Graph

graph@1 defines the relationship-oriented execution semantics of the Forge Pool execution platform.

Graph workloads model computation over connected structures, where relationships between entities are as important as the entities themselves.

Like every primitive family, graph@1 executes through the same canonical execution contract, deterministic execution doctrine, replay model, and verification framework.

Purpose

Graph execution is designed for workloads where computation depends upon relationships, connectivity, traversal, or structural propagation.

Representative domains include:

counterparty contagion
cascading failures
dependency analysis
network propagation
route evaluation
relationship scoring
connected component discovery

The primitive family defines graph execution semantics.

Execution profiles define the domain-specific graph model.

Operation Identity

Graph workloads are selected through the canonical execution contract.

json

{
  "op": {
    "name": "graph",
    "version": 1,
    "profile": "finance.credit.cascading_failure_graph.v1"
  }
}

Graph execution is submitted through the canonical public endpoint.

http

POST /api/v0/ops/execute

No graph-specific execution endpoint exists.

Execution Characteristics

Graph execution is characterized by:

relationship-aware computation
distributed graph traversal
dependency propagation
execution-unit decomposition
deterministic graph reduction
replay-compatible execution evidence

Execution topology may vary.

Graph semantics remain invariant.

Representative Profiles

Representative graph@1 profiles include:

finance.credit.cascading_failure_graph.v1
insurance.counterparty.contagion.v1

Additional profiles may extend the graph family without modifying the public execution contract.

Execution Parameters

Graph profiles typically define parameters such as:

node sets
edge definitions
traversal constraints
propagation rules
scoring models
termination conditions
artifact preferences

Each execution profile defines its own parameter schema while inheriting the shared graph@1 execution semantics.

Deterministic Execution

Graph execution remains deterministic under equivalent execution contracts.

Equivalent workloads must preserve equivalent:

traversal behavior
propagation semantics
graph reduction
replay metadata
execution evidence

Infrastructure topology, execution routing, runtime placement, and execution timing must not alter computational meaning.

Reduction Semantics

Distributed graph execution produces intermediate graph states that are reduced into one canonical execution result.

Reduction may produce:

propagated graph states
dependency summaries
relationship scores
traversal statistics
influence maps
workload-specific graph outputs

Reduction remains deterministic, versioned, and replay-compatible.

Execution Evidence

Successful graph execution may produce:

execution metrics
traversal summaries
propagation statistics
execution-unit summaries
artifact references
replay metadata
verification outcomes

Execution evidence forms part of the canonical execution result.

Verification

Graph verification confirms that relationship propagation and reduction followed the declared execution contract.

Verification may inspect:

traversal consistency
propagation determinism
reduction behavior
execution evidence
replay metadata
repeated execution equivalence

Verification validates graph execution semantics rather than runtime implementation.

Replay

Replay preserves the computational meaning of graph execution.

Replay depends upon:

operation identity
execution profile
canonical parameters
deterministic traversal
reduction semantics
execution evidence

Replay validates that equivalent graph execution contracts preserve equivalent relationship behavior.

See:

Relationship to Other Primitive Families

Graph is one execution family within the broader execution taxonomy.

Unlike Monte Carlo, Search, Ensemble, or Media, the Graph family specializes in relationship-oriented computation while inheriting the same execution doctrine.

Execution semantics remain consistent across all primitive families.

Relationship to Examples

Concrete Graph capabilities are documented in the Examples section.

Start with:

Examples demonstrate workload behavior.

This document defines primitive-family execution semantics.

Continue with:

Continue in Forge Studio

To explore Graph execution interactively:

Browse Graph capabilities in Capability Explorer
Inspect Graph execution blocks in Block Registry
Execute representative graph workloads
Compare execution evidence across repeated runs
Validate replay metadata and deterministic relationship propagation

Trust should be established through independent verification rather than documentation alone.

Final Note

Graph is not a graph database or a specialized graph service.

It is the relationship-oriented execution family implemented through the same canonical execution contract as every other Forge Pool primitive.

By separating graph semantics from execution infrastructure, Forge Pool enables distributed relationship-oriented workloads to inherit deterministic execution, replay compatibility, execution evidence, and verification guarantees while preserving one stable public API.

Graph ​

Purpose ​

Operation Identity ​

Execution Characteristics ​

Representative Profiles ​

Execution Parameters ​

Deterministic Execution ​

Reduction Semantics ​

Execution Evidence ​

Verification ​

Replay ​

Relationship to Other Primitive Families ​

Relationship to Examples ​

Related Documentation ​

Continue in Forge Studio ​

Final Note ​