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384 lines
12 KiB
Python
384 lines
12 KiB
Python
#!/usr/bin/env python3
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"""
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Relativity Adapter — N-Local Topology
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First-Principles Derivation: N-local topology (cognitive relativity principle)
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Performance Targets:
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- Adaptive topology caching
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- Lazy transformation computation
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- GPU-accelerated coordinate transforms
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- Predictive pre-computation (anticipate user needs)
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Dolphin Principle: Non-Euclidean reality expression for non-human sentience
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"""
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import numpy as np
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from typing import List, Tuple, Optional, Dict
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from dataclasses import dataclass
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from enum import Enum
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import math
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class CognitiveLoadLevel(Enum):
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"""Cognitive load levels for adaptive topology"""
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LOW = "low"
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MEDIUM = "medium"
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HIGH = "high"
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OVERWHELMED = "overwhelmed"
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@dataclass
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class CognitiveLoadVector:
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"""Cognitive load measurement"""
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information_density: float # Information density (0-1)
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complexity: float # Complexity score (0-1)
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novelty: float # Novelty score (0-1)
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uncertainty: float # Uncertainty score (0-1)
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timestamp: float # Timestamp
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def get_level(self) -> CognitiveLoadLevel:
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"""Get cognitive load level"""
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total = (self.information_density + self.complexity + self.novelty + self.uncertainty) / 4.0
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if total < 0.25:
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return CognitiveLoadLevel.LOW
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elif total < 0.5:
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return CognitiveLoadLevel.MEDIUM
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elif total < 0.75:
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return CognitiveLoadLevel.HIGH
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else:
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return CognitiveLoadLevel.OVERWHELMED
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@dataclass
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class NLocalTopology:
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"""N-local topology (relational distance, not Euclidean)"""
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topology_id: str
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distance_metric: str # "relational", "semantic", "topological"
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adjacency_matrix: np.ndarray # Relational adjacency matrix
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coordinates: np.ndarray # N-local coordinates
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cognitive_load_level: CognitiveLoadLevel
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def __repr__(self) -> str:
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return f"NLocalTopology(metric={self.distance_metric}, load={self.cognitive_load_level.value})"
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class RelativityAdapter:
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"""
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Relativity Adapter — N-Local Topology
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Adaptive topology based on cognitive state
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"""
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def __init__(self):
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self.topologies: Dict[str, NLocalTopology] = {}
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self.topology_counter = 0
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self.current_topology: Optional[NLocalTopology] = None
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self.cognitive_load_history: List[CognitiveLoadVector] = []
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self.transformation_cache: Dict[Tuple[str, np.ndarray], np.ndarray] = {}
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def measure_cognitive_load(
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self,
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information_density: float,
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complexity: float,
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novelty: float,
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uncertainty: float
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) -> CognitiveLoadVector:
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"""
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Measure cognitive load
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Args:
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information_density: Information density (0-1)
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complexity: Complexity score (0-1)
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novelty: Novelty score (0-1)
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uncertainty: Uncertainty score (0-1)
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Returns:
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Cognitive load vector
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"""
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import time
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timestamp = time.time()
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load_vector = CognitiveLoadVector(
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information_density=information_density,
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complexity=complexity,
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novelty=novelty,
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uncertainty=uncertainty,
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timestamp=timestamp
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)
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self.cognitive_load_history.append(load_vector)
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return load_vector
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def adapt_topology(self, cognitive_load: CognitiveLoadVector) -> NLocalTopology:
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"""
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Adapt topology based on cognitive load
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Args:
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cognitive_load: Current cognitive load
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Returns:
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Adapted N-local topology
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"""
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load_level = cognitive_load.get_level()
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# Select distance metric based on cognitive load
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if load_level == CognitiveLoadLevel.LOW:
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distance_metric = "relational"
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elif load_level == CognitiveLoadLevel.MEDIUM:
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distance_metric = "semantic"
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elif load_level == CognitiveLoadLevel.HIGH:
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distance_metric = "topological"
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else: # OVERWHELMED
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distance_metric = "minimal" # Simplify to minimal topology
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# Create topology
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self.topology_counter += 1
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topology_id = f"topology_{self.topology_counter}"
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# Generate adjacency matrix based on distance metric
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adjacency_matrix = self._generate_adjacency_matrix(distance_metric)
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# Generate N-local coordinates
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coordinates = self._generate_nlocal_coordinates(distance_metric)
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topology = NLocalTopology(
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topology_id=topology_id,
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distance_metric=distance_metric,
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adjacency_matrix=adjacency_matrix,
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coordinates=coordinates,
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cognitive_load_level=load_level
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)
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self.topologies[topology_id] = topology
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self.current_topology = topology
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return topology
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def _generate_adjacency_matrix(self, distance_metric: str, size: int = 14) -> np.ndarray:
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"""
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Generate adjacency matrix based on distance metric
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Args:
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distance_metric: Type of distance metric
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size: Matrix size (14 for concept vectors)
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Returns:
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Adjacency matrix
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"""
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np.random.seed(42)
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if distance_metric == "relational":
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# Relational: symmetric with strong diagonal
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matrix = np.random.rand(size, size)
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matrix = (matrix + matrix.T) / 2 # Symmetric
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np.fill_diagonal(matrix, 1.0) # Strong diagonal
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elif distance_metric == "semantic":
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# Semantic: cluster-based structure
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matrix = np.zeros((size, size))
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for i in range(size):
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cluster = i // 4 # 4 clusters of ~3-4 items
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for j in range(size):
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if j // 4 == cluster:
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matrix[i, j] = 0.8 + np.random.rand() * 0.2
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else:
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matrix[i, j] = np.random.rand() * 0.3
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np.fill_diagonal(matrix, 1.0)
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elif distance_metric == "topological":
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# Topological: tree-like structure
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matrix = np.zeros((size, size))
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for i in range(size):
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if i > 0:
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parent = (i - 1) // 2
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matrix[i, parent] = 1.0
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matrix[parent, i] = 1.0
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matrix[i, i] = 1.0
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else: # minimal
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# Minimal: identity only
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matrix = np.eye(size)
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return matrix
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def _generate_nlocal_coordinates(self, distance_metric: str, size: int = 14) -> np.ndarray:
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"""
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Generate N-local coordinates based on distance metric
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Args:
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distance_metric: Type of distance metric
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size: Number of coordinates
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Returns:
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N-local coordinates
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"""
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np.random.seed(42)
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if distance_metric == "relational":
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# Relational: uniform distribution
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coordinates = np.random.rand(size)
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elif distance_metric == "semantic":
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# Semantic: clustered distribution
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coordinates = np.zeros(size)
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for i in range(size):
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cluster = i // 4
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coordinates[i] = cluster * 0.25 + np.random.rand() * 0.2
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elif distance_metric == "topological":
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# Topological: hierarchical distribution
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coordinates = np.zeros(size)
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for i in range(size):
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coordinates[i] = math.log(i + 1) / math.log(size + 1)
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else: # minimal
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# Minimal: sparse distribution
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coordinates = np.zeros(size)
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for i in range(size):
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if i % 3 == 0:
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coordinates[i] = np.random.rand()
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return coordinates
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def transform(
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self,
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input_vector: np.ndarray,
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from_topology: Optional[str] = None,
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to_topology: Optional[str] = None
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) -> np.ndarray:
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"""
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Transform coordinate between topologies
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Args:
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input_vector: Input coordinate vector
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from_topology: Source topology ID (default: current)
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to_topology: Target topology ID (default: current)
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Returns:
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Transformed coordinate vector
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"""
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if from_topology is None:
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from_topology = self.current_topology.topology_id if self.current_topology else None
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if to_topology is None:
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to_topology = self.current_topology.topology_id if self.current_topology else None
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if from_topology == to_topology or from_topology is None or to_topology is None:
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return input_vector
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# Check cache
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cache_key = (f"{from_topology}_{to_topology}", input_vector.tobytes())
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if cache_key in self.transformation_cache:
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return self.transformation_cache[cache_key]
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# Get topologies
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from_top = self.topologies.get(from_topology)
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to_top = self.topologies.get(to_topology)
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if from_top is None or to_top is None:
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return input_vector
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# Apply transformation
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transformed = self._apply_transformation(input_vector, from_top, to_top)
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# Cache result
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self.transformation_cache[cache_key] = transformed
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return transformed
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def _apply_transformation(
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self,
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input_vector: np.ndarray,
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from_topology: NLocalTopology,
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to_topology: NLocalTopology
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) -> np.ndarray:
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"""
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Apply transformation between topologies
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Args:
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input_vector: Input vector
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from_topology: Source topology
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to_topology: Target topology
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Returns:
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Transformed vector
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"""
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# Simple transformation: scale by coordinate ratio
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from_coords = from_topology.coordinates
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to_coords = to_topology.coordinates
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# Avoid division by zero
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scale = np.where(from_coords > 0, to_coords / from_coords, 1.0)
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transformed = input_vector * scale
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return transformed
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def enable_dolphin_mode(self) -> None:
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"""
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Enable dolphin mode (non-Euclidean visualization)
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Dolphin Principle: Non-Euclidean reality expression for non-human sentience
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"""
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# Create non-Euclidean topology
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load_vector = CognitiveLoadVector(
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information_density=0.9,
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complexity=0.8,
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novelty=0.9,
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uncertainty=0.9,
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timestamp=0.0
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)
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# Override to use non-Euclidean topology
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topology = self.adapt_topology(load_vector)
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self.current_topology = topology
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def get_cognitive_load_history(self, limit: int = 100) -> List[CognitiveLoadVector]:
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"""Get cognitive load history"""
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return self.cognitive_load_history[-limit:]
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def get_topology_statistics(self) -> Dict:
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"""Get topology statistics"""
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return {
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"total_topologies": len(self.topologies),
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"current_topology": self.current_topology.topology_id if self.current_topology else None,
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"cache_size": len(self.transformation_cache),
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"cognitive_load_samples": len(self.cognitive_load_history)
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}
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def main():
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"""Test relativity adapter with sample data"""
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adapter = RelativityAdapter()
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# Measure cognitive load
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load = adapter.measure_cognitive_load(
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information_density=0.5,
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complexity=0.6,
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novelty=0.4,
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uncertainty=0.3
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)
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print(f"Cognitive load: {load}, level: {load.get_level()}")
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# Adapt topology
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topology = adapter.adapt_topology(load)
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print(f"Adapted topology: {topology}")
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# Transform coordinates
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input_vector = np.array([0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 0.1, 0.2, 0.3, 0.4])
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transformed = adapter.transform(input_vector)
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print(f"Transformed vector: {transformed}")
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# Enable dolphin mode
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adapter.enable_dolphin_mode()
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print(f"Dolphin mode enabled: {adapter.current_topology}")
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# Get statistics
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stats = adapter.get_topology_statistics()
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print(f"Topology statistics: {stats}")
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if __name__ == "__main__":
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main()
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