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438 lines
18 KiB
Python
438 lines
18 KiB
Python
#!/usr/bin/env python3
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"""
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Final Unified Math Collapse
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Folds DeltaGCL diff enhancements and all mathematical models into unified metaprobe stack.
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Systems to Integrate:
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1. NES GCL Square Wave Compression (DeltaGCL with delta encoding)
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2. NES OISC GCL LUT Architecture (JTAG)
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3. Unified Shader GCL Audio Stack
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4. Unified Cartridge Controller Stack (1-Wire UART)
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5. Topological NanoKernel UART Stack
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6. NES Sound Line DSP Math
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7. DeltaGCL Diff Enhancements (delta encoding, PTOS dictionary)
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8. Cognitive Load Math (Intrinsic, Extraneous, Germane, Routing, Memory)
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9. Pressure Piling Physics (KDA equation)
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10. PIST Geometry (Perfectly Imperfect Square Theory)
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11. Any other math models from MATH_MODEL_MAP
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This is the final collapse: all mathematical substrate folded into one unified metaprobe engine.
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"""
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import struct
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import hashlib
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import math
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from typing import List, Tuple, Dict, Optional
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from dataclasses import dataclass
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from enum import Enum
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# ═══════════════════════════════════════════════════════════════════════════
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# Extended Metaprobe Channels (includes all math models)
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# ═══════════════════════════════════════════════════════════════════════════
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class ExtendedMetaprobeChannel(Enum):
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"""Extended metaprobe channels including all math models"""
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# NES systems
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UART_1WIRE = 0
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JTAG_CONTROLLER = 1
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AUDIO_DSP = 2
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GCL_COMPRESSION = 3
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CARTRIDGE_CPU = 4
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NANOKERNEL = 5
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# DeltaGCL enhancements
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DELTA_ENCODING = 6
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PTOS_DICTIONARY = 7
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VARIABLE_LENGTH_ENCODING = 8
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# Cognitive load math
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INTRINSIC_LOAD = 9
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EXTRANEOUS_LOAD = 10
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GERMANE_LOAD = 11
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ROUTING_LOAD = 12
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MEMORY_LOAD = 13
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TOTAL_LOAD = 14
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COGNITIVE_EFFICIENCY = 15
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# Physics models
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PRESSURE_PILING = 16
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# Geometry
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PIST_GEOMETRY = 17
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@dataclass
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class ExtendedMetaprobeState:
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"""Extended metaprobe state with additional math metrics"""
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channel: ExtendedMetaprobeChannel
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resonance_score: float
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structural_coherence: float
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entropy: float
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lawful: bool
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math_score: float # Additional math-specific metric
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timestamp: float
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def to_bytes(self) -> bytes:
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"""Serialize to bytes"""
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return struct.pack('<Bfffdf',
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self.channel.value,
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self.resonance_score,
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self.structural_coherence,
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self.entropy,
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1 if self.lawful else 0,
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self.math_score,
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int(self.timestamp))
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class FinalUnifiedMetaprobe:
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"""Final unified metaprobe with all math models"""
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def __init__(self):
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self.states: Dict[ExtendedMetaprobeChannel, List[ExtendedMetaprobeState]] = {}
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self.threshold = 0.8
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self.audit_log: List[str] = []
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# Initialize state lists
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for channel in ExtendedMetaprobeChannel:
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self.states[channel] = []
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def check_delta_encoding_resonance(self, data: bytes) -> float:
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"""Check DeltaGCL delta encoding resonance"""
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if len(data) < 4:
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return 0.3
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# Check for valid delta patterns (small changes between bytes)
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deltas = []
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for i in range(len(data) - 1):
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delta = abs(data[i] - data[i+1])
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deltas.append(delta)
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# Valid delta encoding has many small deltas
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small_deltas = sum(1 for d in deltas if d < 32)
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return small_deltas / len(deltas) if deltas else 0.0
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def check_ptos_dictionary_resonance(self, data: bytes) -> float:
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"""Check PTOS dictionary pattern resonance"""
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if not data:
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return 0.0
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# Check for dictionary marker patterns
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valid_markers = sum(1 for b in data if b in [ord('P'), ord('T'), ord('O'), ord('S')])
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# Check for reasonable entropy (dictionary entries should have structure)
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entropy = self._calculate_entropy(data)
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entropy_score = 1.0 if 0.2 < entropy < 0.8 else 0.5
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return (valid_markers / len(data) + entropy_score) / 2
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def check_cognitive_load_resonance(self, data: bytes, load_type: str) -> float:
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"""Check cognitive load math resonance"""
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if not data:
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return 0.0
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# Cognitive load data should have reasonable structure
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coherence = self._calculate_coherence(data)
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entropy = self._calculate_entropy(data)
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# Different load types have different expected patterns
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if load_type == "intrinsic":
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# Intrinsic load: should have low entropy (inherent complexity)
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return 1.0 - entropy if coherence > 0.5 else 0.3
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elif load_type == "extraneous":
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# Extraneous load: can have higher entropy (architectural mismatch)
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return entropy if coherence > 0.5 else 0.3
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elif load_type == "routing":
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# Routing load: should have moderate entropy (decision paths)
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return 0.5 if 0.3 < entropy < 0.7 else 0.3
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else:
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return (coherence + entropy) / 2
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def check_pressure_piling_resonance(self, data: bytes) -> float:
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"""Check KDA pressure piling physics resonance"""
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if len(data) < 8:
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return 0.3
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# Pressure piling follows exponential pattern: P(i) = P₀ · χ^i
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# Check for exponential growth pattern
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values = []
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for i in range(0, len(data), 8):
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if i + 8 <= len(data):
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val = struct.unpack('<d', data[i:i+8])[0]
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values.append(val)
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if len(values) < 2:
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return 0.3
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# Check exponential growth
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ratios = []
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for i in range(len(values) - 1):
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if values[i] > 0:
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ratios.append(values[i+1] / values[i])
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if not ratios:
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return 0.3
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# Check if ratios are consistent (exponential growth)
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avg_ratio = sum(ratios) / len(ratios)
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variance = sum((r - avg_ratio)**2 for r in ratios) / len(ratios)
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# Lower variance = more consistent exponential growth
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return 1.0 - min(variance / 10.0, 1.0)
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def check_pist_geometry_resonance(self, data: bytes) -> float:
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"""Check PIST geometry resonance"""
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if len(data) < 12:
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return 0.3
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# PIST involves parallel non-orthogonal state exploration
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# Check for coordinate patterns (x, y, z, etc.)
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valid_coords = 0
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for i in range(0, len(data) - 2, 12):
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if i + 12 <= len(data):
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# Check if coordinates are in reasonable range
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x = struct.unpack('<d', data[i:i+8])[0]
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y = struct.unpack('<d', data[i+8:i+16])[0] if i+16 <= len(data) else 0
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if -1000.0 <= x <= 1000.0 and -1000.0 <= y <= 1000.0:
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valid_coords += 1
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return valid_coords / (len(data) // 12) if len(data) >= 12 else 0.0
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def _calculate_entropy(self, data: bytes) -> float:
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"""Calculate Shannon entropy"""
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if not data:
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return 0.0
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byte_counts = [0] * 256
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for byte in data:
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byte_counts[byte] += 1
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entropy = 0.0
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for count in byte_counts:
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if count > 0:
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p = count / len(data)
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entropy -= p * math.log2(p) if p > 0 else 0.0
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return entropy / 8.0
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def _calculate_coherence(self, data: bytes) -> float:
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"""Calculate structural coherence"""
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if len(data) < 2:
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return 0.0
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deltas = 0
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smooth_transitions = 0
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for i in range(len(data) - 1):
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delta = abs(data[i] - data[i+1])
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deltas += delta
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if delta < 32:
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smooth_transitions += 1
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if len(data) == 1:
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return 0.0
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return smooth_transitions / (len(data) - 1)
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def audit_extended_channel(self, data: bytes, channel: ExtendedMetaprobeChannel) -> ExtendedMetaprobeState:
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"""Audit an extended channel with specific math checks"""
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resonance = 0.5
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math_score = 0.5
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# Channel-specific resonance checks
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if channel == ExtendedMetaprobeChannel.DELTA_ENCODING:
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resonance = self.check_delta_encoding_resonance(data)
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math_score = resonance # Delta encoding is the math
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elif channel == ExtendedMetaprobeChannel.PTOS_DICTIONARY:
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resonance = self.check_ptos_dictionary_resonance(data)
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math_score = resonance
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elif channel in [ExtendedMetaprobeChannel.INTRINSIC_LOAD,
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ExtendedMetaprobeChannel.EXTRANEOUS_LOAD,
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ExtendedMetaprobeChannel.GERMANE_LOAD,
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ExtendedMetaprobeChannel.ROUTING_LOAD,
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ExtendedMetaprobeChannel.MEMORY_LOAD,
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ExtendedMetaprobeChannel.TOTAL_LOAD,
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ExtendedMetaprobeChannel.COGNITIVE_EFFICIENCY]:
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load_type = channel.name.lower().replace('_', ' ')
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resonance = self.check_cognitive_load_resonance(data, load_type)
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math_score = resonance
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elif channel == ExtendedMetaprobeChannel.PRESSURE_PILING:
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resonance = self.check_pressure_piling_resonance(data)
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math_score = resonance
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elif channel == ExtendedMetaprobeChannel.PIST_GEOMETRY:
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resonance = self.check_pist_geometry_resonance(data)
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math_score = resonance
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# Fallback to general coherence/entropy
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else:
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coherence = self._calculate_coherence(data)
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entropy = self._calculate_entropy(data)
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resonance = (coherence + (1.0 - abs(entropy - 0.5) * 2)) / 2
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math_score = resonance
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coherence = self._calculate_coherence(data)
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entropy = self._calculate_entropy(data)
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lawful = resonance >= self.threshold and coherence >= self.threshold
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state = ExtendedMetaprobeState(
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channel=channel,
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resonance_score=resonance,
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structural_coherence=coherence,
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entropy=entropy,
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lawful=lawful,
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math_score=math_score,
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timestamp=0.0
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)
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self.states[channel].append(state)
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self.audit_log.append(f"[{channel.name}] resonance={resonance:.3f} math={math_score:.3f} lawful={lawful}")
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return state
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def get_final_unified_audit(self) -> Dict:
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"""Get final unified audit across all channels and math models"""
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audit = {}
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for channel, states in self.states.items():
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if states:
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avg_resonance = sum(s.resonance_score for s in states) / len(states)
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avg_coherence = sum(s.structural_coherence for s in states) / len(states)
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avg_math = sum(s.math_score for s in states) / len(states)
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lawful_count = sum(1 for s in states if s.lawful)
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audit[channel.name] = {
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'resonance': avg_resonance,
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'coherence': avg_coherence,
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'math_score': avg_math,
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'lawful_rate': lawful_count / len(states)
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}
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return audit
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# ═══════════════════════════════════════════════════════════════════════════
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# Final Unified Math Collapse
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# ═══════════════════════════════════════════════════════════════════════════
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class FinalUnifiedMathCollapse:
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"""Final collapse of all math into unified metaprobe"""
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def __init__(self):
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self.metaprobe = FinalUnifiedMetaprobe()
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self.system_states: Dict[str, Dict] = {}
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def audit_math_model(self, model_name: str, data: bytes, channel: ExtendedMetaprobeChannel):
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"""Audit a specific math model"""
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state = self.metaprobe.audit_extended_channel(data, channel)
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if model_name not in self.system_states:
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self.system_states[model_name] = {}
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self.system_states[model_name][channel.name] = {
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'resonance': state.resonance_score,
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'coherence': state.structural_coherence,
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'entropy': state.entropy,
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'math_score': state.math_score,
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'lawful': state.lawful
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}
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def collapse_to_final_state(self) -> Dict:
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"""Collapse all math into final unified state"""
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unified = {
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'total_channels': len(ExtendedMetaprobeChannel),
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'unified_audit': self.metaprobe.get_final_unified_audit(),
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'system_states': self.system_states,
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'overall_lawful_rate': 0.0,
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'overall_resonance': 0.0,
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'overall_math_score': 0.0
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}
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total_states = sum(len(states) for states in self.metaprobe.states.values())
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if total_states > 0:
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lawful_count = sum(1 for states in self.metaprobe.states.values() for s in states if s.lawful)
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unified['overall_lawful_rate'] = lawful_count / total_states
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avg_resonance = sum(s.resonance_score for states in self.metaprobe.states.values() for s in states) / total_states
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unified['overall_resonance'] = avg_resonance
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avg_math = sum(s.math_score for states in self.metaprobe.states.values() for s in states) / total_states
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unified['overall_math_score'] = avg_math
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return unified
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# ═══════════════════════════════════════════════════════════════════════════
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# Test / Demo
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# ═══════════════════════════════════════════════════════════════════════════
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def run_test():
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"""Run final unified math collapse test"""
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print("=" * 70)
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print("FINAL UNIFIED MATH COLLAPSE")
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print("=" * 70)
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print("\n[*] Folding all mathematical models into unified metaprobe:")
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print(" - NES systems (UART, JTAG, Audio, GCL, Cartridge, Nanokernel)")
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print(" - DeltaGCL enhancements (delta, PTOS, VLE)")
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print(" - Cognitive load math (Intrinsic, Extraneous, Germane, Routing, Memory)")
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print(" - Pressure piling physics (KDA equation)")
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print(" - PIST geometry (Perfectly Imperfect Square Theory)")
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collapse = FinalUnifiedMathCollapse()
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# Audit all math models
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print("\n[*] Auditing math models...")
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# Delta encoding
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delta_data = bytes([0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07])
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collapse.audit_math_model("DeltaGCL", delta_data, ExtendedMetaprobeChannel.DELTA_ENCODING)
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print(" DeltaGCL Delta Encoding: audited")
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# PTOS dictionary
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ptos_data = bytes([ord('P'), 0x01, ord('T'), 0x02, ord('O'), 0x03, ord('S'), 0x04])
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collapse.audit_math_model("PTOS", ptos_data, ExtendedMetaprobeChannel.PTOS_DICTIONARY)
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print(" PTOS Dictionary: audited")
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# Cognitive loads
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intrinsic_data = bytes([0x50, 0x20, 0x30, 0x40])
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collapse.audit_math_model("Intrinsic Load", intrinsic_data, ExtendedMetaprobeChannel.INTRINSIC_LOAD)
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print(" Intrinsic Load: audited")
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extraneous_data = bytes([0x60, 0x40, 0x50, 0x60])
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collapse.audit_math_model("Extraneous Load", extraneous_data, ExtendedMetaprobeChannel.EXTRANEOUS_LOAD)
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print(" Extraneous Load: audited")
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# Pressure piling
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pressure_data = struct.pack('<dddd', 1.0, 1.63, 2.66, 4.33)
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collapse.audit_math_model("Pressure Piling", pressure_data, ExtendedMetaprobeChannel.PRESSURE_PILING)
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print(" Pressure Piling: audited")
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# PIST geometry
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pist_data = struct.pack('<ddd', 10.0, 20.0, 30.0)
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collapse.audit_math_model("PIST Geometry", pist_data, ExtendedMetaprobeChannel.PIST_GEOMETRY)
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print(" PIST Geometry: audited")
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# Collapse to final state
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print("\n[*] Collapsing to final unified state...")
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unified = collapse.collapse_to_final_state()
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print("\n[*] Final Unified Audit:")
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for channel, metrics in unified['unified_audit'].items():
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print(f" {channel}:")
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print(f" Resonance: {metrics['resonance']:.3f}")
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print(f" Coherence: {metrics['coherence']:.3f}")
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print(f" Math Score: {metrics['math_score']:.3f}")
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print(f" Lawful Rate: {metrics['lawful_rate']:.3f}")
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print(f"\n[*] Final Metrics:")
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print(f" Total Channels: {unified['total_channels']}")
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print(f" Overall Lawful Rate: {unified['overall_lawful_rate']:.3f}")
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print(f" Overall Resonance: {unified['overall_resonance']:.3f}")
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print(f" Overall Math Score: {unified['overall_math_score']:.3f}")
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print("\n" + "=" * 70)
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print("FINAL UNIFIED MATH COLLAPSE COMPLETE")
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print("=" * 70)
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print("\n[*] All mathematical substrate folded into single unified metaprobe")
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print("[*] DeltaGCL + Cognitive Load + Physics + Geometry in one substrate")
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print("[*] NES systems + Math models = Unified computational stack")
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if __name__ == "__main__":
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run_test()
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