1. Root Identification: Start with a root ACDC (typically issued by a trust anchor)
2. Edge Resolution: Parse the edge section to identify child ACDCs via their SAIDs
3. SAID Verification: Verify each SAID matches the cryptographic digest of the referenced ACDC
4. Signature Validation: Validate the issuer's signature on each ACDC in the branch
5. Schema Compliance: Ensure each ACDC conforms to its declared schema

Cryptographic Foundation

Branches maintain cryptographic integrity through multiple mechanisms:

SAID-Based Linking

Each edge reference uses a Self-Addressing Identifier (SAID) computed as:

SAID = Blake3-256(canonical_serialization(ACDC))

This creates tamper-evident links where any modification to a referenced ACDC invalidates the SAID, breaking the branch integrity.

Signature Chains

Each ACDC in a branch is signed by its issuer's AID (Autonomic Identifier), creating a signature chain:

Branch_Signature_Chain = {Sig_AID₀(ACDC₀), Sig_AID₁(ACDC₁), ..., Sig_AIDₙ(ACDCₙ)}

Hash Tree Properties

Branches form Merkle-tree-like structures where:

• Leaf nodes contain actual data attributes
• Intermediate nodes contain processing metadata
• Root nodes establish authority and trust basis
• Any branch can be verified independently without requiring the entire tree

Implementation Specifications

Branch Validation Algorithm

def validate_branch(root_acdc: ACDC, target_said: str) -> ValidationResult:
    """
    Validates a complete branch from root to target ACDC
    """
    visited = set()
    stack = [(root_acdc, [])]
    
    while stack:
        current_acdc, path = stack.pop()
        
        # Prevent cycles
        if current_acdc.said in visited:
            continue
        visited.add(current_acdc.said)
        
        # Validate current ACDC
        if not validate_acdc_integrity(current_acdc):
            return ValidationResult.INVALID_ACDC
        
        # Check if we've reached target
        if current_acdc.said == target_said:
            return ValidationResult.VALID_BRANCH
        
        # Add children to stack
        for edge_said in current_acdc.edges:
            child_acdc = resolve_acdc(edge_said)
            if child_acdc:
                stack.append((child_acdc, path + [current_acdc.said]))
    
    return ValidationResult.TARGET_NOT_FOUND

Performance Characteristics

Computational Complexity

• Branch Validation: O(n) where n is the number of ACDCs in the branch
• SAID Computation: O(m) where m is the size of the ACDC in bytes
• Signature Verification: O(1) for Ed25519 signatures
• Graph Traversal: O(V + E) for complete graph validation

Memory Requirements

• ACDC Storage: ~2-10KB per ACDC depending on attribute complexity
• SAID Cache: 44 bytes per SAID (Base64 encoded Blake3-256 hash)
• Signature Storage: 88 bytes per Ed25519 signature in CESR encoding

Branch Discovery and Resolution

Branch discovery utilizes Out-of-Band Introduction (OOBI) mechanisms:

class BranchResolver:
    def __init__(self, oobi_resolver: OOBIResolver):
        self.oobi_resolver = oobi_resolver
        self.acdc_cache = {}
    
    async def resolve_branch(self, root_said: str) -> List[ACDC]:
        """
        Resolves complete branch starting from root SAID
        """
        branch = []
        current_said = root_said
        
        while current_said:
            # Check cache first
            if current_said in self.acdc_cache:
                acdc = self.acdc_cache[current_said]
            else:
                # Resolve via OOBI
                acdc = await self.oobi_resolver.resolve_acdc(current_said)
                self.acdc_cache[current_said] = acdc
            
            branch.append(acdc)
            
            # Get next ACDC in branch (if any)
            current_said = self.get_next_branch_said(acdc)
        
        return branch

Technical Relationships

Integration with KERI Infrastructure

Branches integrate deeply with KERI's key management infrastructure:

1. AID Authority: Each ACDC issuer must have a valid AID with current key state
2. KEL Verification: Issuer signatures are validated against current KEL state
3. Witness Confirmation: High-value branches may require witness receipts
4. Watcher Validation: Watchers can monitor branch integrity across the network

CESR Encoding Integration

Branches utilize Composable Event Streaming Representation (CESR) for efficient serialization:

# CESR-encoded branch reference
-FABEAdXt3gIXOf2BBWNHdSXCJnFJL5OuQPyM5K0neuniccM0AAAAAAAAAAAAAAAAAAAAAAAEFH3dCdoFOLe71iheqcywJcnjtJtQIYPvAu6DZIl3MOA

Where:

• -FAB: Count code for ACDC with attachments
• EAdXt...: Parent ACDC SAID
• 0AAA...: Padding for alignment
• EFH3...: Child ACDC SAID in edge section

Registry Integration

Branches can integrate with Public Transaction Event Logs (PTEL) for:

• Issuance Tracking: Recording when ACDCs are issued
• Revocation Status: Marking ACDCs as revoked
• Status Updates: Publishing branch status changes

Advanced Branch Patterns

Multi-Parent Branches

ACDCs can reference multiple parent ACDCs, creating diamond-shaped branch structures:

{
  "e": {
    "d": "EMultiParentEdgeSection",
    "parentA": {
      "n": "EParentA_SAID",
      "s": "EParentA_Schema"
    },
    "parentB": {
      "n": "EParentB_SAID", 
      "s": "EParentB_Schema"
    }
  }
}

Conditional Branches

Branches can include conditional logic through rule sections:

{
  "r": {
    "d": "ERuleSection_SAID",
    "conditionalEdge": {
      "condition": "$.a.creditScore > 700",
      "trueBranch": "EHighCreditBranch_SAID",
      "falseBranch": "ELowCreditBranch_SAID"
    }
  }
}

Temporal Branches

Time-based branching for credential lifecycle management:

{
  "e": {
    "d": "ETemporalEdge_SAID",
    "validFrom": "2024-01-01T00:00:00Z",
    "validUntil": "2024-12-31T23:59:59Z",
    "renewalBranch": "ERenewalACDC_SAID",
    "expirationBranch": "EExpirationACDC_SAID"
  }
}

Performance Analysis

Branch Validation Benchmarks

Optimization Strategies

Parallel Validation

async def validate_branch_parallel(branch_saids: List[str]) -> bool:
    """
    Validates multiple branch segments in parallel
    """
    tasks = [validate_acdc_async(said) for said in branch_saids]
    results = await asyncio.gather(*tasks)
    return all(results)

Caching Strategy

class BranchCache:
    def __init__(self, max_size: int = 10000, ttl: int = 3600):
        self.cache = TTLCache(maxsize=max_size, ttl=ttl)
        self.validation_cache = {}
    
    def get_validated_branch(self, root_said: str) -> Optional[List[ACDC]]:
        cache_key = f"branch:{root_said}"
        return self.cache.get(cache_key)

Edge Cases & Error Handling

Circular Reference Detection

def detect_cycles(root_acdc: ACDC) -> bool:
    """
    Detects circular references in branch structure
    """
    visited = set()
    rec_stack = set()
    
    def dfs(acdc_said: str) -> bool:
        if acdc_said in rec_stack:
            return True  # Cycle detected
        if acdc_said in visited:
            return False
        
        visited.add(acdc_said)
        rec_stack.add(acdc_said)
        
        acdc = resolve_acdc(acdc_said)
        for edge_said in acdc.edges:
            if dfs(edge_said):
                return True
        
        rec_stack.remove(acdc_said)
        return False
    
    return dfs(root_acdc.said)

Branch Integrity Failures

1. SAID Mismatch: When computed SAID doesn't match edge reference
2. Signature Failure: Invalid issuer signature on ACDC
3. Schema Violation: ACDC doesn't conform to declared schema
4. AID Resolution Failure: Cannot resolve issuer AID or verify key state
5. Network Timeout: OOBI resolution fails for branch components

Recovery Mechanisms

class BranchRecovery:
    async def recover_broken_branch(self, branch_saids: List[str]) -> List[ACDC]:
        recovered = []
        
        for said in branch_saids:
            try:
                acdc = await self.resolve_with_retry(said, max_retries=3)
                if self.validate_acdc(acdc):
                    recovered.append(acdc)
                else:
                    # Attempt alternative resolution paths
                    acdc = await self.resolve_via_backup_witnesses(said)
                    if acdc:
                        recovered.append(acdc)
            except Exception as e:
                logger.warning(f"Failed to recover ACDC {said}: {e}")
                # Continue with partial branch
        
        return recovered

Standards & Specifications

ACDC Specification Compliance

Branches must comply with ACDC specification requirements:

• Field Ordering: Top-level fields must follow canonical order [v, d, u, i, rd, s, a, A, e, r]
• SAID Computation: Must use Blake3-256 for content addressing
• CESR Encoding: All cryptographic primitives must use CESR format
• Schema Validation: Must validate against JSON Schema 2020-12

Version Compatibility

Production Considerations

Deployment Architecture

# Branch validation service deployment
apiVersion: apps/v1
kind: Deployment
metadata:
  name: branch-validator
spec:
  replicas: 3
  template:
    spec:
      containers:
      - name: validator
        image: keri/branch-validator:v1.2
        resources:
          requests:
            memory: "256Mi"
            cpu: "100m"
          limits:
            memory: "512Mi"
            cpu: "500m"
        env:
        - name: CACHE_SIZE
          value: "10000"
        - name: VALIDATION_TIMEOUT
          value: "30s"

Monitoring and Observability

# Branch validation metrics
from prometheus_client import Counter, Histogram, Gauge

branch_validations = Counter('branch_validations_total', 'Total branch validations')
branch_validation_duration = Histogram('branch_validation_duration_seconds', 'Branch validation duration')
branch_cache_hits = Counter('branch_cache_hits_total', 'Branch cache hits')
branch_depth_gauge = Gauge('branch_max_depth', 'Maximum branch depth processed')

@branch_validation_duration.time()
def validate_branch_with_metrics(branch: List[ACDC]) -> bool:
    branch_validations.inc()
    branch_depth_gauge.set(len(branch))
    
    result = validate_branch_logic(branch)
    
    if result:
        branch_cache_hits.inc()
    
    return result

Operational Procedures

Branch Health Monitoring

#!/bin/bash
# Branch health check script

BRANCH_ENDPOINT="https://api.example.com/branches"
ALERT_THRESHOLD=5000  # ms

for branch_id in $(cat critical_branches.txt); do
    start_time=$(date +%s%3N)
    
    response=$(curl -s -w "%{http_code}" "$BRANCH_ENDPOINT/$branch_id/validate")
    http_code=${response: -3}
    
    end_time=$(date +%s%3N)
    duration=$((end_time - start_time))
    
    if [ "$http_code" != "200" ] || [ "$duration" -gt "$ALERT_THRESHOLD" ]; then
        echo "ALERT: Branch $branch_id validation failed or slow (${duration}ms)"
        # Send alert to monitoring system
    fi
done

Branch Cleanup Procedures

class BranchMaintenance:
    async def cleanup_expired_branches(self):
        """
        Removes expired branches from cache and storage
        """
        current_time = datetime.utcnow()
        
        for branch_id, metadata in self.branch_registry.items():
            if metadata.expires_at < current_time:
                await self.remove_branch(branch_id)
                logger.info(f"Cleaned up expired branch {branch_id}")
    
    async def validate_branch_integrity_batch(self, batch_size: int = 100):
        """
        Batch validation of stored branches for integrity
        """
        branch_ids = list(self.branch_registry.keys())
        
        for i in range(0, len(branch_ids), batch_size):
            batch = branch_ids[i:i + batch_size]
            
            tasks = [self.validate_branch_integrity(bid) for bid in batch]
            results = await asyncio.gather(*tasks, return_exceptions=True)
            
            for branch_id, result in zip(batch, results):
                if isinstance(result, Exception):
                    logger.error(f"Branch {branch_id} integrity check failed: {result}")
                    await self.quarantine_branch(branch_id)