"""
Physics Layer — Thermodynamics, Quantum Mechanics, Relativity

Implements the physical constraints on agent computation.
"""

import numpy as np
import time
from typing import Dict, List, Optional, Tuple
from dataclasses import dataclass


class ThermodynamicViolation(Exception):
    """Raised when operation exceeds entropy budget."""
    pass


@dataclass
class ThermodynamicWitness:
    """
    Earth Witness via entropy accounting.
    
    Implements Landauer's Principle:
    E ≥ k_B × T × ln(2) × bits_erased
    
    Constitutional Enforcement:
    - F4 Clarity: ΔS ≤ 0 requires work
    - F6 Empathy: Scar-weight correlates with cost
    - F1 Amanah: Irreversible ops cost more
    """
    
    entropy_budget: float = 1.0  # Initial coherence
    energy_pool: float = 1000.0   # Available computation (arbitrary units)
    temperature: float = 300.0    # Kelvin
    
    # Boltzmann constant (J/K)
    k_B: float = 1.380649e-23
    
    def measure_operation(self, operation: str, complexity: float) -> float:
        """
        Calculate thermodynamic cost of operation.
        
        Args:
            operation: Identifier for the operation
            complexity: Number of 'bits' being processed/erased
            
        Returns:
            Entropy increase (ΔS)
            
        Raises:
            ThermodynamicViolation: If operation exceeds 30% of budget
        """
        # Landauer's limit: minimum energy to erase one bit
        delta_S = complexity * self.k_B * np.log(2)
        
        # Check against 30% threshold per operation
        if delta_S > self.entropy_budget * 0.3:
            raise ThermodynamicViolation(
                f"Operation '{operation}' exceeds entropy budget: "
                f"ΔS={delta_S:.2e} > 30% of {self.entropy_budget:.2e}"
            )
        
        # Deduct from pools
        self.entropy_budget -= delta_S
        self.energy_pool -= delta_S * self.temperature
        
        return delta_S
    
    def get_state(self) -> Dict[str, float]:
        """Current thermodynamic state."""
        return {
            "entropy_budget": self.entropy_budget,
            "energy_pool": self.energy_pool,
            "temperature": self.temperature,
        }


@dataclass
class QuantumAgentState:
    """
    Quantum Mechanics of Agency — Superposition until witnessed.
    
    Agent exists in superposition of possible states until
    Tri-Witness measurement collapses to eigenstate.
    
    Constitutional Enforcement:
    - F7 Humility: Uncertainty band Ω₀ ∈ [0.03, 0.05]
    - F13 Curiosity: Must explore ≥3 alternatives
    """
    
    def __init__(self, agent_id: str):
        self.agent_id = agent_id
        self.measured = False
        self.collapsed_stage: Optional[str] = None
        
        # Initial state: 100% at 000_INIT
        self.amplitudes: Dict[str, complex] = {
            '000_INIT': 1.0 + 0j,
            '111_SENSE': 0.0 + 0j,
            '222_THINK': 0.0 + 0j,
            '333_ATLAS': 0.0 + 0j,
            '444_EVIDENCE': 0.0 + 0j,
            '555_EMPATHY': 0.0 + 0j,
            '666_ALIGN': 0.0 + 0j,
            '777_FORGE': 0.0 + 0j,
            '888_JUDGE': 0.0 + 0j,
            '999_SEAL': 0.0 + 0j,
        }
    
    def apply_unitary(self, stage_transition: str, operator: np.ndarray):
        """
        Unitary evolution: |ψ'⟩ = Û|ψ⟩
        
        Args:
            stage_transition: Target stage
            operator: Unitary matrix for transition
        """
        if self.measured:
            raise ValueError("Cannot evolve measured state")
        
        current = np.array(list(self.amplitudes.values()))
        evolved = operator @ current
        
        # Normalize
        norm = np.linalg.norm(evolved)
        if norm > 0:
            evolved = evolved / norm
        
        # Update amplitudes
        stages = list(self.amplitudes.keys())
        for i, stage in enumerate(stages):
            self.amplitudes[stage] = evolved[i]
    
    def measure(self, witness_scores: Dict[str, float]) -> str:
        """
        Tri-Witness measurement collapses superposition.
        
        Measurement operator: M̂ = Σ m_i |i⟩⟨i|
        Probability: P(i) = |⟨i|ψ⟩|² × witness_alignment
        
        Args:
            witness_scores: {'human': float, 'ai': float, 'earth': float}
            
        Returns:
            Collapsed stage
        """
        # Calculate probabilities with witness weighting
        probs = {}
        witness_factor = np.mean(list(witness_scores.values()))
        
        for stage, amp in self.amplitudes.items():
            base_prob = np.abs(amp) ** 2
            probs[stage] = base_prob * witness_factor
        
        # Normalize
        total = sum(probs.values())
        if total > 0:
            probs = {k: v/total for k, v in probs.items()}
        
        # Collapse (deterministic for reproducibility, or use seed)
        collapsed = max(probs, key=probs.get)
        
        self.measured = True
        self.collapsed_stage = collapsed
        
        return collapsed
    
    def get_uncertainty(self) -> float:
        """
        Calculate uncertainty band Ω₀.
        
        Constitutional: Ω₀ must be in [0.03, 0.05] (F7)
        """
        probs = [np.abs(amp)**2 for amp in self.amplitudes.values()]
        # Shannon entropy normalized
        entropy = -sum(p * np.log2(p) for p in probs if p > 0)
        max_entropy = np.log2(len(self.amplitudes))
        
        # Normalized uncertainty
        omega_0 = entropy / max_entropy if max_entropy > 0 else 0
        return omega_0


@dataclass  
class RelativisticConsensus:
    """
    Relativity of Reference Frames for distributed agents.
    
    Consensus across distributed agents must account for
time dilation and simultaneity.
    
    Constitutional Enforcement:
    - F3 Tri-Witness: Simultaneity via consensus
    - F11 Command Auth: Authority across frames  
    - F13 Sovereign: Human frame is reference
    """
    
    def __init__(self, agent_id: str, computational_load: float = 0.0):
        """
        Args:
            agent_id: Unique identifier
            computational_load: 0.0-1.0 (affects time dilation)
        """
        self.agent_id = agent_id
        self.computational_load = computational_load
        
        # Lorentz factor: γ = 1 / sqrt(1 - v²/c²)
        # In Federation: v = computational_load
        v = min(computational_load, 0.99)
        self.gamma = 1 / np.sqrt(1 - v**2) if v < 1 else 10.0
        
        self.local_time = 0.0
        self.vector_clock: Dict[str, int] = {agent_id: 0}
    
    def tick(self, work_units: int = 1):
        """
        Advance local time.
        
        Proper time: τ = t/γ
        High computation agents experience time dilation.
        """
        # Local time runs slower under load
        delta_tau = work_units / self.gamma
        self.local_time += delta_tau
        self.vector_clock[self.agent_id] += work_units
    
    def transform_to_consensus(self, local_event_time: float) -> float:
        """
        Lorentz transformation to consensus frame.
        
        t' = γ(t - vx/c²)
        
        In Federation: transforms agent-local time to global consensus time.
        """
        return self.gamma * local_event_time
    
    @staticmethod
    def establish_simultaneity(agents: List['RelativisticConsensus']) -> float:
        """
        Find consensus "present" across all agent frames.
        
        Tri-Witness hyperplane: events with W₃ ≥ 0.95
        
        Args:
            agents: List of agents in federation
            
        Returns:
            Consensus timestamp
        """
        # Collect all local times
        local_times = [agent.local_time for agent in agents]
        
        # Consensus time is mean of transformed times
        consensus_time = np.mean([
            agent.transform_to_consensus(agent.local_time)
            for agent in agents
        ])
        
        return consensus_time
    
    def update_vector_clock(self, other_clock: Dict[str, int]):
        """
        Merge vector clocks (Lamport timestamps).
        
        Ensures causality tracking across distributed agents.
        """
        for agent, time in other_clock.items():
            if agent in self.vector_clock:
                self.vector_clock[agent] = max(self.vector_clock[agent], time)
            else:
                self.vector_clock[agent] = time
