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). 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.

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 a mallory-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 }].