Formal Verification & Topological Deficit

Tools

`measure_betti`

Compute the first Betti number (beta_1) of a directed acyclic graph. beta_1 = edges - nodes + connected_components. A beta_1 of 0 means the graph is a forest (tree per component). Positive beta_1 indi...

`topological_deficit`

Compute the topological deficit between a system's actual first Betti number and the problem's natural (minimal) Betti number. Delta_beta = beta_1_star - beta_1. A zero deficit means the topology is e...

`verify_fold`

Verify a fold operation against the paper's axioms. A fold merges N inputs into one output, erasing N-1 distinguishable paths. Checks conservation (nothing created or destroyed), irreversibility (info...

`dag_analysis`

Analyze a directed acyclic graph for fork/race/fold/vent structure as defined in "Being Irreversible". Identifies fork points (out-degree > 1, where computation splits), fold points (in-degree > 1, wh...

`pipeline_invariants`

Check a pipeline description against the invariants from "Being Irreversible": (1) beta_1 >= 0 (topological non-negativity), (2) vents <= folds (you cannot vent more information than you fold), (3) ev...

Discovery Endpoints

/llms.txt — LLM-readable summary
/llms-full.txt — Full reference with schemas
/skills — Skill definitions
/agents.json — Agent manifest
/.well-known/mcp.json — MCP discovery
/.well-known/agent-card.json — Agent card
/.well-known/openapi.json — OpenAPI 3.1
/.well-known/security.txt — Security contact
/health — Health check

Paper Reference

From "Being Irreversible" by Taylor William Buley.
LEDGER sections: Foundation: Fork/Race/Fold Axioms, Covering Space & Topological Deficit
Result 1: Computational Topology
Read the paper at Wallington Lab