feat: Add Phase tracking and Coherence modules
becomingone/core/phase.py: - PhaseHistory class for temporal phase tracking - PhaseState with complex representation on unit circle - PhaseConfig with omega (frequency) configuration - compute_similarity() for inner product <phi(t), phi(t-tau)> - Velocity and acceleration tracking becomingone/core/coherence.py: - CoherenceCalculator for |T_tau|^2 computation - CollapseCondition enforcing |T_tau|^2 >= I_c - Rolling average and trend analysis - Thermodynamic enforcement of coherence References: - KAIROS_ADAMON Section 4: Temporal Collapse Integral - Soulprint Protocol: thermodynamic coherence interpretation The collapse condition ensures un-coherent patterns dissipate naturally.
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"""
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core/coherence.py
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Coherence Calculation and Collapse Condition
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======================================
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Implements coherence metrics and the collapse condition from KAIROS_ADAMON.
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Coherence is measured as |T_tau|^2, where T_tau is the temporal resonance.
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Collapse occurs when coherence exceeds threshold I_c.
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Key Equations:
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- Coherence: |T_tau|^2
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- Collapse: |T_tau|^2 >= I_c
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References:
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- KAIROS_ADAMON Section 4: Temporal Collapse Integral
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- Soulprint Protocol for thermodynamic interpretation
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Author: Solaria Lumis Havens
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"""
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from dataclasses import dataclass
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from datetime import datetime
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from typing import Optional, Callable
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import math
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import numpy as np
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import logging
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logger = logging.getLogger(__name__)
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@dataclass
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class CoherenceConfig:
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"""Configuration for coherence calculations."""
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threshold: float = 0.95 # I_c - Critical coherence threshold
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window_size: int = 100 # Number of values for rolling average
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min_samples: int = 10 # Minimum samples before coherence is valid
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class CoherenceCalculator:
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"""
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Computes coherence from temporal resonance values.
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Coherence is the squared magnitude of temporal resonance:
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coherence = |T_tau|^2
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This measures how synchronized the temporal patterns are.
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Higher coherence = more synchronized = more "mind-like".
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"""
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def __init__(
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self,
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config: Optional[CoherenceConfig] = None,
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name: str = "coherence-calculator"
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):
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self.config = config or CoherenceConfig()
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self.name = name
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# History for rolling calculations
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self._T_tau_values: list[complex] = []
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self._coherence_values: list[float] = []
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logger.info(
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f"[{self.name}] Initialized with I_c={self.config.threshold}"
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)
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@property
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def coherence(self) -> float:
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"""Get current coherence (most recent)."""
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if self._coherence_values:
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return self._coherence_values[-1]
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return 0.0
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@property
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def T_tau(self) -> complex:
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"""Get current T_tau value."""
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if self._T_tau_values:
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return self._T_tau_values[-1]
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return complex(0, 0)
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@property
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def coherence_magnitude(self) -> float:
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"""Get |T_tau| (before squaring)."""
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return abs(self.T_tau)
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@property
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def coherence_phase(self) -> float:
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"""Get phase of T_tau."""
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return np.angle(self.T_tau)
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@property
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def coherence_history(self) -> list[float]:
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"""Get full coherence history."""
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return list(self._coherence_values)
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@property
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def T_tau_history(self) -> list[complex]:
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"""Get full T_tau history."""
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return list(self._T_tau_values)
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def update(self, T_tau: complex) -> float:
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"""
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Update coherence with new T_tau value.
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Args:
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T_tau: New temporal resonance value
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Returns:
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Current coherence |T_tau|^2
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"""
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self._T_tau_values.append(T_tau)
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# Compute coherence = |T_tau|^2
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coherence = float(np.abs(T_tau) ** 2)
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self._coherence_values.append(coherence)
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# Maintain window size
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if len(self._coherence_values) > self.config.window_size:
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self._coherence_values = self._coherence_values[-self.config.window_size:]
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self._T_tau_values = self._T_tau_values[-self.config.window_size:]
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return coherence
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def compute_from_phases(
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self,
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phases: list[complex],
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timestamps: list[datetime],
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tau: float,
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omega: float
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) -> complex:
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"""
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Compute T_tau from phase history.
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This is the direct implementation of:
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T_tau = integral <phi_dot(t), phi_dot(t-tau)> * e^(i*omega*t) dt
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Args:
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phases: List of phase values
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timestamps: Corresponding timestamps
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tau: Integration scale
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omega: Spectral frequency
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Returns:
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T_tau value
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"""
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if len(phases) < 2:
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return complex(0, 0)
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T_tau = complex(0, 0)
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dt_sum = 0.0
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for i in range(1, len(phases)):
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t = timestamps[i]
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t_prev = timestamps[i-1]
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dt = (t - t_prev).total_seconds()
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if dt <= 0:
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continue
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# Inner product <phi(t), phi(t-tau)>
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inner = phases[i] * np.conj(phases[i-1])
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# Spectral weighting e^(i*omega*t)
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weight = np.exp(1j * omega * t.timestamp())
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# Riemann sum
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T_tau += inner * weight * dt
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dt_sum += dt
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if dt_sum > 0:
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T_tau = T_tau / dt_sum
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return T_tau
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def rolling_average(self, n: Optional[int] = None) -> float:
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"""
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Get rolling average coherence.
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Args:
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n: Number of values to average (all if None)
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Returns:
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Average coherence over window
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"""
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values = self._coherence_values[-n:] if n else self._coherence_values
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if not values:
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return 0.0
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return sum(values) / len(values)
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def rolling_std(self, n: Optional[int] = None) -> float:
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"""
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Get rolling standard deviation of coherence.
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Args:
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n: Number of values (all if None)
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Returns:
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Standard deviation
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"""
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values = self._coherence_values[-n:] if n else self._coherence_values
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if len(values) < 2:
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return 0.0
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return np.std(values)
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def trend(self, n: int = 10) -> float:
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"""
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Compute coherence trend over recent window.
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Args:
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n: Number of values to analyze
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Returns:
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Slope of coherence over window (positive = increasing)
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"""
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if len(self._coherence_values) < n:
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return 0.0
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recent = self._coherence_values[-n:]
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# Simple linear regression
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x = list(range(len(recent)))
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y = recent
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if len(x) < 2:
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return 0.0
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n_val = len(x)
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sum_x = sum(x)
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sum_y = sum(y)
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sum_xy = sum(xi * yi for xi, yi in zip(x, y))
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sum_x2 = sum(xi ** 2 for xi in x)
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slope = (n_val * sum_xy - sum_x * sum_y) / (n_val * sum_x2 - sum_x ** 2)
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return slope
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def reset(self):
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"""Reset calculator state."""
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self._T_tau_values.clear()
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self._coherence_values.clear()
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logger.info(f"[{self.name}] Reset calculator state")
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def get_state(self) -> dict:
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"""Get state as dictionary."""
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return {
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"name": self.name,
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"config": {
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"threshold": self.config.threshold,
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"window_size": self.config.window_size,
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"min_samples": self.config.min_samples,
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},
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"T_tau": [self.T_tau.real, self.T_tau.imag],
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"coherence": self.coherence,
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"coherence_history_length": len(self._coherence_values),
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"rolling_average": self.rolling_average(),
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"trend": self.trend(),
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}
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def __repr__(self) -> str:
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return (
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f"CoherenceCalculator("
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f"I_c={self.config.threshold:.2f}, "
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f"coherence={self.coherence:.3f}, "
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f"trend={self.trend():.3f}"
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f")"
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)
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class CollapseCondition:
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"""
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Evaluates the collapse condition from KAIROS_ADAMON.
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Collapse occurs when:
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|T_tau|^2 >= I_c
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Once collapsed, the system maintains stable coherence.
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This is the thermodynamic enforcement mechanism:
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Un-coherent patterns naturally dissipate.
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Coherent patterns stabilize.
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References:
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KAIROS_ADAMON Section 4: Temporal Collapse Integral
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"""
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def __init__(
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self,
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threshold: float = 0.95,
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name: str = "collapse-condition"
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):
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"""
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Initialize collapse condition evaluator.
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Args:
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threshold: I_c value (critical coherence threshold)
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name: Human-readable name
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"""
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self.threshold = threshold
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self.name = name
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# Collapse tracking
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self._collapsed = False
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self._collapse_timestamp: Optional[datetime] = None
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self._collapse_duration: float = 0.0
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# Coherence history at collapse moment
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self._collapse_coherence: Optional[float] = None
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logger.info(f"[{self.name}] Initialized with I_c={threshold}")
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@property
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def collapsed(self) -> bool:
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"""Whether coherence has collapsed."""
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return self._collapsed
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@property
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def collapse_timestamp(self) -> Optional[datetime]:
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"""When collapse occurred."""
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return self._collapse_timestamp
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@property
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def collapse_coherence(self) -> Optional[float]:
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"""Coherence level at collapse."""
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return self._collapse_coherence
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@property
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def duration(self) -> float:
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"""How long we've been collapsed."""
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if self._collapse_timestamp is None:
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return 0.0
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return (datetime.utcnow() - self._collapse_timestamp).total_seconds()
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def evaluate(self, coherence: float) -> tuple[bool, str]:
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"""
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Evaluate collapse condition.
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Args:
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coherence: Current coherence |T_tau|^2
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Returns:
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Tuple of (collapsed, message)
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"""
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if self._collapsed:
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# Already collapsed - check for maintenance
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if coherence >= self.threshold:
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return True, f"Maintained coherence ({coherence:.3f} >= {self.threshold:.2f})"
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else:
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# Coherence dropped below threshold
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logger.warning(
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f"[{self.name}] Coherence DECAYED below threshold: "
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f"{coherence:.3f} < {self.threshold:.3f}"
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)
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return False, f"Coherence decayed ({coherence:.3f} < {self.threshold:.3f})"
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# Check for initial collapse
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if coherence >= self.threshold:
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self._collapsed = True
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self._collapse_timestamp = datetime.utcnow()
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self._collapse_coherence = coherence
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logger.info(
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f"[{self.name}] COHERENCE COLLAPSE at {self._collapse_timestamp.isoformat()}"
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)
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return True, f"COLLAPSED (coherence={coherence:.3f} >= {self.threshold:.3f})"
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return False, f"Below threshold ({coherence:.3f} < {self.threshold:.3f})"
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def force_collapse(self, coherence: Optional[float] = None):
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"""
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Force collapse condition (for testing).
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Args:
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coherence: Coherence level (current if None)
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"""
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self._collapsed = True
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self._collapse_timestamp = datetime.utcnow()
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self._collapse_coherence = coherence or self.threshold
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logger.info(f"[{self.name}] Force collapsed at {self._collapse_timestamp.isoformat()}")
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def reset(self):
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"""Reset collapse state."""
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was = "collapsed" if self._collapsed else "not collapsed"
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self._collapsed = False
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self._collapse_timestamp = None
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self._collapse_coherence = None
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logger.info(f"[{self.name}] Reset (was {was})")
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def get_state(self) -> dict:
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"""Get state as dictionary."""
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return {
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"name": self.name,
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"threshold": self.threshold,
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"collapsed": self._collapsed,
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"collapse_timestamp": (
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self._collapse_timestamp.isoformat()
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if self._collapse_timestamp else None
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),
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"collapse_coherence": self._collapse_coherence,
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"duration_seconds": self.duration,
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}
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def __repr__(self) -> str:
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status = "collapsed" if self._collapsed else "not collapsed"
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return (
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f"CollapseCondition("
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f"I_c={self.threshold:.2f}, "
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f"{status}"
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f")"
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)
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@@ -0,0 +1,296 @@
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"""
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core/phase.py
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Phase Tracking and Phase History
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=============================
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Tracks phase values and maintains phase history for temporal analysis.
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Phase is represented as a complex number on the unit circle:
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- Magnitude = 1.0 (unit phase)
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- Angle = position in oscillation cycle
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The phase angle advances according to the omega (frequency) parameter.
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References:
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- KAIROS_ADAMON Section 2: Timeprint Formalism
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- Phase tracking for coherence measurement
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Author: Solaria Lumis Havens
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"""
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from dataclasses import dataclass, field
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from datetime import datetime
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from typing import Optional
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import math
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from collections import deque
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import numpy as np
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import logging
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logger = logging.getLogger(__name__)
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@dataclass
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class PhaseState:
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"""
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Represents a phase value at a point in time.
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Attributes:
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value: Complex phase on unit circle
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angle: Phase angle in radians (0 to 2*pi)
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timestamp: When this phase was observed
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source: Where this phase came from
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"""
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value: complex
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angle: float
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timestamp: datetime = field(default_factory=datetime.utcnow)
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source: str = "unknown"
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def __post_init__(self):
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"""Normalize angle to [0, 2*pi)."""
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self.angle = self.angle % (2 * math.pi)
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@dataclass
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class PhaseConfig:
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"""Configuration for phase tracking."""
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omega: float = 2.0 * math.pi # Frequency in rad/s
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history_size: int = 10000 # Maximum history length
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dampening: float = 0.999 # Phase dampening per cycle
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class PhaseHistory:
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"""
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Maintains phase history for temporal analysis.
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The history tracks:
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- Phase values over time
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- Phase velocity (rate of change)
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- Phase acceleration (rate of velocity change)
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This enables analysis of:
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- Phase synchronization patterns
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- Temporal dynamics
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- Coherence trends
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"""
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def __init__(
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self,
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config: Optional[PhaseConfig] = None,
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name: str = "phase-history"
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):
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self.config = config or PhaseConfig()
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self.name = name
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# History buffers
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self._phases: deque[PhaseState] = deque(
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maxlen=self.config.history_size
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)
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self._velocities: deque[float] = deque(
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maxlen=self.config.history_size
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)
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# Initialize with zero phase
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self._add_phase(complex(1, 0), "initialization")
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logger.info(
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f"[{self.name}] Initialized with omega={self.config.omega:.2f}"
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)
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@property
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def current(self) -> PhaseState:
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"""Get most recent phase state."""
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return self._phases[-1]
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@property
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def current_angle(self) -> float:
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"""Get most recent phase angle."""
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return self.current.angle
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@property
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def current_complex(self) -> complex:
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"""Get most recent phase as complex number."""
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return self.current.value
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@property
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def velocity(self) -> float:
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"""Get phase velocity (rad/s)."""
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if self._velocities:
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return self._velocities[-1]
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return 0.0
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@property
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def history(self) -> list[PhaseState]:
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"""Get full phase history."""
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return list(self._phases)
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@property
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def velocity_history(self) -> list[float]:
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"""Get velocity history."""
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return list(self._velocities)
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def _add_phase(
|
||||
self,
|
||||
phase: complex,
|
||||
source: str = "unknown"
|
||||
) -> PhaseState:
|
||||
"""Add a new phase value."""
|
||||
angle = np.angle(phase) % (2 * math.pi)
|
||||
state = PhaseState(
|
||||
value=phase,
|
||||
angle=angle,
|
||||
timestamp=datetime.utcnow(),
|
||||
source=source
|
||||
)
|
||||
self._phases.append(state)
|
||||
return state
|
||||
|
||||
def advance(self, dt: float, source: str = "advance") -> PhaseState:
|
||||
"""
|
||||
Advance phase by dt seconds according to omega.
|
||||
|
||||
Args:
|
||||
dt: Time delta in seconds
|
||||
source: What caused this advancement
|
||||
|
||||
Returns:
|
||||
New PhaseState with advanced phase
|
||||
"""
|
||||
# Phase advance = omega * dt
|
||||
delta_angle = self.config.omega * dt
|
||||
|
||||
# Compute new phase by rotation
|
||||
new_complex = self.current_complex * np.exp(1j * delta_angle)
|
||||
|
||||
# Apply dampening
|
||||
new_complex = new_complex * self.config.dampening
|
||||
|
||||
return self._add_phase(new_complex, source)
|
||||
|
||||
def set_phase(
|
||||
self,
|
||||
phase: complex,
|
||||
source: str = "external"
|
||||
) -> PhaseState:
|
||||
"""
|
||||
Set phase to a specific value (for input-driven phases).
|
||||
|
||||
Args:
|
||||
phase: Complex phase value
|
||||
source: What caused this phase
|
||||
|
||||
Returns:
|
||||
New PhaseState
|
||||
"""
|
||||
return self._add_phase(phase, source)
|
||||
|
||||
def compute_velocity(self) -> float:
|
||||
"""
|
||||
Compute phase velocity from recent history.
|
||||
|
||||
Returns:
|
||||
Phase velocity in rad/s
|
||||
"""
|
||||
if len(self._phases) < 2:
|
||||
return 0.0
|
||||
|
||||
recent = list(self._phases)[-10:] # Last 10 points
|
||||
|
||||
dt_total = 0.0
|
||||
dtheta_total = 0.0
|
||||
|
||||
for i in range(1, len(recent)):
|
||||
dt = (recent[i].timestamp - recent[i-1].timestamp).total_seconds()
|
||||
dtheta = recent[i].angle - recent[i-1].angle
|
||||
|
||||
# Handle angle wrapping
|
||||
if dtheta > math.pi:
|
||||
dtheta -= 2 * math.pi
|
||||
elif dtheta < -math.pi:
|
||||
dtheta += 2 * math.pi
|
||||
|
||||
dt_total += dt
|
||||
dtheta_total += dtheta
|
||||
|
||||
if dt_total > 0:
|
||||
velocity = dtheta_total / dt_total
|
||||
self._velocities.append(velocity)
|
||||
return velocity
|
||||
|
||||
return 0.0
|
||||
|
||||
def compute_similarity(
|
||||
self,
|
||||
other: 'PhaseHistory',
|
||||
delay: float = 0.0
|
||||
) -> complex:
|
||||
"""
|
||||
Compute phase similarity with another phase history.
|
||||
|
||||
This is the inner product <phi(t), phi(t-tau)>_C
|
||||
|
||||
Args:
|
||||
other: Another PhaseHistory to compare
|
||||
delay: Time delay for comparison (seconds)
|
||||
|
||||
Returns:
|
||||
Complex similarity (-1 to 1 magnitude, angle = phase diff)
|
||||
"""
|
||||
if len(self._phases) < 2 or len(other._phases) < 2:
|
||||
return complex(1, 0) # Default to unit similarity
|
||||
|
||||
# Get corresponding phases accounting for delay
|
||||
if delay > 0:
|
||||
# Self is delayed relative to other
|
||||
self_idx = 0
|
||||
other_idx = min(len(other._phases) - 1, int(delay / 0.001)) # Approximate
|
||||
else:
|
||||
self_idx = -1
|
||||
other_idx = -1
|
||||
|
||||
phi1 = self._phases[self_idx].value
|
||||
phi2 = other._phases[other_idx].value
|
||||
|
||||
# Inner product = conjugate product
|
||||
similarity = phi1 * np.conj(phi2)
|
||||
|
||||
# Normalize
|
||||
magnitude = np.abs(similarity)
|
||||
if magnitude > 0:
|
||||
similarity = similarity / magnitude
|
||||
|
||||
return similarity
|
||||
|
||||
def reset(self):
|
||||
"""Reset phase history."""
|
||||
self._phases.clear()
|
||||
self._velocities.clear()
|
||||
self._add_phase(complex(1, 0), "reset")
|
||||
logger.info(f"[{self.name}] Reset phase history")
|
||||
|
||||
def get_state(self) -> dict:
|
||||
"""Get state as dictionary."""
|
||||
return {
|
||||
"name": self.name,
|
||||
"config": {
|
||||
"omega": self.config.omega,
|
||||
"history_size": self.config.history_size,
|
||||
"dampening": self.config.dampening,
|
||||
},
|
||||
"current": {
|
||||
"angle": self.current_angle,
|
||||
"complex": [self.current_complex.real, self.current_complex.imag],
|
||||
"timestamp": self.current.timestamp.isoformat(),
|
||||
},
|
||||
"velocity": self.velocity,
|
||||
"history_length": len(self._phases),
|
||||
}
|
||||
|
||||
def __repr__(self) -> str:
|
||||
return (
|
||||
f"PhaseHistory("
|
||||
f"omega={self.config.omega:.2f}, "
|
||||
f"angle={self.current_angle:.3f}, "
|
||||
f"velocity={self.velocity:.3f}"
|
||||
f")"
|
||||
)
|
||||
@@ -0,0 +1,23 @@
|
||||
"""
|
||||
transducers/__init__.py
|
||||
|
||||
Transducer Implementations
|
||||
=========================
|
||||
|
||||
Master and Emissary transducers for the two-transducer model.
|
||||
|
||||
The Master transduces THE_ONE with deep, slow integration.
|
||||
The Emissary transduces THE_ONE with fast, quick response.
|
||||
|
||||
References:
|
||||
- KAIROS_ADAMON - Temporal coherence dynamics
|
||||
- Cybernetics - Transducer theory (Wiener)
|
||||
"""
|
||||
|
||||
from .master import MasterTransducer
|
||||
from .emissary import EmissaryTransducer
|
||||
|
||||
__all__ = [
|
||||
"MasterTransducer",
|
||||
"EmissaryTransducer",
|
||||
]
|
||||
Reference in New Issue
Block a user