Detect and reason through circular dependencies (cycles) in knowledge.
kappa is the cycle-complexity invariant — it measures how entangled the knowledge is:
kappa = 0 — acyclic DAG, no cycles. Safe for fast retrieval.
kappa = 1 — simple cycle (A->B->C->A). Deliberation may help for high-stakes decisions.
kappa = 2+ — nested/overlapping cycles. Deliberation strongly recommended.
SCCs (Strongly Connected Components) are maximal cyclic clusters — groups of nodes where every node can reach every other node through directed edges.
Fault-line edges are the weakest links in a cycle — the assumptions most likely to be wrong. Examining these first is the fastest path to resolving contradictions.
Question to deliberate: $ARGUMENTS
Read-only diagnostic — understand the structure:
route(action: "topology", query: "<topic>")Parameters:
node_ids (optional) — explicit array of node IDs to analyze
query (optional) — retrieve nodes by query, then analyze
Neither — analyzes full graph
If both node_ids and query are provided, node_ids takes precedence.
Response fields:
routing — "fast" or "deliberate"
max_kappa — highest kappa value found
sccs — array of strongly connected components, each with its own routing and kappa
fault_line_edges — weakest edges in cycles (examine these first)
deliberation_budget — max_iterations and focus_edges to guide deliberation effort
recommendation — human-readable guidance
selection — how nodes were resolved (explicit/query/full_graph)
approximate — whether analysis used approximation for large graphs
Reason through cyclic knowledge and optionally persist conclusions:
route(action: "deliberate",
query: "Should we use approach A or B given the conflicting evidence?",
node_ids: ["<node1>", "<node2>"],
write_back: true
)Response fields:
conclusions — array of resolved conclusions, each with source_scc_id, source_kappa, fault_lines_examined
deliberation.converged — whether deliberation reached stable conclusions
deliberation.iterations_used — how many reasoning passes were needed
deliberation.topology_change — kappa_before, kappa_after, new_nodes_created
write_backwrite_back: true — crystallizes conclusions as new nodes. Use when you've reached a resolution you want to persist (reduces kappa for future retrievals).
write_back: false — reasoning only, no graph changes. Use for exploration or when you're not confident in the conclusion yet.
Detect — retrieve(action: "context", ...) returns topology.routing: "deliberate"
Diagnose — route(action: "topology", query: "...") for detailed cycle info and fault-lines
Examine fault-lines — inspect the weakest edges identified in step 2
Deliberate — route(action: "deliberate", query: "...", write_back: true) to reason through and resolve
Verify — re-run route(action: "topology", ...) to confirm kappa decreased after resolution
When routing: "fast" — normal retrieval is sufficient
For low-stakes decisions — deliberation has a cost
When there are no cycles (kappa = 0) — nothing to deliberate about
Over-deliberation is an anti-pattern — only deliberate when routing recommends it or you suspect contradictions