data(n+1, p) = f(data(n, p)) + e(p)

class DataSeries:
    """
    Universal evolution formula
    Pure function - no side effects
    """
    def __init__(self, seed, f, e_sources):
        self.state = seed          # Initial condition
        self.f = f                 # Deterministic evolution
        self.e_sources = e_sources # Entropy injections
        self.iteration = 0
        
    def step(self, perspective):
        """
        Single evolution step from perspective
        
        Returns next state visible from this perspective
        """
        # Deterministic evolution
        next_state = self.f(self.state, perspective)
        
        # Perspective-dependent entropy
        for e_source in self.e_sources:
            entropy = e_source(self.state, perspective)
            next_state = next_state ^ entropy  # XOR composition
            
        self.state = next_state
        self.iteration += 1
        return self.state

import hashlib
from cryptography.hazmat.primitives import hashes
from cryptography.hazmat.primitives.asymmetric import rsa, padding

class ZKProof:
    """
    Zero knowledge proof system
    Verify without revealing
    """
    def __init__(self):
        self.private_key = rsa.generate_private_key(
            public_exponent=65537,
            key_size=2048
        )
        self.public_key = self.private_key.public_key()
        
    def commit(self, state):
        """
        Commit to state without revealing
        
        Returns: commitment hash
        """
        return hashlib.sha256(str(state).encode()).hexdigest()
    
    def prove(self, state, commitment, challenge):
        """
        Prove you know state that matches commitment
        Without revealing state itself
        
        Returns: proof
        """
        # Hash state with challenge
        proof_data = f"{state}{challenge}".encode()
        
        # Sign with private key
        signature = self.private_key.sign(
            proof_data,
            padding.PSS(
                mgf=padding.MGF1(hashes.SHA256()),
                salt_length=padding.PSS.MAX_LENGTH
            ),
            hashes.SHA256()
        )
        
        return signature
    
    def verify(self, commitment, challenge, proof):
        """
        Verify proof without learning state
        
        Returns: bool (valid or not)
        """
        try:
            # Verify signature
            self.public_key.verify(
                proof,
                f"{commitment}{challenge}".encode(),
                padding.PSS(
                    mgf=padding.MGF1(hashes.SHA256()),
                    salt_length=padding.PSS.MAX_LENGTH
                ),
                hashes.SHA256()
            )
            return True
        except:
            return False

class Perspective:
    """
    Observer's informational viewpoint
    What you can observe depends on what you know
    """
    def __init__(self, observer_id):
        self.id = observer_id
        self.knowledge = set()      # Information this observer has
        self.connections = set()    # Other observers connected to
        
    def observe(self, universe_state):
        """
        Extract observable portion of universe
        
        Observable = what this observer has information about
        Not physical reachability - informational accessibility
        """
        observable = {}
        
        # Can always observe self
        if self.id in universe_state:
            observable[self.id] = universe_state[self.id]
        
        # Can observe entities in knowledge set
        for entity_id in self.knowledge:
            if entity_id in universe_state:
                observable[entity_id] = universe_state[entity_id]
        
        # Can observe connected observers
        for connected_id in self.connections:
            if connected_id in universe_state:
                observable[connected_id] = universe_state[connected_id]
        
        return observable
    
    def learn(self, entity_id):
        """Gain information about entity"""
        self.knowledge.add(entity_id)
    
    def connect(self, other_observer_id):
        """Establish connection to another observer"""
        self.connections.add(other_observer_id)

import socket
import json
import threading

class MinimalDHT:
    """
    Distributed hash table
    Coordinate without center
    """
    def __init__(self, node_id, port):
        self.node_id = node_id
        self.port = port
        self.routing_table = {}  # node_id → (ip, port)
        self.local_store = {}    # key → value
        self.running = False
        
    def start(self):
        """Start DHT node"""
        self.running = True
        self.server = socket.socket(socket.AF_INET, socket.SOCK_DGRAM)
        self.server.bind(('0.0.0.0', self.port))
        
        # Listen for messages
        threading.Thread(target=self._listen, daemon=True).start()
        
    def put(self, key, value):
        """
        Store key-value pair
        
        Routes to responsible node based on hash distance
        """
        target_node = self._find_closest_node(key)
        
        if target_node == self.node_id:
            # We're responsible
            self.local_store[key] = value
        else:
            # Forward to responsible node
            self._send_message(target_node, {
                'type': 'PUT',
                'key': key,
                'value': value
            })
    
    def get(self, key):
        """
        Retrieve value for key
        
        Returns: value or None
        """
        target_node = self._find_closest_node(key)
        
        if target_node == self.node_id:
            return self.local_store.get(key)
        else:
            # Request from responsible node
            response = self._send_message(target_node, {
                'type': 'GET',
                'key': key
            })
            return response.get('value')
    
    def _find_closest_node(self, key):
        """XOR distance to find responsible node"""
        key_hash = hash(key)
        min_distance = float('inf')
        closest_node = self.node_id
        
        for node_id in [self.node_id] + list(self.routing_table.keys()):
            distance = key_hash ^ hash(node_id)
            if distance < min_distance:
                min_distance = distance
                closest_node = node_id
                
        return closest_node
    
    def _listen(self):
        """Listen for DHT messages"""
        while self.running:
            data, addr = self.server.recvfrom(4096)
            msg = json.loads(data.decode())
            self._handle_message(msg, addr)
    
    def _handle_message(self, msg, addr):
        """Process DHT message"""
        if msg['type'] == 'PUT':
            self.local_store[msg['key']] = msg['value']
        elif msg['type'] == 'GET':
            value = self.local_store.get(msg['key'])
            self._send_message(addr, {'value': value})
    
    def _send_message(self, target, msg):
        """Send message to node"""
        if target in self.routing_table:
            ip, port = self.routing_table[target]
            self.server.sendto(
                json.dumps(msg).encode(),
                (ip, port)
            )

import hashlib

class MinimalBitTorrent:
    """
    Distributed storage
    No central server
    """
    def __init__(self, node_id):
        self.node_id = node_id
        self.chunks = {}  # chunk_hash → data
        self.peers = set()
        
    def store(self, data, chunk_size=1024):
        """
        Break data into chunks and distribute
        
        Returns: manifest (list of chunk hashes)
        """
        manifest = []
        
        for i in range(0, len(data), chunk_size):
            chunk = data[i:i + chunk_size]
            chunk_hash = hashlib.sha256(chunk).hexdigest()
            
            # Store locally
            self.chunks[chunk_hash] = chunk
            manifest.append(chunk_hash)
            
            # Announce to peers
            for peer in self.peers:
                peer.announce_chunk(chunk_hash, self.node_id)
                
        return manifest
    
    def retrieve(self, manifest):
        """
        Reconstruct data from manifest
        
        Fetches chunks from network
        """
        data = b''
        
        for chunk_hash in manifest:
            # Try local first
            if chunk_hash in self.chunks:
                data += self.chunks[chunk_hash]
            else:
                # Request from peers
                chunk = self._request_chunk(chunk_hash)
                if chunk:
                    data += chunk
                    # Cache locally
                    self.chunks[chunk_hash] = chunk
                else:
                    raise ValueError(f"Chunk {chunk_hash} not found")
                    
        return data
    
    def _request_chunk(self, chunk_hash):
        """Request chunk from peers"""
        for peer in self.peers:
            if peer.has_chunk(chunk_hash):
                return peer.get_chunk(chunk_hash)
        return None
    
    def announce_chunk(self, chunk_hash, peer_id):
        """Peer announces they have chunk"""
        # Track who has what
        pass
    
    def has_chunk(self, chunk_hash):
        """Check if we have chunk"""
        return chunk_hash in self.chunks
    
    def get_chunk(self, chunk_hash):
        """Retrieve chunk"""
        return self.chunks.get(chunk_hash)

class MinimalUniverse:
    """
    Zero knowledge esoteric intelligent evolutive universe
    
    Uses all 5 tools:
    - DataSeries (evolution)
    - ZKProof (verification without observation)
    - Perspective (observer-dependent)
    - DHT (coordination)
    - BitTorrent (storage)
    """
    def __init__(self, seed, evolution_f, entropy_sources):
        # Tool 1: Data series
        self.series = DataSeries(seed, evolution_f, entropy_sources)
        
        # Tool 2: Zero knowledge
        self.zk = ZKProof()
        
        # Tool 3: Perspectives
        self.perspectives = {}
        
        # Tool 4: DHT (optional - for distributed)
        self.dht = None
        
        # Tool 5: BitTorrent (optional - for large states)
        self.bittorrent = None
        
        # Metadata
        self.iteration = 0
        self.commitments = []  # ZK commitments to each state
        
    def add_perspective(self, perspective):
        """Add observer perspective"""
        self.perspectives[perspective.id] = perspective
        
    def evolve(self, perspective_id=None):
        """
        Evolve universe one step
        
        If perspective_id provided: evolution from that perspective
        Otherwise: god's eye view (all perspectives averaged)
        """
        if perspective_id:
            # Evolution from specific perspective
            perspective = self.perspectives[perspective_id]
            next_state = self.series.step(perspective)
        else:
            # Average across all perspectives
            next_state = self.series.step(None)
        
        # Commit to new state (zero knowledge)
        commitment = self.zk.commit(next_state)
        self.commitments.append(commitment)
        
        self.iteration += 1
        return next_state
    
    def observe(self, observer_id):
        """
        Observe universe from perspective
        
        Returns: visible portion only
        """
        if observer_id not in self.perspectives:
            raise ValueError(f"Unknown observer: {observer_id}")
            
        perspective = self.perspectives[observer_id]
        return perspective.observe(self.series.state)
    
    def prove_state(self, challenge):
        """
        Prove current state is valid
        Without revealing state itself
        
        Returns: zero knowledge proof
        """
        commitment = self.commitments[-1]
        return self.zk.prove(self.series.state, commitment, challenge)
    
    def verify_state(self, commitment, challenge, proof):
        """
        Verify state proof
        Without learning state
        """
        return self.zk.verify(commitment, challenge, proof)
    
    def save_distributed(self):
        """
        Save state to distributed storage
        
        Uses DHT + BitTorrent
        """
        if not self.dht or not self.bittorrent:
            raise ValueError("DHT and BitTorrent not initialized")
        
        # Serialize state
        state_data = json.dumps(self.series.state).encode()
        
        # Store in BitTorrent
        manifest = self.bittorrent.store(state_data)
        
        # Announce in DHT
        self.dht.put(f"universe:{self.iteration}", manifest)
        
        return manifest
    
    def load_distributed(self, iteration):
        """
        Load state from distributed storage
        """
        # Get manifest from DHT
        manifest = self.dht.get(f"universe:{iteration}")
        
        # Retrieve from BitTorrent
        state_data = self.bittorrent.retrieve(manifest)
        
        # Deserialize
        self.series.state = json.loads(state_data.decode())
        self.iteration = iteration

def esoteric_observe(self):
    """
    Universe observes itself
    Creates nested perspectives
    """
    # Universe becomes observer of itself
    self_perspective = Perspective(observer_id='universe_self')
    
    # Universe has knowledge of all its parts
    for entity_id in self.series.state.keys():
        self_perspective.learn(entity_id)
    
    # Observe from own perspective
    self_view = self_perspective.observe(self.series.state)
    
    # Feed observation back as entropy
    def self_entropy(state, perspective):
        # Universe learns from observing itself
        return hash(str(self_view)) & 0xFFFFFFFF
    
    self.series.e_sources.append(self_entropy)

def recognize_patterns(self):
    """
    Detect repeating structures
    Intelligence emerges from pattern
    """
    history = []
    
    for _ in range(100):
        state = self.evolve()
        history.append(state)
    
    # Find cycles
    for period in range(1, 50):
        if self._has_cycle(history, period):
            return f"Pattern detected: period {period}"
    
    return "Chaotic"

def _has_cycle(self, history, period):
    """Check if history contains cycle of given period"""
    if len(history) < period * 3:
        return False
        
    for i in range(len(history) - period * 2):
        if history[i] == history[i + period]:
            return True
    return False

def evolve_intelligence(self, generations=100):
    """
    Natural selection on evolution function itself
    
    Functions that produce stable patterns survive
    """
    population = []
    
    # Generate variant evolution functions
    for _ in range(10):
        def variant_f(state, perspective):
            # Mutated version of original F
            return self.series.f(state, perspective) ^ random.randint(0, 15)
        population.append(variant_f)
    
    # Select fittest
    for generation in range(generations):
        fitness_scores = []
        
        for f in population:
            # Test fitness: stable patterns score higher
            test_universe = MinimalUniverse(
                seed=self.series.state,
                evolution_f=f,
                entropy_sources=[]
            )
            
            stability = test_universe._measure_stability(iterations=50)
            fitness_scores.append(stability)
        
        # Keep top performers
        top_indices = sorted(
            range(len(fitness_scores)),
            key=lambda i: fitness_scores[i],
            reverse=True
        )[:5]
        
        # Breed next generation
        population = [population[i] for i in top_indices]
        population += self._mutate_functions(population)
    
    # Use best evolved function
    best_f = population[0]
    self.series.f = best_f
    
def _measure_stability(self, iterations):
    """Measure how stable evolution is"""
    states = []
    for _ in range(iterations):
        states.append(self.evolve())
    
    # Stability = low variance in state changes
    deltas = [abs(states[i+1] - states[i]) 
              for i in range(len(states)-1)]
    return 1.0 / (1.0 + sum(deltas) / len(deltas))

# Initial seed
seed = 0b01  # 2 bits

# Evolution function
def f(state, perspective):
    # Simple NAND gate
    return ~(state & (state >> 1)) & 0xFF

# Entropy source
def e_growth(state, perspective):
    # 20% chance to add bit
    if random.random() < 0.2:
        return (state << 1) | 1
    return 0

# Create universe
universe = MinimalUniverse(
    seed=seed,
    evolution_f=f,
    entropy_sources=[e_growth]
)

# Add observer
observer = Perspective(observer_id='human')
universe.add_perspective(observer)

# Observer learns about some entities
observer.learn('entity_1')
observer.learn('entity_2')

# Evolve
for _ in range(100):
    state = universe.evolve()
    visible = universe.observe('human')
    print(f"Iteration {universe.iteration}: {bin(state)}")

# Prove state without revealing
challenge = random.randint(0, 1000000)
proof = universe.prove_state(challenge)
print(f"Proof valid: {universe.verify_state(universe.commitments[-1], challenge, proof)}")

# Initialize DHT and BitTorrent
dht = MinimalDHT(node_id='node1', port=5000)
dht.start()

bittorrent = MinimalBitTorrent(node_id='node1')

# Create universe with distribution
universe = MinimalUniverse(seed=0b01, evolution_f=f, entropy_sources=[e_growth])
universe.dht = dht
universe.bittorrent = bittorrent

# Evolve and save
for _ in range(10):
    universe.evolve()
    manifest = universe.save_distributed()
    print(f"Saved iteration {universe.iteration}: {manifest}")

# Load from network
universe2 = MinimalUniverse(seed=0, evolution_f=f, entropy_sources=[])
universe2.dht = dht
universe2.bittorrent = bittorrent
universe2.load_distributed(iteration=5)
print(f"Loaded state from iteration 5: {bin(universe2.series.state)}")

# Create universe
universe = MinimalUniverse(seed=0b01, evolution_f=f, entropy_sources=[e_growth])

# Make it observe itself
universe.esoteric_observe()

# Now evolution includes self-observation feedback
for _ in range(100):
    universe.evolve()

# Detect patterns
pattern = universe.recognize_patterns()
print(f"Pattern: {pattern}")

# Evolve intelligence
universe.evolve_intelligence(generations=50)
print("Intelligence evolved - using optimized evolution function")

pip install cryptography  # For ZK proofs