Platforms/Grok/8-Formulas.py

#!/usr/bin/env python3
'''
Quillan-Ronin Quantum-Inspired Cognitive Formulas Toolkit
Mathematical framework for advanced cognitive enhancement and optimization.
Upgraded to V5.0 (Absolute Limit / Theoretical Max)
Precision: complex128 / float64
Created by: CrashOverrideX
'''

import cmath
import logging
from abc import ABC, abstractmethod
from typing import Any, Dict, List, Optional

import numpy as np
from pydantic import BaseModel, Field, validator

#  1. Core Abstractions and Data Structures 

class FormulaResult(BaseModel):
    """Container for formula computation results with metadata."""
    name: str
    value: Any
    description: str
    parameters: Dict[str, Any]
    metrics: Optional[Dict[str, float]] = None

    class Config:
        arbitrary_types_allowed = True

class Formula(ABC):
    """Abstract base class for all formula strategies."""
    @abstractmethod
    def execute(self, config: BaseModel, rng: np.random.Generator) -> FormulaResult:
        pass

#  2. Formula Implementations (Absolute Limit) 

#  Formula 1: AQCS (Adaptive Quantum Cognitive Superposition) 
# Upgrade: Added Phase angles (theta) for interference effects.
# Math: |Ψ⟩ = (1/√Z) * Σ (α_i * e^{iθ_i} * |h_i⟩)

class AQCSConfig(BaseModel):
    hypotheses: List[str] = Field(..., min_items=1)
    alphas: List[float] = Field(..., description="Magnitude weights")
    thetas: Optional[List[float]] = Field(None, description="Phase angles in radians")
    basis_vectors: Optional[List[List[complex]]] = Field(None, description="Orthonormal basis vectors")

    @validator('alphas', 'thetas')
    def check_lengths(cls, v, values):
        if v and 'hypotheses' in values and len(v) != len(values['hypotheses']):
            raise ValueError("Parameter length must match number of hypotheses")
        return v

class AdaptiveQuantumCognitiveSuperposition(Formula):
    def execute(self, config: AQCSConfig, rng: np.random.Generator) -> FormulaResult:
        n = len(config.hypotheses)
        
        # 1. Initialize Inputs (High Precision)
        alphas = np.array(config.alphas, dtype=np.float64)
        thetas = np.array(config.thetas if config.thetas else rng.uniform(0, 2*np.pi, n), dtype=np.float64)
        
        # Default basis: Standard basis vectors in C^N
        if config.basis_vectors:
            basis = np.array(config.basis_vectors, dtype=np.complex128)
        else:
            basis = np.eye(n, dtype=np.complex128)

        # 2. Calculate Complex Coefficients: c_i = α_i * e^(iθ_i)
        coefficients = alphas * (np.cos(thetas) + 1j * np.sin(thetas))
        
        # 3. Construct Superposition State: |Ψ_unnorm⟩ = Σ c_i |h_i⟩
        psi_unnorm = np.sum(coefficients[:, np.newaxis] * basis, axis=0)
        
        # 4. Normalization (Born Rule consistency)
        norm_factor = np.linalg.norm(psi_unnorm)
        if norm_factor < 1e-15:
            raise ValueError("State vector collapse: zero norm detected.")
            
        psi_normalized = psi_unnorm / norm_factor
        
        # 5. Coherence Metric (Interference potential)
        density_matrix = np.outer(psi_normalized, np.conj(psi_normalized))
        coherence = np.sum(np.abs(density_matrix)) - np.trace(density_matrix).real

        return FormulaResult(
            name="AQCS",
            value=psi_normalized,
            description="Normalized quantum superposition state vector with phase interference.",
            parameters=config.dict(exclude={'basis_vectors'}),
            metrics={"norm": float(norm_factor), "quantum_coherence": float(coherence)}
        )

#  Formula 4: DQRO (Dynamic Quantum Resource Optimization) 
# Upgrade: Transverse Field Ising Model (Hamiltonian Mechanics)
# Math: H = -0.5*sJs - hs - ΓΣσx

class DQROConfig(BaseModel):
    j_matrix: np.ndarray
    h_vector: np.ndarray
    gamma_tunneling: float = Field(1.0, description="Transverse field strength")
    temperature: float = 1.0
    anneal_steps: int = 1000

    @validator('j_matrix', 'h_vector', pre=True)
    def to_numpy(cls, v):
        return np.array(v, dtype=np.float64)

    class Config:
        arbitrary_types_allowed = True

class DynamicQuantumResourceOptimization(Formula):
    def execute(self, config: DQROConfig, rng: np.random.Generator) -> FormulaResult:
        n = len(config.h_vector)
        # Initialize spins (classical state)
        spins = rng.choice([-1.0, 1.0], size=n).astype(np.float64)
        
        # Verify symmetry of J
        if not np.allclose(config.j_matrix, config.j_matrix.T):
            # Symmetrize if needed
            config.j_matrix = 0.5 * (config.j_matrix + config.j_matrix.T)

        current_spins = spins.copy()
        best_spins = spins.copy()
        
        # Transverse Field Quantum Annealing Simulation (Path Integral Monte Carlo approximation simplified)
        # Here we simulate the effective energy landscape including quantum fluctuations
        
        def calculate_energy(s, gamma):
            # Classical Ising Energy: E_c = -0.5 * s^T * J * s - h * s
            interaction = -0.5 * np.dot(s, np.dot(config.j_matrix, s))
            bias = -np.dot(config.h_vector, s)
            
            # Quantum tunneling proxy (Transverse field energy contribution)
            # In pure ground state calculation this usually lowers energy via superposition
            # For this simulation, we treat it as a fluctuation potential
            tunneling = -gamma * np.sum(np.abs(s)) # Simplification for effective Hamiltonian
            
            return interaction + bias + tunneling

        min_energy = float('inf')
        
        # Annealing Schedule
        gammas = np.linspace(config.gamma_tunneling, 0, config.anneal_steps)
        temps = np.linspace(config.temperature, 1e-5, config.anneal_steps)

        for gamma, temp in zip(gammas, temps):
            # Monte Carlo update
            idx = rng.integers(n)
            delta_s = -2 * current_spins[idx]
            
            # Calculate energy delta approx
            # ΔE = E_new - E_old
            # Efficient update for interaction: -s_i * sum(J_ij * s_j)
            row_interaction = np.dot(config.j_matrix[idx, :], current_spins) - (config.j_matrix[idx, idx] * current_spins[idx])
            delta_interaction = -(delta_s * row_interaction) 
            delta_bias = -(delta_s * config.h_vector[idx])
            
            delta_E = delta_interaction + delta_bias
            
            # Metropolis-Hastings with Quantum Tunneling term
            # Tunneling probability allows crossing barriers independent of thermal height
            tunnel_prob = np.exp(-2 * gamma) # WKB-like factor
            thermal_prob = np.exp(-delta_E / temp) if delta_E > 0 else 1.0
            
            if delta_E < 0 or rng.random() < max(thermal_prob, tunnel_prob):
                current_spins[idx] *= -1
                
                # Check global minimum
                E_curr = calculate_energy(current_spins, 0) # Measure classical energy
                if E_curr < min_energy:
                    min_energy = E_curr
                    best_spins = current_spins.copy()

        return FormulaResult(
            name="DQRO",
            value=best_spins,
            description="Ground state configuration via Transverse Field Quantum Annealing.",
            parameters={"gamma_start": config.gamma_tunneling},
            metrics={"ground_state_energy": float(min_energy)}
        )

#  Formula 10: JQLD (Joshua's Quantum Leap Dynamo) 
# Upgrade: Driven Damped Harmonic Oscillator in Complex Plane
# Math: Ψ(t) = P_{base} * exp(i(ωt - kx)) * Π [1 + η_j * sin(Ω_j t + φ_j)]

class JQLDConfig(BaseModel):
    p_base: complex = Field(..., description="Base complex amplitude")
    omega_carrier: float = Field(..., description="Carrier frequency")
    time_t: float
    q_factors: List[float] = Field(..., description="Modulation amplitudes")
    frequencies_omega: List[float] = Field(..., description="Modulation frequencies")
    phases_phi: Optional[List[float]] = None

class JoshuasQuantumLeapDynamo(Formula):
    def execute(self, config: JQLDConfig, rng: np.random.Generator) -> FormulaResult:
        # High precision types
        p_base = complex(config.p_base)
        t = float(config.time_t)
        
        # 1. Carrier Wave (Phasor)
        carrier = cmath.exp(1j * config.omega_carrier * t)
        
        # 2. Multi-Frequency Modulation (The "Quantum Leap" drivers)
        q_factors = np.array(config.q_factors, dtype=np.float64)
        omegas = np.array(config.frequencies_omega, dtype=np.float64)
        
        if config.phases_phi:
            phis = np.array(config.phases_phi, dtype=np.float64)
        else:
            phis = np.zeros_like(omegas)
            
        # Π [1 + η_j * sin(Ω_j t + φ_j)]
        modulation_terms = 1.0 + q_factors * np.sin(omegas * t + phis)
        total_modulation = np.prod(modulation_terms)
        
        # 3. Final State Calculation
        psi_t = p_base * carrier * total_modulation
        
        # Metrics
        power_density = abs(psi_t)**2
        phase_angle = cmath.phase(psi_t)

        return FormulaResult(
            name="JQLD",
            value=psi_t,
            description="Time-evolved performance state vector.",
            parameters=config.dict(),
            metrics={
                "amplitude": abs(psi_t),
                "power_density": power_density,
                "phase_rad": phase_angle
            }
        )

#  Formula 13: Token Latency (Extended Amdahl) 
# Upgrade: Includes Parallel Scaling, Comm Overhead (Kappa), Memory Bandwidth
# Math: L = max(T_s, T_p/N) + κ*N*log(N) + D/BW

class TokenLatencyConfig(BaseModel):
    t_serial: float = Field(..., gt=0, description="Serial execution time")
    t_parallel: float = Field(..., gt=0, description="Parallelizable execution time")
    n_cores: int = Field(..., gt=0, description="Number of processing units")
    data_size_gb: float = Field(..., gt=0, description="Data size in GB")
    bw_memory_gbs: float = Field(..., gt=0, description="Memory Bandwidth GB/s")
    kappa_overhead: float = Field(0.001, description="Communication overhead coefficient")

class QuillanTokenLatency(Formula):
    def execute(self, config: TokenLatencyConfig, rng: np.random.Generator) -> FormulaResult:
        N = float(config.n_cores)
        
        # 1. Computational Latency (Amdahl's Law with infinite scaling assumption)
        t_comp = config.t_serial + (config.t_parallel / N)
        
        # 2. Communication Overhead (The "Log" penalty for synchronization)
        t_comm = config.kappa_overhead * N * np.log2(N)
        
        # 3. Memory Bound (Von Neumann Bottleneck)
        t_mem = config.data_size_gb / config.bw_memory_gbs
        
        # 4. Total Latency (Critical Path Analysis)
        # Latency is governed by the slowest component between (Compute+Comm) vs Memory
        total_processing_time = t_comp + t_comm
        final_latency = max(total_processing_time, t_mem)
        
        bottleneck = "Memory" if t_mem > total_processing_time else "Compute/Comm"
        
        return FormulaResult(
            name="Quillan_TokenLatency",
            value=final_latency,
            description="Absolute limit latency estimation.",
            parameters=config.dict(),
            metrics={
                "compute_time": t_comp,
                "comm_overhead": t_comm,
                "memory_time": t_mem,
                "bottleneck_factor": bottleneck,
                "efficiency": config.t_parallel / (final_latency * N) # Parallel efficiency
            }
        )

#  3. Formula Engine 

class FormulaEngine:
    """Robust strategy engine for executing verified cognitive formulas."""
    def __init__(self, seed: Optional[int] = None):
        self._formulas: Dict[str, Formula] = {}
        self.rng = np.random.default_rng(seed)
        self.logger = logging.getLogger("QuillanMathCore")

    def register(self, name: str, formula: Formula):
        self._formulas[name] = formula

    def execute(self, name: str, config: BaseModel) -> FormulaResult:
        if name not in self._formulas:
            raise ValueError(f"Formula '{name}' is not registered.")
        
        try:
            return self._formulas[name].execute(config, self.rng)
        except Exception as e:
            self.logger.error(f"Critical math error in {name}: {e}")
            raise

#  4. Main Execution (Verification) 

def main():
    logging.basicConfig(level=logging.INFO, format='%(asctime)s - [MATH-CORE] - %(message)s')
    print("=" * 80)
    print("🧠 QUILLAN-RONIN MATH CORE v5.0 (ABSOLUTE LIMIT)")
    print("=" * 80)

    engine = FormulaEngine(seed=1337)
    engine.register("AQCS", AdaptiveQuantumCognitiveSuperposition())
    engine.register("DQRO", DynamicQuantumResourceOptimization())
    engine.register("JQLD", JoshuasQuantumLeapDynamo())
    engine.register("TokenLatency", QuillanTokenLatency())

    # 1. Test AQCS (Quantum Superposition)
    print("\n[1] AQCS - Quantum Interference Check")
    aqcs_res = engine.execute("AQCS", AQCSConfig(
        hypotheses=["State |0⟩", "State |1⟩"],
        alphas=[1.0, 1.0],
        thetas=[0.0, np.pi] # Destructive interference setup
    ))
    print(f"State Vector: {aqcs_res.value}")
    print(f"Coherence: {aqcs_res.metrics['quantum_coherence']:.4f}")

    # 2. Test DQRO (Quantum Annealing)
    print("\n[2] DQRO - Transverse Field Optimization")
    # Simple frustrated system (Antiferromagnetic ring)
    J = np.array([[0, 1, 1], [1, 0, 1], [1, 1, 0]]) 
    h = np.array([0, 0, 0])
    dqro_res = engine.execute("DQRO", DQROConfig(j_matrix=J, h_vector=h, gamma_tunneling=2.0))
    print(f"Optimal Spin Config: {dqro_res.value}")
    print(f"Ground State Energy: {dqro_res.metrics['ground_state_energy']:.4f}")

    # 3. Test JQLD (Driven Dynamics)
    print("\n[3] JQLD - Complex Dynamics")
    jqld_res = engine.execute("JQLD", JQLDConfig(
        p_base=1+0j, omega_carrier=10.0, time_t=0.5,
        q_factors=[0.5, 0.2], frequencies_omega=[5.0, 20.0]
    ))
    print(f"Output Amplitude: {jqld_res.metrics['amplitude']:.4f}")
    print(f"Power Density: {jqld_res.metrics['power_density']:.4f}")

    # 4. Test Token Latency (Architecture Bound)
    print("\n[4] Latency - Amdahl Extended")
    lat_res = engine.execute("TokenLatency", TokenLatencyConfig(
        t_serial=0.1, t_parallel=10.0, n_cores=64, 
        data_size_gb=16, bw_memory_gbs=512
    ))
    print(f"Estimated Latency: {lat_res.value:.6f} s")
    print(f"Bottleneck: {lat_res.metrics['bottleneck_factor']}")

    print("\n" + "=" * 80)
    print("✅ ALL FORMULAS OPERATIONAL AT THEORETICAL LIMIT")
    print("=" * 80)

if __name__ == "__main__":
    main()