Pure Binary PyTorch Implementations for Observer Collapse Engine

Overview

All operations in Chapters 1-6 can be implemented using pure PyTorch binary operations. This demonstrates the fundamental binary nature of collapse-aware computation.

Chapter 1: Self-Reflexive Core (Binary)

import torch

class BinarySelfReflexiveCore:
    """
    ψ₀ = ψ₀(ψ₀) in pure binary.
    All operations use only 0 and 1.
    """
    
    def __init__(self, dim: int = 8):
        self.dim = dim
        # Binary state vector
        self.core_state = torch.randint(0, 2, (dim,), dtype=torch.uint8)
        # Binary idempotent matrix (M² = M)
        self.self_matrix = self._create_idempotent_binary_matrix(dim)
        
    def _create_idempotent_binary_matrix(self, dim: int) -> torch.Tensor:
        """Create binary matrix where M² = M using projection."""
        # Random binary matrix
        M = torch.randint(0, 2, (dim, dim), dtype=torch.uint8)
        # Make idempotent: M = M @ M (in binary)
        M2 = (M @ M) > 0
        return M2.to(torch.uint8)
    
    def psi_0(self, x: torch.Tensor) -> torch.Tensor:
        """Binary self-application: ψ₀(x) = ψ₀(ψ₀(x))."""
        # Binary matrix multiplication (AND + XOR)
        y = self._binary_matmul(x, self.self_matrix)
        # Verify idempotency
        z = self._binary_matmul(y, self.self_matrix)
        assert torch.equal(y, z), "Binary idempotency violated"
        return y
    
    def _binary_matmul(self, vec: torch.Tensor, mat: torch.Tensor) -> torch.Tensor:
        """Binary matrix multiplication using AND and XOR."""
        result = torch.zeros(mat.shape[0], dtype=torch.uint8)
        for i in range(mat.shape[0]):
            # Binary dot product: XOR of ANDs
            dot = torch.sum(vec & mat[i]) % 2
            result[i] = dot
        return result
    
    def collapse(self, superposition: torch.Tensor) -> torch.Tensor:
        """Binary collapse through observation."""
        # obs_random: Each bit is a quantum choice
        obs_bits = torch.randint(0, 2, superposition.shape, dtype=torch.uint8)
        # XOR creates interference pattern
        collapsed = superposition ^ obs_bits
        # Project onto eigenspace (binary)
        return self._binary_matmul(collapsed, self.self_matrix)

Chapter 2: Golden Vector System (Binary)

class BinaryGoldenVectorSystem:
    """
    Fibonacci-bounded binary vectors.
    No consecutive 1s allowed.
    """
    
    def __init__(self, max_length: int = 16):
        self.max_length = max_length
        self.fibonacci = self._compute_fibonacci(max_length + 2)
        
    def _compute_fibonacci(self, n: int) -> list:
        """Compute Fibonacci numbers."""
        fib = [1, 1]
        for i in range(2, n):
            fib.append(fib[-1] + fib[-2])
        return fib
    
    def is_golden(self, vec: torch.Tensor) -> bool:
        """Check if binary vector has no consecutive 1s."""
        if len(vec) < 2:
            return True
        # Check consecutive positions
        for i in range(len(vec) - 1):
            if vec[i] == 1 and vec[i+1] == 1:
                return False
        return True
    
    def encode_to_golden_binary(self, index: int, length: int) -> torch.Tensor:
        """Encode integer as golden binary vector."""
        vec = torch.zeros(length, dtype=torch.uint8)
        
        # Zeckendorf representation (greedy algorithm)
        remaining = index
        for i in range(length-1, -1, -1):
            if remaining >= self.fibonacci[i]:
                vec[length-1-i] = 1
                remaining -= self.fibonacci[i]
                
        return vec
    
    def apply_golden_constraint(self, vec: torch.Tensor) -> torch.Tensor:
        """Force vector to satisfy golden constraint."""
        result = vec.clone()
        for i in range(len(result) - 1):
            if result[i] == 1 and result[i+1] == 1:
                result[i+1] = 0  # Remove consecutive 1
        return result
    
    def golden_binary_evolution(self, vec: torch.Tensor) -> torch.Tensor:
        """Evolve binary vector maintaining golden property."""
        # Shift register with golden feedback
        new_vec = torch.zeros_like(vec)
        
        # XOR feedback maintains golden property
        feedback = vec[0] ^ vec[2] if len(vec) > 2 else vec[0]
        
        # Shift with feedback
        new_vec[1:] = vec[:-1]
        new_vec[0] = feedback
        
        # Ensure golden constraint
        return self.apply_golden_constraint(new_vec)

Chapter 3: Binary Trace Collapse

class BinaryTraceCollapse:
    """
    Execution paths as binary traces.
    Each bit represents a collapse decision.
    """
    
    def __init__(self, trace_length: int = 32):
        self.trace_length = trace_length
        self.golden = BinaryGoldenVectorSystem(trace_length)
        
    def create_binary_superposition(self, n_paths: int = 4) -> torch.Tensor:
        """Create superposition of binary execution paths."""
        # Each row is a possible path
        paths = torch.randint(0, 2, (n_paths, self.trace_length), dtype=torch.uint8)
        # Apply golden constraint to each path
        for i in range(n_paths):
            paths[i] = self.golden.apply_golden_constraint(paths[i])
        return paths
    
    def collapse_to_binary_path(self, superposition: torch.Tensor) -> torch.Tensor:
        """Collapse superposition to single binary path."""
        n_paths = superposition.shape[0]
        
        # obs_selector: Binary selection vector
        obs_selector = torch.randint(0, 2, (n_paths,), dtype=torch.uint8)
        
        # Find first 1 in selector (or default to 0)
        selected_idx = torch.argmax(obs_selector.float())
        if obs_selector.sum() == 0:
            selected_idx = 0
            
        return superposition[selected_idx]
    
    def binary_path_distance(self, path1: torch.Tensor, path2: torch.Tensor) -> int:
        """Hamming distance between binary paths."""
        return torch.sum(path1 ^ path2).item()
    
    def execute_binary_step(self, current_state: torch.Tensor, 
                          instruction: torch.Tensor) -> torch.Tensor:
        """Execute one step of binary computation."""
        # XOR for state transition
        next_state = current_state ^ instruction
        # AND with mask for conditional execution
        mask = torch.randint(0, 2, current_state.shape, dtype=torch.uint8)
        return (next_state & mask) | (current_state & ~mask)

Chapter 4: Binary Collapse Entropy

class BinaryCollapseEntropy:
    """
    Entropy from binary divergence patterns.
    Randomness emerges from XOR distances.
    """
    
    def __init__(self, state_bits: int = 16):
        self.state_bits = state_bits
        
    def binary_divergence(self, state1: torch.Tensor, state2: torch.Tensor) -> int:
        """Hamming distance as divergence measure."""
        return torch.sum(state1 ^ state2).item()
    
    def compute_binary_entropy(self, states: torch.Tensor) -> float:
        """Entropy from binary state distribution."""
        n_states = states.shape[0]
        
        # Count unique patterns
        unique_patterns = {}
        for i in range(n_states):
            pattern = tuple(states[i].tolist())
            unique_patterns[pattern] = unique_patterns.get(pattern, 0) + 1
            
        # Binary entropy calculation
        total = sum(unique_patterns.values())
        entropy = 0.0
        for count in unique_patterns.values():
            p = count / total
            if p > 0:
                entropy -= p * torch.log2(torch.tensor(p))
                
        return entropy.item()
    
    def generate_max_entropy_binary(self, n_bits: int) -> torch.Tensor:
        """Generate maximum entropy binary pattern."""
        # Alternating pattern maximizes transitions
        pattern = torch.zeros(n_bits, dtype=torch.uint8)
        pattern[::2] = 1  # 101010...
        
        # Add controlled randomness
        noise = torch.randint(0, 2, (n_bits,), dtype=torch.uint8)
        mask = torch.randint(0, 2, (n_bits,), dtype=torch.uint8)
        
        return pattern ^ (noise & mask)
    
    def binary_entropy_evolution(self, initial: torch.Tensor, steps: int) -> list:
        """Evolve entropy through binary operations."""
        history = [initial.clone()]
        current = initial
        
        for _ in range(steps):
            # Linear feedback shift register (LFSR)
            feedback = current[0] ^ current[2] ^ current[5] ^ current[7]
            current = torch.roll(current, 1)
            current[0] = feedback
            history.append(current.clone())
            
        return history

Chapter 5: Binary Echo Sensitivity

class BinaryObserverEcho:
    """
    Observer as binary echo patterns.
    Sensitivity emerges from XOR resonance.
    """
    
    def __init__(self, echo_bits: int = 16):
        self.echo_bits = echo_bits
        self.sensitivity_threshold = 5  # Hamming distance threshold
        
    def create_binary_echo(self, state: torch.Tensor, depth: int = 1) -> torch.Tensor:
        """Create echo through binary reflection."""
        echo = state.clone()
        
        for d in range(depth):
            # obs_reflection: Binary interference pattern
            reflection = torch.randint(0, 2, state.shape, dtype=torch.uint8)
            # XOR creates echo
            echo = echo ^ reflection
            # Circular shift for temporal effect
            echo = torch.roll(echo, d + 1)
            
        return echo
    
    def binary_echo_sensitivity(self, state: torch.Tensor) -> int:
        """Measure echo sensitivity as bit flip count."""
        echo = self.create_binary_echo(state)
        sensitivity = torch.sum(state ^ echo).item()
        return sensitivity
    
    def create_binary_observer(self, base_state: torch.Tensor) -> torch.Tensor:
        """Create observer state through echo cascade."""
        if self.binary_echo_sensitivity(base_state) < self.sensitivity_threshold:
            return base_state  # No observer emerges
            
        # Binary echo cascade
        observer = base_state.clone()
        for i in range(3):  # 3 echo levels
            echo = self.create_binary_echo(observer, depth=i+1)
            observer = observer ^ echo  # XOR accumulation
            
        return observer
    
    def binary_resonance(self, state1: torch.Tensor, state2: torch.Tensor) -> float:
        """Measure resonance through binary correlation."""
        # Count matching bits
        matches = torch.sum(~(state1 ^ state2)).float()
        total = len(state1)
        return matches / total

Chapter 6: Binary Interference Agent

class BinaryInterferenceAgent:
    """
    Observer as binary interference agent.
    Actively shapes collapse through bit manipulation.
    """
    
    def __init__(self, agent_bits: int = 16, memory_size: int = 8):
        self.agent_bits = agent_bits
        self.memory_size = memory_size
        
        # Binary internal state
        self.internal_state = torch.randint(0, 2, (agent_bits,), dtype=torch.uint8)
        
        # Binary memory buffer (circular)
        self.memory = torch.zeros((memory_size, agent_bits), dtype=torch.uint8)
        self.memory_ptr = 0
        
    def create_interference_mask(self, quantum_state: torch.Tensor) -> torch.Tensor:
        """Generate binary interference mask."""
        # Combine internal state with quantum state
        combined = self.internal_state ^ quantum_state
        
        # Create interference through bit rotation
        interference = torch.roll(combined, 3)
        
        # Apply memory influence
        memory_influence = self.memory.sum(dim=0) % 2  # Parity of memory
        interference = interference ^ memory_influence
        
        return interference
    
    def interfere_with_binary_collapse(self, superposition: torch.Tensor) -> torch.Tensor:
        """Actively interfere with binary collapse."""
        n_branches = superposition.shape[0]
        
        # Generate interference mask
        mask = self.create_interference_mask(superposition[0])
        
        # Apply interference to each branch
        interfered = torch.zeros_like(superposition)
        for i in range(n_branches):
            interfered[i] = superposition[i] ^ (mask & torch.randint(0, 2, mask.shape, dtype=torch.uint8))
            
        # Select branch based on internal state alignment
        alignments = torch.zeros(n_branches)
        for i in range(n_branches):
            alignments[i] = torch.sum(~(interfered[i] ^ self.internal_state))
            
        selected_idx = torch.argmax(alignments)
        collapsed = interfered[selected_idx]
        
        # Update memory
        self.memory[self.memory_ptr] = collapsed
        self.memory_ptr = (self.memory_ptr + 1) % self.memory_size
        
        return collapsed
    
    def binary_agent_evolution(self, steps: int = 10) -> list:
        """Evolve agent through binary feedback."""
        history = []
        
        for _ in range(steps):
            # Create quantum superposition
            superposition = torch.randint(0, 2, (4, self.agent_bits), dtype=torch.uint8)
            
            # Interfere and collapse
            collapsed = self.interfere_with_binary_collapse(superposition)
            
            # Update internal state through XOR feedback
            self.internal_state = self.internal_state ^ torch.roll(collapsed, 1)
            
            history.append({
                'internal': self.internal_state.clone(),
                'collapsed': collapsed.clone()
            })
            
        return history

Unified Binary Interface

class UnifiedBinaryEngine:
    """
    Combines all binary operations into unified engine.
    Pure binary implementation of Observer Collapse Engine.
    """
    
    def __init__(self, bits: int = 16):
        self.bits = bits
        self.core = BinarySelfReflexiveCore(bits)
        self.golden = BinaryGoldenVectorSystem(bits)
        self.trace = BinaryTraceCollapse(bits)
        self.entropy = BinaryCollapseEntropy(bits)
        self.echo = BinaryObserverEcho(bits)
        self.agent = BinaryInterferenceAgent(bits)
        
    def complete_binary_cycle(self, initial_state: torch.Tensor) -> dict:
        """Execute complete observer-collapse cycle in binary."""
        # 1. Self-reflexive transformation
        reflexive = self.core.psi_0(initial_state)
        
        # 2. Apply golden constraint
        golden = self.golden.apply_golden_constraint(reflexive)
        
        # 3. Create execution trace
        trace_super = self.trace.create_binary_superposition()
        trace = self.trace.collapse_to_binary_path(trace_super)
        
        # 4. Measure entropy
        states = torch.stack([initial_state, reflexive, golden, trace[:self.bits]])
        entropy = self.entropy.compute_binary_entropy(states)
        
        # 5. Create echo observer
        observer = self.echo.create_binary_observer(golden)
        
        # 6. Agent interference
        superposition = torch.stack([golden, observer, trace[:self.bits]])
        final = self.agent.interfere_with_binary_collapse(superposition)
        
        return {
            'initial': initial_state,
            'reflexive': reflexive,
            'golden': golden,
            'trace': trace,
            'entropy': entropy,
            'observer': observer,
            'final': final
        }

Key Binary Operations Summary

1. AND (&): Conditional execution, masking
2. OR (|): Combining states, union operations
3. XOR (^): Creating echoes, interference, state transitions
4. NOT (~): Inversion, complement
5. SHIFT (roll): Temporal effects, feedback
6. Population Count (sum): Hamming weight, correlation

All quantum collapse phenomena emerge from these simple binary operations!