# EXO-AI 2025: Pseudocode Design

## SPARC Phase 2: Algorithm Design

This document presents high-level pseudocode for the core algorithms in the EXO-AI cognitive substrate.

---

## 1. Learned Manifold Engine

### 1.1 Manifold Retrieval via Gradient Descent

```pseudocode
FUNCTION ManifoldRetrieve(query_vector, k, manifold_network):
    // Initialize search position at query
    position = query_vector
    visited_positions = []

    // Gradient descent toward high-relevance regions
    FOR step IN 1..MAX_DESCENT_STEPS:
        // Forward pass through learned manifold
        relevance_field = manifold_network.forward(position)

        // Compute gradient of relevance
        gradient = manifold_network.backward(relevance_field)

        // Update position following relevance gradient
        position = position - LEARNING_RATE * gradient
        visited_positions.append(position)

        // Check convergence
        IF norm(gradient) < CONVERGENCE_THRESHOLD:
            BREAK

    // Extract k nearest patterns from converged region
    results = []
    FOR pos IN visited_positions.last(k):
        patterns = ExtractPatternsNear(pos, manifold_network)
        results.extend(patterns)

    RETURN TopK(results, k)
```

### 1.2 Continuous Manifold Deformation

```pseudocode
FUNCTION ManifoldDeform(pattern, salience, manifold_network, optimizer):
    // No discrete insert - continuous deformation instead

    // Encode pattern as tensor
    embedding = Tensor(pattern.embedding)

    // Compute deformation loss
    // Loss = how much the manifold needs to change to represent this pattern
    current_relevance = manifold_network.forward(embedding)
    target_relevance = salience
    deformation_loss = (current_relevance - target_relevance)^2

    // Add regularization for manifold smoothness
    smoothness_loss = ManifoldCurvatureRegularizer(manifold_network)
    total_loss = deformation_loss + LAMBDA * smoothness_loss

    // Gradient update to manifold weights
    gradients = total_loss.backward()
    optimizer.step(gradients)

    // Return delta for logging
    RETURN ManifoldDelta(embedding, salience, total_loss)
```

### 1.3 Strategic Forgetting

```pseudocode
FUNCTION StrategicForget(manifold_network, decay_rate, salience_threshold):
    // Identify low-salience regions
    low_salience_regions = []

    FOR region IN manifold_network.sample_regions():
        avg_salience = ComputeAverageSalience(region)
        IF avg_salience < salience_threshold:
            low_salience_regions.append(region)

    // Apply smoothing kernel to low-salience regions
    // This effectively "forgets" by reducing specificity
    FOR region IN low_salience_regions:
        ForgetKernel = GaussianKernel(sigma=decay_rate)
        manifold_network.apply_kernel(region, ForgetKernel)

    // Optional: prune near-zero weights
    manifold_network.prune_weights(threshold=1e-6)
```

---

## 2. Hypergraph Substrate

### 2.1 Hyperedge Creation

```pseudocode
FUNCTION CreateHyperedge(entities, relation, hypergraph):
    // Validate all entities exist
    FOR entity IN entities:
        IF NOT hypergraph.base_graph.contains(entity):
            RAISE EntityNotFoundError(entity)

    // Generate hyperedge ID
    hyperedge_id = GenerateUUID()

    // Create hyperedge record
    hyperedge = Hyperedge(
        id = hyperedge_id,
        entities = entities,
        relation = relation,
        created_at = NOW(),
        weight = 1.0
    )

    // Insert into hyperedge storage
    hypergraph.hyperedges.insert(hyperedge_id, hyperedge)

    // Update inverted index (entity -> hyperedges)
    FOR entity IN entities:
        hypergraph.entity_index[entity].append(hyperedge_id)

    // Update relation type index
    hypergraph.relation_index[relation.type].append(hyperedge_id)

    // Update simplicial complex for TDA
    simplex = entities.as_simplex()
    hypergraph.topology.add_simplex(simplex)

    RETURN hyperedge_id
```

### 2.2 Persistent Homology Computation

```pseudocode
FUNCTION ComputePersistentHomology(hypergraph, dimension, epsilon_range):
    // Build filtration (nested sequence of simplicial complexes)
    filtration = BuildFiltration(hypergraph.topology, epsilon_range)

    // Initialize boundary matrix for column reduction
    boundary_matrix = BuildBoundaryMatrix(filtration, dimension)

    // Column reduction algorithm (standard persistent homology)
    reduced_matrix = ColumnReduction(boundary_matrix)

    // Extract persistence pairs
    pairs = []
    FOR col_j IN reduced_matrix.columns:
        IF reduced_matrix.low(j) != NULL:
            i = reduced_matrix.low(j)
            birth = filtration.birth_time(i)
            death = filtration.birth_time(j)
            pairs.append((birth, death))
        ELSE IF col_j is a cycle:
            birth = filtration.birth_time(j)
            death = INFINITY  // Essential feature
            pairs.append((birth, death))

    // Build persistence diagram
    diagram = PersistenceDiagram(
        pairs = pairs,
        dimension = dimension
    )

    RETURN diagram

FUNCTION ColumnReduction(matrix):
    // Standard algorithm from computational topology
    FOR j IN 1..matrix.num_cols:
        WHILE EXISTS j' < j WITH low(j') = low(j):
            // Add column j' to column j to reduce
            matrix.column(j) = matrix.column(j) XOR matrix.column(j')
    RETURN matrix
```

### 2.3 Sheaf Consistency Check

```pseudocode
FUNCTION CheckSheafConsistency(sheaf, sections):
    // Sheaf consistency: local sections should agree on overlaps

    inconsistencies = []

    // Check all pairs of overlapping sections
    FOR (section_a, section_b) IN Pairs(sections):
        overlap = section_a.domain.intersect(section_b.domain)

        IF overlap.is_empty():
            CONTINUE

        // Restriction maps
        restricted_a = sheaf.restrict(section_a, overlap)
        restricted_b = sheaf.restrict(section_b, overlap)

        // Check agreement
        IF NOT ApproximatelyEqual(restricted_a, restricted_b, tolerance=EPSILON):
            inconsistencies.append(
                SheafInconsistency(
                    sections = (section_a, section_b),
                    overlap = overlap,
                    discrepancy = Distance(restricted_a, restricted_b)
                )
            )

    IF inconsistencies.is_empty():
        RETURN SheafConsistencyResult.Consistent
    ELSE:
        RETURN SheafConsistencyResult.Inconsistent(inconsistencies)
```

---

## 3. Temporal Memory Coordinator

### 3.1 Causal Cone Query

```pseudocode
FUNCTION CausalQuery(query, reference_time, cone_type, temporal_memory):
    // Determine valid time range based on causal cone
    SWITCH cone_type:
        CASE Past:
            time_range = (MIN_TIME, reference_time)
        CASE Future:
            time_range = (reference_time, MAX_TIME)
        CASE LightCone(velocity):
            // Relativistic constraint: |delta_x| <= c * |delta_t|
            time_range = ComputeLightCone(reference_time, query.origin, velocity)

    // Filter candidates by time range
    candidates = temporal_memory.long_term.filter_by_time(time_range)

    // Similarity search within temporal constraint
    similarities = []
    FOR candidate IN candidates:
        sim = CosineSimilarity(query.embedding, candidate.embedding)
        causal_dist = temporal_memory.causal_graph.shortest_path(
            query.origin,
            candidate.id
        )
        similarities.append((candidate, sim, causal_dist))

    // Rank by combined temporal and causal relevance
    scored = []
    FOR (candidate, sim, causal_dist) IN similarities:
        temporal_score = 1.0 / (1.0 + abs(candidate.timestamp - reference_time))
        causal_score = 1.0 / (1.0 + causal_dist) IF causal_dist != INF ELSE 0.0

        combined = ALPHA * sim + BETA * temporal_score + GAMMA * causal_score
        scored.append((candidate, combined))

    RETURN sorted(scored, by=combined, descending=True)
```

### 3.2 Memory Consolidation

```pseudocode
FUNCTION Consolidate(temporal_memory):
    // Biological-inspired memory consolidation
    // Short-term -> Long-term with salience filtering

    // Compute salience for all short-term items
    salience_scores = []
    FOR item IN temporal_memory.short_term:
        salience = ComputeSalience(item, temporal_memory)
        salience_scores.append((item, salience))

    // Salience computation factors:
    // - Frequency of access
    // - Recency of access
    // - Causal importance (how many things depend on it)
    // - Surprise (deviation from expected)

    FUNCTION ComputeSalience(item, memory):
        access_freq = memory.access_counts[item.id]
        recency = 1.0 / (1.0 + (NOW() - item.last_accessed))
        causal_importance = memory.causal_graph.out_degree(item.id)
        surprise = ComputeSurprise(item, memory.long_term)

        RETURN W1*access_freq + W2*recency + W3*causal_importance + W4*surprise

    // Filter by salience threshold
    salient_items = [item FOR (item, s) IN salience_scores IF s > THRESHOLD]

    // Integrate into long-term (manifold deformation)
    FOR item IN salient_items:
        temporal_memory.long_term.manifold.deform(item, salience)

    // Strategic forgetting for low-salience items
    FOR item IN temporal_memory.short_term:
        IF item NOT IN salient_items:
            // Don't integrate - let it decay
            PASS

    // Clear short-term buffer
    temporal_memory.short_term.clear()

    // Decay low-salience regions in long-term
    temporal_memory.long_term.strategic_forget(DECAY_RATE)
```

### 3.3 Predictive Anticipation

```pseudocode
FUNCTION Anticipate(hints, temporal_memory):
    // Pre-compute likely future queries based on hints
    // This enables "predictive retrieval before queries are issued"

    predicted_queries = []

    FOR hint IN hints:
        SWITCH hint.type:
            CASE SequentialPattern:
                // If A then B pattern detected
                recent = temporal_memory.recent_queries()
                FOR pattern IN temporal_memory.sequential_patterns:
                    IF pattern.matches_prefix(recent):
                        predicted = pattern.next_likely_query()
                        predicted_queries.append(predicted)

            CASE TemporalCycle:
                // Time-of-day or periodic patterns
                current_phase = GetTemporalPhase(NOW())
                historical = temporal_memory.queries_at_phase(current_phase)
                predicted_queries.extend(historical.top_k(5))

            CASE CausalChain:
                // Causal dependencies predict next queries
                current_context = hint.current_context
                downstream = temporal_memory.causal_graph.downstream(current_context)
                FOR node IN downstream:
                    predicted_queries.append(QueryFor(node))

    // Pre-fetch and cache
    FOR query IN predicted_queries:
        cache_key = Hash(query)
        IF cache_key NOT IN temporal_memory.prefetch_cache:
            result = temporal_memory.long_term.search(query)
            temporal_memory.prefetch_cache[cache_key] = result
```

---

## 4. Federated Cognitive Mesh

### 4.1 Post-Quantum Federation Handshake

```pseudocode
FUNCTION JoinFederation(local_node, peer_address):
    // CRYSTALS-Kyber key exchange

    // Generate ephemeral keypair
    (local_public, local_secret) = Kyber.KeyGen()

    // Send public key to peer
    SendMessage(peer_address, FederationRequest(local_public))

    // Receive peer's encapsulated shared secret
    response = ReceiveMessage(peer_address)
    ciphertext = response.ciphertext

    // Decapsulate to get shared secret
    shared_secret = Kyber.Decapsulate(ciphertext, local_secret)

    // Derive session keys from shared secret
    (encrypt_key, mac_key) = DeriveKeys(shared_secret)

    // Establish encrypted channel
    channel = EncryptedChannel(peer_address, encrypt_key, mac_key)

    // Exchange capabilities and negotiate federation terms
    local_caps = local_node.capabilities()
    peer_caps = channel.exchange(local_caps)

    terms = NegotiateFederationTerms(local_caps, peer_caps)

    // Create federation token
    token = FederationToken(
        peer = peer_address,
        channel = channel,
        terms = terms,
        expires = NOW() + TOKEN_VALIDITY
    )

    RETURN token
```

### 4.2 Onion-Routed Query

```pseudocode
FUNCTION OnionQuery(query, destination, relay_nodes, local_keys):
    // Privacy-preserving query routing through onion network

    // Build onion layers (innermost to outermost)
    layers = [destination] + relay_nodes  // Reverse order for wrapping

    // Start with plaintext query
    current_payload = SerializeQuery(query)

    // Wrap in layers
    FOR node IN layers:
        // Encrypt with node's public key
        encrypted = AsymmetricEncrypt(current_payload, node.public_key)

        // Add routing header
        header = OnionHeader(
            next_hop = node.address,
            payload_type = "onion_layer"
        )

        current_payload = header + encrypted

    // Send to first relay
    first_relay = relay_nodes.last()
    SendMessage(first_relay, current_payload)

    // Receive response (also onion-wrapped)
    encrypted_response = ReceiveMessage(first_relay)

    // Unwrap response layers
    current_response = encrypted_response
    FOR node IN reverse(relay_nodes):
        current_response = AsymmetricDecrypt(current_response, local_keys.secret)

    // Final decryption with destination's response
    result = DeserializeResponse(current_response)

    RETURN result
```

### 4.3 CRDT Reconciliation

```pseudocode
FUNCTION ReconcileCRDT(responses, local_state):
    // Conflict-free merge of federated query results

    // Use G-Set CRDT for search results (grow-only set)
    merged_results = GSet()

    FOR response IN responses:
        FOR result IN response.results:
            // G-Set merge: union operation
            merged_results.add(result)

    // For rankings, use LWW-Register (last-writer-wins)
    ranking_map = LWWMap()

    FOR response IN responses:
        FOR (result_id, score, timestamp) IN response.rankings:
            ranking_map.set(result_id, score, timestamp)

    // Combine: results from G-Set, scores from LWW-Map
    final_results = []
    FOR result IN merged_results:
        score = ranking_map.get(result.id)
        final_results.append((result, score))

    // Sort by reconciled scores
    final_results.sort(by=score, descending=True)

    RETURN final_results
```

### 4.4 Byzantine Fault Tolerant Commit

```pseudocode
FUNCTION ByzantineCommit(update, federation):
    // PBFT-style consensus for state updates
    n = federation.node_count()
    f = (n - 1) / 3  // Maximum Byzantine faults tolerable
    threshold = 2*f + 1  // Required agreement

    // Phase 1: Pre-prepare (leader proposes)
    IF federation.is_leader():
        proposal = SignedProposal(update, sequence_number=NEXT_SEQ)
        Broadcast(federation.nodes, PrePrepare(proposal))

    // Phase 2: Prepare (nodes acknowledge receipt)
    pre_prepare = ReceivePrePrepare()
    IF ValidateProposal(pre_prepare):
        prepare_msg = Prepare(pre_prepare.digest, federation.local_id)
        Broadcast(federation.nodes, prepare_msg)

    // Collect prepare messages
    prepares = CollectMessages(type=Prepare, count=threshold)

    IF len(prepares) < threshold:
        RETURN CommitResult.InsufficientPrepares

    // Phase 3: Commit (nodes commit to proposal)
    commit_msg = Commit(pre_prepare.digest, federation.local_id)
    Broadcast(federation.nodes, commit_msg)

    // Collect commit messages
    commits = CollectMessages(type=Commit, count=threshold)

    IF len(commits) >= threshold:
        // Execute update
        federation.apply_update(update)
        proof = CommitProof(commits)
        RETURN CommitResult.Success(proof)
    ELSE:
        RETURN CommitResult.InsufficientCommits
```

---

## 5. Backend Abstraction

### 5.1 Backend Selection

```pseudocode
FUNCTION SelectBackend(requirements, available_backends):
    // Automatic backend selection based on requirements

    scored_backends = []

    FOR backend IN available_backends:
        score = 0.0

        // Evaluate against requirements
        IF requirements.latency_target:
            latency_score = 1.0 / backend.expected_latency
            score += W_LATENCY * latency_score

        IF requirements.energy_target:
            energy_score = 1.0 / backend.expected_energy
            score += W_ENERGY * energy_score

        IF requirements.accuracy_target:
            accuracy_score = backend.expected_accuracy
            score += W_ACCURACY * accuracy_score

        IF requirements.scale_target:
            scale_score = backend.max_scale / requirements.scale_target
            score += W_SCALE * min(scale_score, 1.0)

        // Check hard constraints
        IF requirements.wasm_required AND NOT backend.supports_wasm:
            CONTINUE

        IF requirements.post_quantum_required AND NOT backend.supports_pq:
            CONTINUE

        scored_backends.append((backend, score))

    // Select highest scoring backend
    best_backend = max(scored_backends, by=score)

    RETURN best_backend
```

### 5.2 Hybrid Execution

```pseudocode
FUNCTION HybridExecute(operation, backends):
    // Execute across multiple backends, combine results

    // Partition operation if possible
    partitions = PartitionOperation(operation)

    // Assign partitions to backends based on suitability
    assignments = []
    FOR partition IN partitions:
        best_backend = SelectBackendForPartition(partition, backends)
        assignments.append((partition, best_backend))

    // Execute in parallel
    futures = []
    FOR (partition, backend) IN assignments:
        future = backend.execute_async(partition)
        futures.append(future)

    // Await all results
    results = AwaitAll(futures)

    // Merge partition results
    merged = MergePartitionResults(results, operation.type)

    RETURN merged
```

---

## 6. Consciousness Metrics (Research)

### 6.1 Phi (Integrated Information) Approximation

```pseudocode
FUNCTION ApproximatePhi(substrate_region):
    // Compute integrated information (IIT-inspired)
    // Full Phi computation is intractable; this is an approximation

    // Step 1: Compute whole-system effective information
    whole_state = substrate_region.current_state()
    perturbed_states = []
    FOR _ IN 1..NUM_PERTURBATIONS:
        perturbed = ApplyRandomPerturbation(whole_state)
        evolved = substrate_region.evolve(perturbed)
        perturbed_states.append(evolved)

    whole_EI = MutualInformation(whole_state, perturbed_states)

    // Step 2: Find minimum information partition (MIP)
    partitions = GeneratePartitions(substrate_region)
    min_partition_EI = INFINITY

    FOR partition IN partitions:
        partition_EI = 0.0
        FOR part IN partition:
            part_state = part.current_state()
            part_perturbed = [ApplyRandomPerturbation(part_state) FOR _ IN 1..NUM_PERTURBATIONS]
            part_evolved = [part.evolve(p) FOR p IN part_perturbed]
            partition_EI += MutualInformation(part_state, part_evolved)

        IF partition_EI < min_partition_EI:
            min_partition_EI = partition_EI
            mip = partition

    // Step 3: Phi = whole - minimum partition
    phi = whole_EI - min_partition_EI

    RETURN max(phi, 0.0)  // Phi cannot be negative
```

---

## Summary

These pseudocode algorithms define the core computational patterns for the EXO-AI cognitive substrate:

| Component | Key Algorithm | Complexity |
|-----------|---------------|------------|
| Manifold Engine | Gradient descent retrieval | O(k × d × steps) |
| Hypergraph | Persistent homology | O(n³) worst case |
| Temporal Memory | Causal cone query | O(n × log n) |
| Federation | Byzantine consensus | O(n²) messages |
| Phi Metric | Partition enumeration | O(B(n)) Bell numbers |

Where:
- k = number of results
- d = embedding dimension
- n = number of entities/nodes
- steps = gradient descent iterations