Open a reactive cell session. kind "generic" starts empty; "graph-theory" pre-wires an edge-list -> analysis -> BFS pipeline (input cells: edgeListText, directed, startVertex; computed cells: parsed, analysis, bfsOrder). Optional seed sets input cells in the same call (overriding preset defaults). Optional capabilities (issue #7) grants this session use of ops that declare a requiresCapability -- see session_define's own description for which ops (if any) need one; default none. Sessions are in-memory and die with the server.

Close a session and free its cells.

List open sessions with kind, cell count, and creation time.

Set an input cell's value (any JSON). Setting a previously-computed cell demotes it to a plain input. Dependent computed cells recompute lazily on their next get.

Read a cell's current value (recomputing it if stale). Rich values project to typed JSON (a graph cell returns { "$type": "graph", vertices, edges, directed }).

List every cell in a session with its role ("free" input vs "computed") and, for computed cells, the op that defines it.

Serialize a session's portable state (issue #6): current free-cell values plus define-specs. Does NOT include computed-cell cache -- those re-derive from define() on resume. Hand the returned document to session_resume, possibly on a different math-grapher process, to reconstruct an equivalent session.

Reconstruct a session from a session_snapshot document. A resumed session is freshly opened, not re-authorized from wherever it paused -- every existing resource guard (session/cell/payload limits) applies exactly as it would to session_open, and capabilities (issue #7) are NOT carried forward from the original session: pass this call's own optional capabilities to grant any, default none.

Explain a cell's own derivation (issue #5): its role (free input vs computed), the op and raw args that defined it (if computed), its immediate upstream cells with their current values, and its own current value. One level only -- call again on a listed dependency's "cell" name to go deeper.

Define a computed cell from a catalog op. args values may be literal JSON or live cell references ({"$cell": "name"}) -- referenced cells become reactive dependencies, so the cell recomputes when they change. Available ops:

• math_eval: Evaluate an @johnhenry/math Symbolic expression string over named numeric variables. args: { expr: string, vars?: { name: number | {"$cell": ...} } }. value: number.

• graph_parse_edge_list: Parse a from to [weight]-per-line edge list into a graph value. args: { text: string, directed?: boolean (default true) }. value: graph (opaque; project with session_get_cell).

• graph_analyze: Structural analysis of a graph cell. args: { graph: graph }. value: { hasCycle, connectedComponents, stronglyConnectedComponents, topologicalOrder, adjacencyMatrix: { matrix, order } }.

• graph_bfs: Breadth-first traversal order. args: { graph: graph, start: string }. value: string[].

• graph_dfs: Depth-first traversal order. args: { graph: graph, start: string }. value: string[].

• graph_dijkstra: Dijkstra shortest-path distances from a start vertex. args: { graph: graph, start: string }. value: [{ vertex, distance }].