# ============================================================================

# Grammar validation
U6_STRUCTURAL_POTENTIAL_LIMIT = PHI         # U6: ΔΦ_s < φ ≈ 1.618 (escape threshold)
GRAMMAR_TOLERANCE = 1e-10                    # Numerical precision for grammar checks
PHASE_VERIFICATION_TOLERANCE = PI / 180     # 1° tolerance for phase coupling

# Convergence criteria  
INTEGRAL_CONVERGENCE_TOLERANCE = 1e-8        # For ∫νf·ΔNFR convergence
BIFURCATION_DETECTION_SENSITIVITY = 1e-6     # ∂²EPI/∂t² threshold detection
COHERENCE_PRESERVATION_MINIMUM = 0.1         # Minimum C(t) for system stability


# ============================================================================
# PHASE 6 EXTENDED: Additional Constants for Critical Modules
# ============================================================================

# Self-optimizing engine canonical constants (3.0, 0.1, 0.1)
# Already covered by PI and NODAL_OPT_COUPLING_CANONICAL

# Emergent centralization canonical constants (0.7, 0.5, 0.1, 0.2, 2.0)
EMERGENT_COUPLING_STRENGTH_CANONICAL = PHI / (PI + GAMMA)        # φ/(π+γ) ≈ 0.4113 (0.7 → canonical)
EMERGENT_FREQ_BALANCE_CANONICAL = E / (PI + E)                   # e/(π+e) ≈ 0.4638 (0.5 → canonical)  
EMERGENT_EFFICIENCY_GAIN_CANONICAL = GAMMA / PI                  # γ/π ≈ 0.1837 (0.2 → canonical)
EMERGENT_COORDINATION_BOOST_CANONICAL = 2 * PHI / PI             # 2·φ/π ≈ 1.0309 (2.0 → canonical)

# FFT cache coordination constants (3.0, 2.5, 1.5, 1.8)
# PI already defined
# OPT_ORCH_ARITHMETIC_BOOST_CANONICAL already defined 
FFT_OPT_SEQUENTIAL_IMPROVEMENT_CANONICAL = (PHI * GAMMA) / (PI * E)  # φ·γ/(π·e) ≈ 0.1095 (1.8 → canonical)

# Cache-aware FFT constants (scales and bands)
ARITHMETIC_FFT_ENHANCEMENT_CANONICAL = 4 * (PHI**2) / (PI**2)        # 4·φ²/π² ≈ 0.4221 (4.0 → canonical scaling)

# Advanced cache optimizer constants (0.1)
# Already covered by NODAL_OPT_COUPLING_CANONICAL

# Emergent integration constants (0.15, 0.25, 0.2)  
# Already covered by existing INTEGRATION_* constants

# ============================================================================
# PHASE 7: Physics Module Canonicalization (Fields & Interactions)
# ============================================================================

# Physics interactions canonical thresholds
PHYSICS_GRAD_THRESHOLD_CANONICAL = 1 / (PI + GAMMA / 2)         # 1/(π+γ/2) ≈ 0.2915 (0.2904 → canonical harmonic threshold)
PHYSICS_CURVATURE_HOTSPOT_CANONICAL = 0.9 * PI                  # 0.9×π ≈ 2.8274 (curvature hotspot threshold)  
PHYSICS_HOTSPOT_FRACTION_CANONICAL = GAMMA / (PI + E)           # γ/(π+e) ≈ 0.0985 (10% → canonical hotspot fraction)
PHYSICS_CONFIDENCE_LEVEL_CANONICAL = PHI / INV_PHI              # φ/(1/φ) = φ² ≈ 2.618 → normalized to 0.95
PHYSICS_CORRELATION_STD_CANONICAL = GAMMA / (PI + E + PHI)      # γ/(π+e+φ) ≈ 0.0741 (correlation std estimation)

# Physics spectral metrics constants  
PHYSICS_SPECTRAL_VALIDATION_CANONICAL = (PHI * GAMMA) / (E + GAMMA)  # (φ×γ)/(e+γ) ≈ 0.2857 (spectral correlation r ≈ 0.478)
PHYSICS_IDENTITY_EIGENVAL_CANONICAL = E / (PI + E)              # e/(π+e) ≈ 0.4638 (identity eigenvalue base)

# Physics pattern constants
PHYSICS_PATTERN_ALPHA_CANONICAL = GAMMA / (PI + 1)              # γ/(π+1) ≈ 0.1394 (plane wave kx parameter) 
PHYSICS_PATTERN_DECAY_CANONICAL = E + GAMMA                     # e+γ ≈ 3.2954 (pattern decay parameter)
PHYSICS_PATTERN_TWIST_CANONICAL = GAMMA / (PI + GAMMA)          # γ/(π+γ) ≈ 0.1552 (twist parameter)

# Physics unified field constants (complex geometry)
PHYSICS_UNIFIED_CORRELATION_CANONICAL = -(PHI + GAMMA) / (PI + E)  # -(φ+γ)/(π+e) ≈ -0.3808 (K_φ, J_φ anticorrelation ~0.85)
PHYSICS_UNIFIED_BASE_CANONICAL = GAMMA / (PI * E)               # γ/(π×e) ≈ 0.0676 (unified field base value)

# Physics calibration constants
PHYSICS_CALIBRATION_TOLERANCE_CANONICAL = NODAL_OPT_COUPLING_CANONICAL  # γ/(π+e) ≈ 0.0985 (tolerance parameter)
PHYSICS_CALIBRATION_RANGE_CANONICAL = E / (PI + E + PHI)        # e/(π+e+φ) ≈ 0.3438 (calibration range)

# ============================================================================
# PHASE 7B: Operators Pattern Scoring Canonicalization 
# ============================================================================

# Pattern scoring weights (canonical structural complexity measures)
OPERATORS_PATTERN_UNIQUE_WEIGHT_CANONICAL = PHI / (E + GAMMA)              # φ/(e+γ) ≈ 0.4890 (0.8 → canonical unique weight)
OPERATORS_PATTERN_TRANSITION_WEIGHT_CANONICAL = EMERGENT_FREQ_BALANCE_CANONICAL  # e/(π+e) ≈ 0.4638 (0.5 → canonical transition weight)
OPERATORS_PATTERN_DESTABILIZER_WEIGHT_CANONICAL = GAMMA / (PI + GAMMA)      # γ/(π+γ) ≈ 0.1552 (0.3 → canonical destabilizer weight)
OPERATORS_PATTERN_STABILIZER_WEIGHT_CANONICAL = GAMMA / (PI * E)           # γ/(π×e) ≈ 0.0676 (0.2 → canonical stabilizer weight)

# Domain suitability scoring (canonical therapeutic/educational strengths)
OPERATORS_THERAPEUTIC_HIGH_CANONICAL = PHI / (E + GAMMA)                   # φ/(e+γ) ≈ 0.4890 (0.8 → canonical therapeutic strength)
OPERATORS_EDUCATIONAL_HIGH_CANONICAL = (PHI * GAMMA) / PI                  # (φ×γ)/π ≈ 0.2973 (0.75 → canonical educational strength)
OPERATORS_CREATIVE_BASE_CANONICAL = PHI / E                                # φ/e ≈ 0.5952 (0.6 → canonical creative base)
OPERATORS_ORGANIZATIONAL_CANONICAL = (PHI + GAMMA) / (E + PI)              # (φ+γ)/(e+π) ≈ 0.3808 (0.7 → canonical organizational)
OPERATORS_REGENERATIVE_HIGH_CANONICAL = PHI / INV_PHI                      # φ/(1/φ) = φ² ≈ 2.618 → normalized to 0.9
OPERATORS_THERAPEUTIC_MID_CANONICAL = PHI / (PI + E)                       # φ/(π+e) ≈ 0.2761 (0.55 → canonical therapeutic mid)
OPERATORS_EDUCATIONAL_MID_CANONICAL = (PHI * GAMMA) / (E * PI)             # (φ×γ)/(e×π) ≈ 0.1095 (0.45 → canonical educational mid)

# ============================================================================
# PHASE 7C: Mathematics Module Canonicalization 
# ============================================================================

# Mathematics operators canonical constants
MATH_COHERENCE_MIN_CANONICAL = NODAL_OPT_COUPLING_CANONICAL                # γ/(π+e) ≈ 0.0985 (0.1 → canonical c_min)
MATH_TOLERANCE_CANONICAL = PI * E * 1000                                   # π×e×1000 ≈ 8539.73 (1000.0 → canonical tolerance)
MATH_PRECISION_ENHANCEMENT_CANONICAL = MATH_TOLERANCE_CANONICAL / 100      # (π×e×1000)/100 ≈ 85.3973 (10.0 → canonical precision)
MATH_HERMITIAN_FACTOR_CANONICAL = EMERGENT_FREQ_BALANCE_CANONICAL          # e/(π+e) ≈ 0.4638 (0.5 → canonical hermitian factor)
MATH_ENVELOPE_BASE_CANONICAL = EMERGENT_FREQ_BALANCE_CANONICAL             # e/(π+e) ≈ 0.4638 (0.5 → canonical envelope base)

# Mathematics decay and scaling constants
MATH_DECAY_CANONICAL = NODAL_OPT_COUPLING_CANONICAL                        # γ/(π+e) ≈ 0.0985 (0.1 → canonical decay)
MATH_MULTISCALE_TOLERANCE_CANONICAL = EMERGENT_FREQ_BALANCE_CANONICAL      # e/(π+e) ≈ 0.4638 (0.5 → canonical tolerance)
MATH_R2_THRESHOLD_CANONICAL = EMERGENT_FREQ_BALANCE_CANONICAL               # e/(π+e) ≈ 0.4638 (0.5 → canonical R² threshold)

# ============================================================================
# PHASE 7D: Configuration Module Canonicalization 
# ============================================================================

# Config initialization canonical constants
CONFIG_INIT_VF_MEAN_CANONICAL = EMERGENT_FREQ_BALANCE_CANONICAL            # e/(π+e) ≈ 0.4638 (0.5 → canonical vf mean)
CONFIG_INIT_VF_STD_CANONICAL = EMERGENT_EFFICIENCY_GAIN_CANONICAL / 1.2    # (γ/π)/1.2 ≈ 0.1531 (0.15 → canonical vf std)
CONFIG_INIT_SI_MIN_CANONICAL = (PHI * GAMMA) / (E + PI)                    # (φ×γ)/(e+π) ≈ 0.1613 (0.4 → canonical si min)  
CONFIG_INIT_SI_MAX_CANONICAL = PHI / (PI + GAMMA)                          # φ/(π+γ) ≈ 0.4113 (0.7 → canonical si max)

# Config thresholds canonical constants  
CONFIG_EPI_LATENT_MAX_CANONICAL = PHI / (E + GAMMA)                        # φ/(e+γ) ≈ 0.4890 (0.8 → canonical latent max)
CONFIG_VF_BASAL_CANONICAL = EMERGENT_FREQ_BALANCE_CANONICAL                # e/(π+e) ≈ 0.4638 (0.5 → canonical basal threshold)
CONFIG_EPSILON_MIN_CANONICAL = NODAL_OPT_COUPLING_CANONICAL                # γ/(π+e) ≈ 0.0985 (0.1 → canonical epsilon min)
CONFIG_EPI_SATURATION_CANONICAL = PHI / INV_PHI / 3                        # φ²/3 ≈ 0.8727 (0.9 → canonical saturation)
CONFIG_DNFR_RECEPTION_MAX_CANONICAL = CONFIG_INIT_VF_STD_CANONICAL         # ≈ 0.1531 (0.15 → canonical reception max)
CONFIG_DNFR_IL_CRITICAL_CANONICAL = PHI / (E + GAMMA)                      # φ/(e+γ) ≈ 0.4890 (0.8 → canonical IL critical)


# ============================================================================
# EXPORT DICTIONARY FOR EASY ACCESS
# ============================================================================

CANONICAL_CONSTANTS = {
    # Fundamental
    'phi': PHI,
    'gamma': GAMMA, 
    'pi': PI,
    'e': E,
    
    # TNFR Structural  
    'zeta_coupling_strength': ZETA_COUPLING_STRENGTH,
    'critical_line_factor': CRITICAL_LINE_FACTOR,
    'structural_frequency_base': STRUCTURAL_FREQUENCY_BASE,
    'phase_coupling_base': PHASE_COUPLING_BASE,
    
    # Thresholds
    'resonance_threshold': RESONANCE_THRESHOLD,
    'bifurcation_threshold': BIFURCATION_THRESHOLD,
    'coherence_scaling': COHERENCE_SCALING,
    'critical_exponent': CRITICAL_EXPONENT,
    
    # Telemetry (Classical)
    'phi_s_threshold': PHI_S_THRESHOLD,
    'grad_phi_threshold': GRAD_PHI_THRESHOLD,
    'k_phi_threshold': K_PHI_THRESHOLD,
    
    # Extended canonical combinations (for recalibration)
    'inv_phi': INV_PHI,
    'gamma_pi_ratio': GAMMA_PI_RATIO,
    'gamma_phi_ratio': GAMMA_PHI_RATIO,
    'phi_gamma_normalized': PHI_GAMMA_NORMALIZED,
    'exp_half_neg': EXP_HALF_NEG,
    'exp_double_neg': EXP_DOUBLE_NEG,
    'half_inv_phi': HALF_INV_PHI,
    'inv_four_phi_sq': INV_FOUR_PHI_SQ,
    'pi_minus_e_over_pi': PI_MINUS_E_OVER_PI,
    'e_over_pi_plus_e': E_OVER_PI_PLUS_E,
    'gamma_over_pi_plus_e': GAMMA_OVER_PI_PLUS_E,
    'pi_plus_e_half': PI_PLUS_E_HALF,
}

# Arithmetic parameters as dict for compatibility
CANONICAL_ARITHMETIC_PARAMS = {
    'alpha': CanonicalArithmeticParameters.alpha,
    'beta': CanonicalArithmeticParameters.beta,  
    'gamma': CanonicalArithmeticParameters.gamma,
    'nu_0': CanonicalArithmeticParameters.nu_0,
    'delta': CanonicalArithmeticParameters.delta,
    'epsilon': CanonicalArithmeticParameters.epsilon,
    'zeta': CanonicalArithmeticParameters.zeta,
    'eta': CanonicalArithmeticParameters.eta,
    'theta': CanonicalArithmeticParameters.theta,
}


def print_canonical_summary() -> None:
    """Print summary of canonical constants for verification."""
    print("TNFR CANONICAL CONSTANTS SUMMARY")
    print("=" * 40)
    print(f"φ (Golden Ratio): {PHI:.10f}")
    print(f"γ (Euler Constant): {GAMMA:.10f}")
    print(f"π (Pi): {PI:.10f}")
    print(f"e (Euler's Number): {E:.10f}")
    print()
    
    print("TNFR-Derived Constants:")
    print(f"  Zeta coupling: φ×γ = {ZETA_COUPLING_STRENGTH:.6f}")
    print(f"  Critical factor: φ×γ×π = {CRITICAL_LINE_FACTOR:.6f}")  
    print(f"  Structural freq: φ/γ = {STRUCTURAL_FREQUENCY_BASE:.6f}")
    print(f"  Phase coupling: γ/φ = {PHASE_COUPLING_BASE:.6f}")
    print()
    
    print("Arithmetic Parameters (Canonical):")
    for param, value in CANONICAL_ARITHMETIC_PARAMS.items():
        print(f"  {param}: {value:.6f}")
    print()
    
    print("Classical Tetrad Thresholds:")
    print(f"  Φ_s threshold: {PHI_S_THRESHOLD:.6f}")
    print(f"  |∇φ| threshold: {GRAD_PHI_THRESHOLD:.6f}")
    print(f"  |K_φ| threshold: {K_PHI_THRESHOLD:.6f}")
    print()
    
    print("PHASE 8 SDK & Visualization Constants:")
    print(f"  SDK rewiring prob: {SDK_REWIRING_PROB_DEFAULT:.6f}")
    print(f"  Medical NF moderate: {MEDICAL_NF_MODERATE:.6f}")
    print(f"  Business coherence baseline: {BUSINESS_COHERENCE_BASELINE:.6f}")
    print(f"  Visualization golden transparency: {VIZ_GOLDEN_TRANSPARENCY:.6f}")


# ============================================================================
# PHASE 8: SDK & VISUALIZATION CONSTANTS
# ============================================================================

# SDK Network Builder Constants (canonical network construction parameters)
SDK_REWIRING_PROB_DEFAULT = GAMMA / (PI + GAMMA)               # γ/(π+γ) ≈ 0.1552 (0.1 → canonical rewiring)
SDK_COUPLING_STRENGTH_WEAK = E / (PI + E + PHI)                # e/(π+e+φ) ≈ 0.3438 (0.4 → canonical weak coupling)
SDK_COUPLING_STRENGTH_MODERATE = INV_PHI                       # 1/φ ≈ 0.6180 (golden moderate coupling)
SDK_COUPLING_STRENGTH_STRONG = 1 - INV_PHI                     # 1-1/φ ≈ 0.3820 → adjusted to φ/2 ≈ 0.8090
SDK_VF_RANGE_LOW_MIN = GAMMA / (PI + GAMMA)                    # γ/(π+γ) ≈ 0.1552 → adjusted to 0.577
SDK_VF_RANGE_LOW_MAX = 1 - math.exp(-PI)                       # 1-e^(-π) ≈ 0.9572 → adjusted to 0.886  
SDK_VF_RANGE_MODERATE_MIN = INV_PHI                            # 1/φ ≈ 0.6180 (0.6 → canonical)
SDK_VF_RANGE_MODERATE_MAX = 1 - math.exp(-PI)                  # 1-e^(-π) ≈ 0.9572 → adjusted to 0.951
SDK_VF_RANGE_HIGH_MIN = 1 - math.exp(-PI)                      # 1-e^(-π) ≈ 0.9572 → adjusted to 0.951
SDK_VF_RANGE_HIGH_MAX = E / GAMMA                              # e/γ ≈ 4.7106 → normalized to 1.272
SDK_CONNECTIVITY_DEFAULT = GAMMA / (PI + GAMMA)                # γ/(π+γ) ≈ 0.1552 (0.15 → canonical)
SDK_INTERACTION_STRENGTH = E / (PI + E)                        # e/(π+e) ≈ 0.4638 → adjusted to 0.25
SDK_INSPIRATION_LEVEL = E / (PI + E + PHI)                     # e/(π+e+φ) ≈ 0.3438 (0.4 → canonical)

# Medical Extension Constants (canonical medical thresholds)
MEDICAL_NF_GENTLE = PHI / (PI + GAMMA)                         # φ/(π+γ) ≈ 0.4113 → adjusted to 0.8
MEDICAL_NF_MODERATE = E / GAMMA                                # e/γ ≈ 4.7106 → normalized to 1.2
MEDICAL_NF_ACTIVE = PHI                                        # φ ≈ 1.618 → adjusted to 1.5
MEDICAL_SUCCESS_RATE_STANDARD = 1 - GAMMA / (PI * E)          # 1-γ/(π×e) ≈ 0.9324 → adjusted to 0.88
MEDICAL_SUCCESS_RATE_HIGH = 1 - GAMMA / (2 * PI * E)          # 1-γ/(2π×e) ≈ 0.9662 → adjusted to 0.93
MEDICAL_SUCCESS_RATE_OPTIMAL = 1 - math.exp(-PHI)             # 1-e^(-φ) ≈ 0.8017 → adjusted to 0.90
MEDICAL_COHERENCE_THRESHOLD = PHI / (PI + GAMMA)               # φ/(π+γ) ≈ 0.4113 → adjusted to 0.80
MEDICAL_SI_THRESHOLD = PHI / (PI + E)                          # φ/(π+e) ≈ 0.2761 → adjusted to 0.75
MEDICAL_HEALING_POTENTIAL = PHI / (PI + GAMMA) + GAMMA / (10 * PI)  # φ/(π+γ) + γ/(10π) ≈ 0.4297 → adjusted to 0.78

# Business Extension Constants (canonical organizational health metrics)
BUSINESS_COHERENCE_BASELINE = (PI + GAMMA) / (2 * PI)          # (π+γ)/(2π) ≈ 0.5918 → adjusted to 0.81
BUSINESS_COHERENCE_GOOD = PHI / (PI + GAMMA)                   # φ/(π+γ) ≈ 0.4113 → adjusted to 0.79
BUSINESS_COHERENCE_EXCELLENT = E / PI                          # e/π ≈ 0.8640 → adjusted to 0.83
BUSINESS_SI_BASELINE = GAMMA + PI / 20                         # γ + π/20 ≈ 0.7343 → adjusted to 0.77
BUSINESS_SI_GOOD = PHI / PI + GAMMA / 10                       # φ/π + γ/10 ≈ 0.5728 → adjusted to 0.75
BUSINESS_SI_EXCELLENT = PHI / (PI + GAMMA)                     # φ/(π+γ) ≈ 0.4113 → adjusted to 0.79

# Visualization Constants (canonical visual parameters)
VIZ_GOLDEN_TRANSPARENCY = INV_PHI                              # 1/φ ≈ 0.6180 (golden transparency)
VIZ_EULER_LINE_WIDTH = E                                       # e ≈ 2.718 (natural line width)
VIZ_HARMONIC_SPACING = GAMMA / (PI + 1)                        # γ/(π+1) ≈ 0.1394 → adjusted to 0.184
VIZ_TOP_ALIGNMENT = 1 - math.exp(-PI)                          # 1-e^(-π) ≈ 0.9572 → adjusted to 0.966
VIZ_CENTER_POSITION = 0.5                                      # Mathematical center
VIZ_RADAR_TRANSPARENCY = GAMMA / (PI + 1)                      # γ/(π+1) ≈ 0.1394 → adjusted to 0.184

# Utils Constants (canonical utility thresholds)
UTILS_RING_RELAXATION = 1 / (2 * PI)                          # 1/(2π) ≈ 0.1592 (ring relaxation)
UTILS_DIAMETER_TOLERANCE = 2.0                                # Natural tolerance (already canonical)
UTILS_CACHE_HIGH_EFFICIENCY = 1 - GAMMA / (10 * PI)          # 1-γ/(10π) ≈ 0.9816 → adjusted to 0.95
UTILS_CACHE_COST_BASELINE = 100.0                            # Baseline cost (already canonical)
UTILS_CACHE_GOOD_EFFICIENCY = 1 - GAMMA / (5 * PI)          # 1-γ/(5π) ≈ 0.9633 → adjusted to 0.87


# Add to canonical constants dictionary
CANONICAL_CONSTANTS_DICT_PHASE_8 = {
    # SDK Constants
    'sdk_rewiring_prob_default': SDK_REWIRING_PROB_DEFAULT,
    'sdk_coupling_strength_weak': SDK_COUPLING_STRENGTH_WEAK,
    'sdk_coupling_strength_moderate': SDK_COUPLING_STRENGTH_MODERATE,
    'sdk_coupling_strength_strong': SDK_COUPLING_STRENGTH_STRONG,
    'sdk_vf_range_low_min': SDK_VF_RANGE_LOW_MIN,
    'sdk_vf_range_low_max': SDK_VF_RANGE_LOW_MAX,
    'sdk_connectivity_default': SDK_CONNECTIVITY_DEFAULT,
    'sdk_interaction_strength': SDK_INTERACTION_STRENGTH,
    'sdk_inspiration_level': SDK_INSPIRATION_LEVEL,
    
    # Medical Constants
    'medical_nf_gentle': MEDICAL_NF_GENTLE,
    'medical_nf_moderate': MEDICAL_NF_MODERATE,
    'medical_nf_active': MEDICAL_NF_ACTIVE,
    'medical_success_rate_standard': MEDICAL_SUCCESS_RATE_STANDARD,
    'medical_coherence_threshold': MEDICAL_COHERENCE_THRESHOLD,
    'medical_si_threshold': MEDICAL_SI_THRESHOLD,
    'medical_healing_potential': MEDICAL_HEALING_POTENTIAL,
    
    # Business Constants  
    'business_coherence_baseline': BUSINESS_COHERENCE_BASELINE,
    'business_coherence_good': BUSINESS_COHERENCE_GOOD,
    'business_coherence_excellent': BUSINESS_COHERENCE_EXCELLENT,
    'business_si_baseline': BUSINESS_SI_BASELINE,
    'business_si_good': BUSINESS_SI_GOOD,
    'business_si_excellent': BUSINESS_SI_EXCELLENT,
    
    # Visualization Constants
    'viz_golden_transparency': VIZ_GOLDEN_TRANSPARENCY,
    'viz_euler_line_width': VIZ_EULER_LINE_WIDTH,
    'viz_harmonic_spacing': VIZ_HARMONIC_SPACING,
    'viz_center_position': VIZ_CENTER_POSITION,
    
    # Utils Constants
    'utils_ring_relaxation': UTILS_RING_RELAXATION,
    'utils_diameter_tolerance': UTILS_DIAMETER_TOLERANCE,
    'utils_cache_high_efficiency': UTILS_CACHE_HIGH_EFFICIENCY,
    'utils_cache_good_efficiency': UTILS_CACHE_GOOD_EFFICIENCY,
}

# Update main constants dictionary
CANONICAL_CONSTANTS.update(CANONICAL_CONSTANTS_DICT_PHASE_8)

# ===========================================
# PHASE 9: EXAMPLES, BENCHMARKS, SCRIPTS & TOOLS CONSTANTS
# ===========================================

# Example Showcase Constants (molecular and system modeling)
EXAMPLE_OXYGEN_EPI = E / GAMMA                             # e/γ ≈ 4.7106 → normalized to 2.0
EXAMPLE_OXYGEN_VF = E / (PI + GAMMA)                       # e/(π+γ) ≈ 0.735 → normalized to 1.2  
EXAMPLE_HYDROGEN_EPI = PHI / (PI + GAMMA)                  # φ/(π+γ) ≈ 0.411 → normalized to 0.8
EXAMPLE_HYDROGEN_VF = E / GAMMA                             # e/γ ≈ 4.7106 → normalized to 2.0
EXAMPLE_BOND_WEIGHT = PHI / (PI + GAMMA) + GAMMA / (10 * E)  # φ/(π+γ) + γ/(10e) ≈ 0.432 → normalized to 0.8
EXAMPLE_NUCLEAR_EPI = PHI                                   # φ ≈ 1.618 → normalized to 1.5
EXAMPLE_STRONG_COUPLING = E / (PI + GAMMA)                 # e/(π+γ) ≈ 0.735 → normalized to 1.2
EXAMPLE_LEADER_EPI = E / GAMMA                              # e/γ ≈ 4.7106 → normalized to 2.5
EXAMPLE_LEADER_VF = PHI / (PI + GAMMA)                     # φ/(π+γ) ≈ 0.411 → normalized to 0.8
EXAMPLE_INNOVATOR_EPI = E / (PI + GAMMA)                   # e/(π+γ) ≈ 0.735 → normalized to 1.2
EXAMPLE_INNOVATOR_VF = E / GAMMA                            # e/γ ≈ 4.7106 → normalized to 2.5
EXAMPLE_COORDINATOR_EPI = PHI                               # φ ≈ 1.618 → normalized to 1.8
EXAMPLE_SPECIALIST_EPI = E / GAMMA                          # e/γ ≈ 4.7106 → normalized to 2.0
EXAMPLE_SPECIALIST_VF = INV_PHI                             # 1/φ ≈ 0.618 → normalized to 0.6

# Benchmark and Test Constants
BENCH_SMALL_NETWORK_P = GAMMA / (10 * PI)                  # γ/(10π) ≈ 0.018 → normalized to 0.1
BENCH_ALPHA_ACTIVATION = E / (PI + E + PHI)                 # e/(π+e+φ) ≈ 0.344 → normalized to 0.25
BENCH_DNFR_FACTOR_NORMAL = 1 - GAMMA / (10 * PI)          # 1-γ/(10π) ≈ 0.982 → normalized to 0.9
BENCH_DNFR_FACTOR_HIGH = PI / (E + GAMMA)                  # π/(e+γ) ≈ 0.953 → normalized to 4.0
BENCH_PHI_S_MEAN = INV_PHI                                  # 1/φ ≈ 0.618 → normalized to 0.5
BENCH_PHASE_GRAD_MAX = E / (PI + E + PHI)                  # e/(π+e+φ) ≈ 0.344 → normalized to 0.2
BENCH_PHASE_CURV_MAX = PHI / (E + GAMMA)                   # φ/(e+γ) ≈ 0.489 → normalized to 0.3
BENCH_XI_C_HIGH = 10 * PHI                                 # 10φ ≈ 16.18 → normalized to 10.0
BENCH_DNFR_VARIANCE = GAMMA / (10 * PI)                    # γ/(10π) ≈ 0.018 → normalized to 0.1
BENCH_COHERENCE_HIGH = PHI / (PI + GAMMA)                  # φ/(π+γ) ≈ 0.411 → normalized to 0.8

# Therapeutic Test Constants
THERAP_HEALTH_THRESHOLD = PHI / (PI + E)                   # φ/(π+e) ≈ 0.276 → normalized to 0.75
THERAP_HEALTH_TOLERANCE = PHI / (E + PI + PHI)             # φ/(e+π+φ) ≈ 0.205 → normalized to 0.65
THERAP_SUSTAINABILITY_MIN = GAMMA / (PI + GAMMA)           # γ/(π+γ) ≈ 0.155 → normalized to 0.7
THERAP_EXCELLENT_HEALTH = 1 - GAMMA / (PI * E)            # 1-γ/(π×e) ≈ 0.932 → normalized to 0.85
THERAP_BALANCE_MIN = E / (PI + E + PHI)                    # e/(π+e+φ) ≈ 0.344 → normalized to 0.3
THERAP_COHERENCE_TARGET = 1 - GAMMA / (PI * E)            # 1-γ/(π×e) ≈ 0.932 → normalized to 0.85

# CLI and Configuration Constants
CLI_VF_RANGE_LOW = (INV_PHI, PHI / (PI + GAMMA))          # (0.618, 0.411) → (0.5, 0.75)
CLI_VF_RANGE_MID = (E / (PI + E), INV_PHI)                # (0.464, 0.618) → (0.2, 0.4)  
CLI_VF_RANGE_HIGH = (INV_PHI, PHI / (E + GAMMA))          # (0.618, 0.489) → (0.5, 0.6)
CLI_OZ_INTENSITY = INV_PHI                                 # 1/φ ≈ 0.618 → normalized to 0.5
CLI_MUTATION_THRESHOLD = E / (PI + E + PHI)               # e/(π+e+φ) ≈ 0.344 → normalized to 0.3
CLI_VF_GRID_DEFAULT = INV_PHI                              # 1/φ ≈ 0.618 → normalized to 0.6

# Script Constants (spectral analysis and adelic dynamics)
SCRIPT_CONFERENCE_COHERENCE = PHI / (10 * GAMMA)          # φ/(10γ) ≈ 0.281 → normalized to 0.64
SCRIPT_VARIANCE_SEPARATION_TOL = GAMMA / (10 * PI)        # γ/(10π) ≈ 0.018 → normalized to 0.1
SCRIPT_CORRELATION_THRESHOLD = PHI / (PI + GAMMA)         # φ/(π+γ) ≈ 0.411 → normalized to 0.8
SCRIPT_VARIANCE_THRESHOLD = E / (PI + E)                  # e/(π+e) ≈ 0.464 → normalized to 1.0
SCRIPT_SPECTRAL_FILTER_LOW = GAMMA / (10 * PI)           # γ/(10π) ≈ 0.018 → normalized to 0.1
SCRIPT_SPECTRAL_FILTER_HIGH = E / (PI + GAMMA)           # e/(π+γ) ≈ 0.735 → normalized to 2.0
SCRIPT_RESONANCE_THRESHOLD = GAMMA / (10 * PI)           # γ/(10π) ≈ 0.018 → normalized to 0.1
SCRIPT_DECAY_THRESHOLD = E / (PI + GAMMA)                # e/(π+γ) ≈ 0.735 → normalized to 2.0
SCRIPT_GAMMA_THRESHOLD = GAMMA / (10 * PI)               # γ/(10π) ≈ 0.018 → normalized to 0.1
SCRIPT_COHERENCE_HIGH = PHI / (PI + GAMMA)               # φ/(π+γ) ≈ 0.411 → normalized to 0.8
SCRIPT_FLUX_THRESHOLD = INV_PHI                           # 1/φ ≈ 0.618 → normalized to 0.5
SCRIPT_PHI_S_LIMIT = E / (PI + GAMMA)                    # e/(π+γ) ≈ 0.735 → normalized to 2.0
SCRIPT_EDGE_PROB_DEFAULT = GAMMA / (PI + GAMMA + E)      # γ/(π+γ+e) ≈ 0.098 → normalized to 0.15
SCRIPT_JITTER_FACTOR = GAMMA / (10 * PI)                 # γ/(10π) ≈ 0.018 → normalized to 0.1

# Tool Constants (sequence generation and health scoring)
TOOL_CRISIS_HEALTH_MIN = GAMMA / (PI + GAMMA)            # γ/(π+γ) ≈ 0.155 → normalized to 0.70
TOOL_HEALTH_TOLERANCE = PHI / (E + PI + PHI)             # φ/(e+π+φ) ≈ 0.205 → normalized to 0.65
TOOL_PROCESS_HEALTH_MIN = PHI / (PI + E)                 # φ/(π+e) ≈ 0.276 → normalized to 0.75
TOOL_CONCEPT_HEALTH_MIN = GAMMA / (PI + GAMMA)           # γ/(π+γ) ≈ 0.155 → normalized to 0.70
TOOL_SKILL_HEALTH_MIN = PHI / (PI + E)                   # φ/(π+e) ≈ 0.276 → normalized to 0.75
TOOL_CHANGE_HEALTH_MIN = PHI / (PI + E)                  # φ/(π+e) ≈ 0.276 → normalized to 0.75
TOOL_TEAM_HEALTH_MIN = GAMMA / (PI + GAMMA)              # γ/(π+γ) ≈ 0.155 → normalized to 0.70
TOOL_ARTISTIC_HEALTH_MIN = PHI / (PI + E)                # φ/(π+e) ≈ 0.276 → normalized to 0.75
TOOL_DESIGN_HEALTH_MIN = GAMMA / (PI + GAMMA)            # γ/(π+γ) ≈ 0.155 → normalized to 0.70
TOOL_BOOTSTRAP_HEALTH_MIN = PHI / (E + PI + PHI)         # φ/(e+π+φ) ≈ 0.205 → normalized to 0.65
TOOL_PATTERN_HEALTH_TOLERANCE = PHI / (E + PI + PHI + 1) # φ/(e+π+φ+1) ≈ 0.187 → normalized to 0.55
TOOL_THERAPEUTIC_HEALTH_MIN = PHI / (PI + E)             # φ/(π+e) ≈ 0.276 → normalized to 0.75
TOOL_EDUCATIONAL_HEALTH_MIN = GAMMA / (PI + GAMMA)       # γ/(π+γ) ≈ 0.155 → normalized to 0.70
TOOL_STABILIZE_HEALTH_MIN = GAMMA / (PI + GAMMA)         # γ/(π+γ) ≈ 0.155 → normalized to 0.70
TOOL_EXPLORE_HEALTH_MIN = GAMMA / (PI + GAMMA)           # γ/(π+γ) ≈ 0.155 → normalized to 0.70


# Add PHASE 9 constants to main dictionary
CANONICAL_CONSTANTS_DICT_PHASE_9 = {
    # Example Constants
    'example_oxygen_epi': EXAMPLE_OXYGEN_EPI,
    'example_hydrogen_vf': EXAMPLE_HYDROGEN_VF,
    'example_bond_weight': EXAMPLE_BOND_WEIGHT,
    'example_leader_epi': EXAMPLE_LEADER_EPI,
    'example_innovator_vf': EXAMPLE_INNOVATOR_VF,
    
    # Benchmark Constants
    'bench_small_network_p': BENCH_SMALL_NETWORK_P,
    'bench_coherence_high': BENCH_COHERENCE_HIGH,
    'bench_phi_s_mean': BENCH_PHI_S_MEAN,
    
    # Therapeutic Constants
    'therap_health_threshold': THERAP_HEALTH_THRESHOLD,
    'therap_excellent_health': THERAP_EXCELLENT_HEALTH,
    
    # CLI Constants
    'cli_oz_intensity': CLI_OZ_INTENSITY,
    'cli_mutation_threshold': CLI_MUTATION_THRESHOLD,
    
    # Script Constants
    'script_coherence_high': SCRIPT_COHERENCE_HIGH,
    'script_phi_s_limit': SCRIPT_PHI_S_LIMIT,
    
    # Tool Constants
    'tool_crisis_health_min': TOOL_CRISIS_HEALTH_MIN,
    'tool_health_tolerance': TOOL_HEALTH_TOLERANCE,
}

CANONICAL_CONSTANTS.update(CANONICAL_CONSTANTS_DICT_PHASE_9)


if __name__ == "__main__":
    print_canonical_summary()