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