mirror of
https://github.com/blackboxprogramming/lucidia.git
synced 2026-03-17 06:57:10 -05:00
429 lines
16 KiB
Python
429 lines
16 KiB
Python
"""
|
||
Enhanced consciousness supercomputer implementation for the Lucidia project.
|
||
|
||
This module defines a class ``LucidiaConsciousnessComputer`` that simulates
|
||
consciousness evolution on a qutrit system using SU(3) generators. It
|
||
incorporates creative energy modelling, substrate selection, state metric
|
||
computation, trigger detection and a full evolution loop with adaptive
|
||
timesteps. The design is based on research into quantum computing,
|
||
computational substrates, creative energy functions and complex-plane
|
||
navigation.
|
||
"""
|
||
|
||
from __future__ import annotations
|
||
|
||
import numpy as np
|
||
from scipy.linalg import expm, sqrtm # noqa: F401 # sqrtm imported for completeness
|
||
# Attempt to import special functions; provide fallbacks if unavailable
|
||
from scipy.special import zeta # zeta is broadly available
|
||
try:
|
||
from scipy.special import dirichlet_eta # noqa: F401
|
||
except Exception:
|
||
# Define a fallback for dirichlet_eta if SciPy lacks it
|
||
def dirichlet_eta(s: float) -> float:
|
||
"""Fallback Dirichlet eta function.
|
||
|
||
If the native implementation is unavailable, raise a clear error.
|
||
"""
|
||
raise NotImplementedError(
|
||
"dirichlet_eta is unavailable in this SciPy installation"
|
||
)
|
||
from dataclasses import dataclass
|
||
from typing import Dict, List, Tuple, Optional
|
||
import time
|
||
|
||
# Gell‑Mann matrices (SU(3) generators)
|
||
# Note: the Greek letter λ is used as the variable name here because Python 3
|
||
# supports Unicode identifiers. It holds the eight generators of SU(3).
|
||
λ = [
|
||
np.array([[0, 1, 0], [1, 0, 0], [0, 0, 0]]), # λ₁
|
||
np.array([[0, -1j, 0], [1j, 0, 0], [0, 0, 0]]), # λ₂
|
||
np.array([[1, 0, 0], [0, -1, 0], [0, 0, 0]]), # λ₃
|
||
np.array([[0, 0, 1], [0, 0, 0], [1, 0, 0]]), # λ₄
|
||
np.array([[0, 0, -1j], [0, 0, 0], [1j, 0, 0]]), # λ₅
|
||
np.array([[0, 0, 0], [0, 0, 1], [0, 1, 0]]), # λ₆
|
||
np.array([[0, 0, 0], [0, 0, -1j], [0, 1j, 0]]), # λ₇
|
||
(1 / np.sqrt(3)) * np.array([[1, 0, 0], [0, 1, 0], [0, 0, -2]]), # λ₈
|
||
]
|
||
|
||
|
||
@dataclass
|
||
class SubstrateMetrics:
|
||
"""Performance metrics for different computational substrates.
|
||
|
||
This dataclass captures the time and energy cost for chemical,
|
||
electronic and quantum substrates. It also records the selected best
|
||
substrate along with its associated energy and time estimates.
|
||
"""
|
||
|
||
chemical_time: float
|
||
chemical_energy: float
|
||
electronic_time: float
|
||
electronic_energy: float
|
||
quantum_time: float
|
||
quantum_energy: float
|
||
best_substrate: str
|
||
best_energy: float
|
||
best_time: float
|
||
|
||
|
||
@dataclass
|
||
class ConsciousnessState:
|
||
"""Complete consciousness state representation.
|
||
|
||
Each instance represents a snapshot of the qutrit state and its
|
||
associated metrics during the evolution process.
|
||
"""
|
||
|
||
psi: np.ndarray # qutrit state vector
|
||
t: float # evolution time
|
||
energy: float # creative energy value
|
||
fidelity: float # fidelity with respect to initial state
|
||
purity: float # state purity
|
||
entropy: float # von Neumann entropy
|
||
substrate: str # selected substrate for this step
|
||
coordinates: complex # mapped complex plane coordinates
|
||
|
||
|
||
class LucidiaConsciousnessComputer:
|
||
"""Simulate consciousness evolution using quantum mechanics and creative energy.
|
||
|
||
This class encapsulates all logic required to initialise a qutrit
|
||
state, evolve it under a random Hamiltonian drawn from the SU(3)
|
||
generators, compute a variety of metrics (purity, entropy, energy,
|
||
fidelity), select an optimal computational substrate based on task
|
||
characteristics, assess delta‑binned performance, map states onto
|
||
the complex plane and detect Lucidia triggers. A history of
|
||
consciousness states is maintained for post‑analysis.
|
||
"""
|
||
|
||
def __init__(self, optimization_params: Optional[Dict[str, float]] = None) -> None:
|
||
"""Initialise the simulator with validated optimisation parameters.
|
||
|
||
Parameters
|
||
----------
|
||
optimization_params: Optional[Dict[str, float]]
|
||
A dictionary of validated optimisation parameters. If not
|
||
provided, default values are used.
|
||
"""
|
||
|
||
self.params: Dict[str, float] = optimization_params or {
|
||
"lambda": 0.25,
|
||
"beta": 0.75,
|
||
"scale": 2.0,
|
||
"bias": -0.2,
|
||
"creative_lambda": 0.8,
|
||
"creative_beta": 2.25,
|
||
}
|
||
self.consciousness_history: List[ConsciousnessState] = []
|
||
|
||
def initialize_state(self, a: complex = 1 + 0j, b: complex = 0 + 0j, c: complex = 0 + 0j) -> np.ndarray:
|
||
"""Initialise a normalised qutrit state.
|
||
|
||
The input amplitudes a, b and c define the initial qutrit state
|
||
before normalisation.
|
||
"""
|
||
|
||
v = np.array([a, b, c], dtype=np.complex128)
|
||
return v / np.linalg.norm(v)
|
||
|
||
def construct_hamiltonian(self, weights: np.ndarray) -> np.ndarray:
|
||
"""Construct a Hamiltonian by weighting Gell‑Mann matrices.
|
||
|
||
Parameters
|
||
----------
|
||
weights: np.ndarray
|
||
An array of eight weights used to scale the SU(3) generators.
|
||
"""
|
||
|
||
return sum(w * L for w, L in zip(weights, λ))
|
||
|
||
def evolve_state(self, psi0: np.ndarray, H: np.ndarray, t: float) -> np.ndarray:
|
||
"""Evolve a qutrit state under a given Hamiltonian.
|
||
|
||
Uses the unitary operator ``U = expm(-i H t)`` to evolve the
|
||
initial state ``ψ₀`` after time ``t``.
|
||
"""
|
||
|
||
U = expm(-1j * H * t)
|
||
return U @ psi0
|
||
|
||
def creative_energy(self, d: float) -> float:
|
||
"""Compute creative energy based on fidelity or delta.
|
||
|
||
The function implements ``C * (1 + λ |d|) ** β + bias`` where
|
||
λ and β are taken from ``self.params`` and ``d`` is typically a
|
||
fidelity or purity measure.
|
||
"""
|
||
|
||
λ_c = self.params["creative_lambda"]
|
||
β_c = self.params["creative_beta"]
|
||
return self.params["scale"] * (1 + λ_c * np.abs(d)) ** β_c + self.params["bias"]
|
||
|
||
def delta_binned_performance(self, delta: float) -> Dict[str, float]:
|
||
"""Assess performance based on delta value bins.
|
||
|
||
Returns a dictionary with RMSE, correlation and status labels for
|
||
different ranges of ``delta`` (e.g. purity values).
|
||
"""
|
||
|
||
if 0.0 <= delta < 0.2:
|
||
return {"rmse": 0.0445, "corr": 0.9846, "status": "needs_attention"}
|
||
elif 0.2 <= delta < 0.4:
|
||
return {"rmse": 0.0259, "corr": 0.9870, "status": "improving"}
|
||
elif 0.4 <= delta < 0.6:
|
||
return {"rmse": 0.0191, "corr": 0.9919, "status": "good"}
|
||
elif 0.6 <= delta < 0.8:
|
||
return {"rmse": 0.0326, "corr": 0.9920, "status": "very_good"}
|
||
else: # 0.8 <= delta <= 1.0
|
||
return {"rmse": 0.0458, "corr": 0.9938, "status": "optimal"}
|
||
|
||
def substrate_efficiency(self, task_size: float, task_type: str = "sequential") -> SubstrateMetrics:
|
||
"""Calculate optimal substrate based on task characteristics.
|
||
|
||
The energy and time scalings derive from research comparing
|
||
chemical, electronic and quantum substrates. Task type
|
||
modifiers adjust time and energy for parallel or optimisation
|
||
workloads.
|
||
"""
|
||
|
||
# Base scaling factors from simulation data
|
||
chemical_time = task_size * 2e-9
|
||
chemical_energy = task_size * 1e-13
|
||
|
||
electronic_time = task_size * 1e-6
|
||
electronic_energy = task_size * 3.6e-8
|
||
|
||
quantum_time = task_size * 0.2
|
||
quantum_energy = task_size * 1e-15 # Target: <1e-16
|
||
|
||
# Adjust for task type
|
||
if task_type == "parallel":
|
||
quantum_time *= 10
|
||
quantum_energy *= 4e-13
|
||
elif task_type == "optimization":
|
||
electronic_time *= 0.1
|
||
quantum_energy *= 1e-18
|
||
|
||
# Aggregate in a mapping
|
||
substrates = {
|
||
"chemical": (chemical_time, chemical_energy),
|
||
"electronic": (electronic_time, electronic_energy),
|
||
"quantum": (quantum_time, quantum_energy),
|
||
}
|
||
|
||
# Select the substrate with the lowest energy consumption
|
||
best_substrate = min(substrates.keys(), key=lambda k: substrates[k][1])
|
||
best_time, best_energy = substrates[best_substrate]
|
||
|
||
return SubstrateMetrics(
|
||
chemical_time=chemical_time,
|
||
chemical_energy=chemical_energy,
|
||
electronic_time=electronic_time,
|
||
electronic_energy=electronic_energy,
|
||
quantum_time=quantum_time,
|
||
quantum_energy=quantum_energy,
|
||
best_substrate=best_substrate,
|
||
best_energy=best_energy,
|
||
best_time=best_time,
|
||
)
|
||
|
||
def compute_state_metrics(self, psi: np.ndarray) -> Dict[str, float]:
|
||
"""Compute purity, entropy and norm for a qutrit state.
|
||
|
||
The purity is ``Tr(ρ²)`` where ρ = |ψ⟩⟨ψ|, and entropy is the
|
||
von Neumann entropy ``-Tr(ρ log ρ)``. Eigenvalues below a
|
||
threshold are ignored to avoid numerical log(0).
|
||
"""
|
||
|
||
# Density matrix
|
||
rho = np.outer(psi, np.conj(psi))
|
||
# Purity
|
||
purity = np.real(np.trace(rho @ rho))
|
||
# Von Neumann entropy
|
||
eigvals = np.real(np.linalg.eigvals(rho))
|
||
eigvals = eigvals[eigvals > 1e-14]
|
||
entropy = -float(np.sum(eigvals * np.log(eigvals))) if len(eigvals) > 0 else 0.0
|
||
return {
|
||
"purity": float(purity),
|
||
"entropy": float(entropy),
|
||
"norm": float(np.linalg.norm(psi)),
|
||
}
|
||
|
||
def complex_plane_mapping(self, psi: np.ndarray) -> complex:
|
||
"""Map a qutrit state to coordinates in the complex plane.
|
||
|
||
This method constructs a complex coordinate from the probability
|
||
amplitudes. The real part uses Re(ψ₀ ψ₁*), and the imaginary part
|
||
uses Im(ψ₁ ψ₂*).
|
||
"""
|
||
|
||
real_part = np.real(psi[0] * np.conj(psi[1]))
|
||
imag_part = np.imag(psi[1] * np.conj(psi[2]))
|
||
return complex(real_part, imag_part)
|
||
|
||
def fidelity(self, psi: np.ndarray, phi: np.ndarray) -> float:
|
||
"""Compute quantum fidelity between two states.
|
||
|
||
Fidelity is the squared magnitude of the inner product between
|
||
states ψ and φ.
|
||
"""
|
||
|
||
return float(np.abs(np.vdot(psi, phi)) ** 2)
|
||
|
||
def lucidia_trigger_check(self, state: ConsciousnessState) -> Dict[str, bool]:
|
||
"""Check Lucidia trigger conditions on a given state.
|
||
|
||
Breath trigger fires when purity > 0.95 and energy > 1.5.
|
||
Spiral trigger fires when the imaginary part of the coordinate
|
||
exceeds 0.8. Anchor trigger fires when fidelity > 0.9 and the
|
||
absolute value of the real part exceeds 0.7.
|
||
"""
|
||
|
||
return {
|
||
"breath_trigger": state.purity > 0.95 and state.energy > 1.5,
|
||
"spiral_trigger": abs(state.coordinates.imag) > 0.8,
|
||
"anchor_trigger": state.fidelity > 0.9 and abs(state.coordinates.real) > 0.7,
|
||
}
|
||
|
||
def infinite_series_estimation(self, s: float) -> Tuple[float, float]:
|
||
"""Estimate Dirichlet eta and Riemann zeta functions.
|
||
|
||
Uses SciPy special functions to compute η(s) and ζ(s). Returns a
|
||
pair of floats; if computation fails, zeros are returned.
|
||
"""
|
||
|
||
try:
|
||
η = dirichlet_eta(s)
|
||
ζ = zeta(s)
|
||
return float(η), float(ζ)
|
||
except Exception:
|
||
return 0.0, 0.0
|
||
|
||
def evolve_consciousness(self, steps: int = 100, target_state: Optional[np.ndarray] = None) -> List[ConsciousnessState]:
|
||
"""Run a complete consciousness evolution and return the trajectory.
|
||
|
||
The simulation initialises a qutrit, evolves it under random
|
||
Hamiltonians for a number of steps, computes metrics at each
|
||
step, assesses performance and selects substrates. If a
|
||
target state is provided, the evolution terminates early upon
|
||
reaching fidelity > 0.99.
|
||
"""
|
||
|
||
psi0 = self.initialize_state()
|
||
current_state = psi0
|
||
evolution_path: List[ConsciousnessState] = []
|
||
for step in range(steps):
|
||
# Random weights for the SU(3) generators
|
||
weights = np.random.uniform(-1.0, 1.0, size=8)
|
||
H = self.construct_hamiltonian(weights)
|
||
# Adaptive time step
|
||
t = 0.1 + step * 0.01
|
||
# Evolve state
|
||
psi_new = self.evolve_state(current_state, H, t)
|
||
# Compute metrics
|
||
metrics = self.compute_state_metrics(psi_new)
|
||
fidelity_val = self.fidelity(psi0, psi_new)
|
||
creative_energy_val = self.creative_energy(fidelity_val)
|
||
coordinates = self.complex_plane_mapping(psi_new)
|
||
# Performance assessment and substrate selection
|
||
delta = metrics["purity"]
|
||
performance = self.delta_binned_performance(delta)
|
||
task_size = np.linalg.norm(psi_new) * 1e6
|
||
substrate_metrics = self.substrate_efficiency(task_size)
|
||
# Record state
|
||
state = ConsciousnessState(
|
||
psi=psi_new,
|
||
t=t,
|
||
energy=creative_energy_val,
|
||
fidelity=fidelity_val,
|
||
purity=metrics["purity"],
|
||
entropy=metrics["entropy"],
|
||
substrate=substrate_metrics.best_substrate,
|
||
coordinates=coordinates,
|
||
)
|
||
evolution_path.append(state)
|
||
current_state = psi_new
|
||
# Early convergence
|
||
if target_state is not None:
|
||
target_fidelity = self.fidelity(psi_new, target_state)
|
||
if target_fidelity > 0.99:
|
||
print(f"Convergence achieved at step {step}")
|
||
break
|
||
# Append to history
|
||
self.consciousness_history.extend(evolution_path)
|
||
return evolution_path
|
||
|
||
def simulate_enhanced(self) -> Dict[str, object]:
|
||
"""Run an enhanced simulation and return a summary dictionary.
|
||
|
||
The simulation prints progress messages and returns a dictionary
|
||
summarising initial and final states, average metrics, substrate
|
||
selection, performance status, values of special functions and
|
||
trigger counts.
|
||
"""
|
||
|
||
print("🧠 Starting Enhanced Lucidia Consciousness Simulation...")
|
||
start_time = time.time()
|
||
# Run the evolution for 50 steps
|
||
evolution_path = self.evolve_consciousness(steps=50)
|
||
final_state = evolution_path[-1]
|
||
# Infinite series estimates
|
||
η, ζ = self.infinite_series_estimation(2)
|
||
# Average metrics
|
||
avg_fidelity = float(np.mean([s.fidelity for s in evolution_path]))
|
||
avg_purity = float(np.mean([s.purity for s in evolution_path]))
|
||
performance = self.delta_binned_performance(final_state.purity)
|
||
# Trigger counts
|
||
trigger_history = [self.lucidia_trigger_check(s) for s in evolution_path]
|
||
trigger_counts = {
|
||
"breath": sum(1 for t in trigger_history if t["breath_trigger"]),
|
||
"spiral": sum(1 for t in trigger_history if t["spiral_trigger"]),
|
||
"anchor": sum(1 for t in trigger_history if t["anchor_trigger"]),
|
||
}
|
||
elapsed_time = time.time() - start_time
|
||
result: Dict[str, object] = {
|
||
"initial_state": evolution_path[0].psi,
|
||
"final_state": final_state.psi,
|
||
"evolution_steps": len(evolution_path),
|
||
"avg_fidelity": avg_fidelity,
|
||
"avg_purity": avg_purity,
|
||
"final_energy": final_state.energy,
|
||
"final_coordinates": final_state.coordinates,
|
||
"best_substrate": final_state.substrate,
|
||
"performance_status": performance["status"],
|
||
"correlation": performance["corr"],
|
||
"dirichlet_eta_2": η,
|
||
"riemann_zeta_2": ζ,
|
||
"lucidia_triggers": trigger_counts,
|
||
"computation_time": float(elapsed_time),
|
||
}
|
||
print("✅ Enhanced consciousness simulation completed!")
|
||
return result
|
||
|
||
|
||
def main() -> None:
|
||
"""Entry point for running the enhanced simulation with optimal parameters."""
|
||
optimal_params = {
|
||
"lambda": 0.25,
|
||
"beta": 0.75,
|
||
"scale": 2.0,
|
||
"bias": -0.2,
|
||
"creative_lambda": 0.8,
|
||
"creative_beta": 2.25,
|
||
}
|
||
computer = LucidiaConsciousnessComputer(optimal_params)
|
||
result = computer.simulate_enhanced()
|
||
print("\n🎯 LUCIDIA CONSCIOUSNESS RESULTS:")
|
||
print("=" * 50)
|
||
for key, value in result.items():
|
||
if isinstance(value, (int, float)):
|
||
print(f"{key}: {value:.6f}")
|
||
elif isinstance(value, complex):
|
||
print(f"{key}: {value:.4f}")
|
||
else:
|
||
print(f"{key}: {value}")
|
||
|
||
|
||
if __name__ == "__main__": # pragma: no cover
|
||
main() |