Birth-session clustering + the prober graph-tools data seam (wave 7 chunk A)

Embeddings are dying (chunk B removes the machinery); the clusters they
used to carry become the session that created them — derived on read.

- New src/core/session-clusters.ts: birthSessionPartition groups merged
  nodes by their FIRST SURVIVING provenance point's chatId (owner-locked
  2026-09-23). Deletion is self-healing by construction: stripped-birth
  survivors re-attribute to their earliest remaining contributor, and
  empty-provenance nodes stay unclustered. Notes imports are birth-sessions
  too (owner ruling) — their label is the file path.
- graphSnapshot: clusters = the birth partition filtered >= MIN_CLUSTER_SIZE
  (the hull presentation rule), id = session id, label = session name (chat
  title / file path; a deleted record renders unlabeled). The persisted
  cluster-labelings join dies; no LLM naming pass needed anymore.
- settleGraphLayout derives the same partition from readNodes — drops its
  readEmbeddings dep. One cluster concept everywhere.
- Prober data seam (core/graph.ts, pure ports-driven like the snapshot):
  graphSessionIndex (every birth session: id, name, chat|file kind,
  createdAt/updatedAt, birth-proposition count, recency-ordered) and
  graphSessionPropositions (a session's birth propositions with the
  extractor's latest understanding level and THAT event's own timestamp —
  owner ruling: quiz outcomes are ledger evidence, they never move the
  evaluation date). Teacher's tool handlers consume these in-process.
- New agent.graphTools subsection { enabled?: boolean } (owner ruling:
  the toggle gates prober tool REGISTRATION — agent capability, agent
  section, its own subsection, NOT the tool-toggles map; absent = ON).
  Lenient sanitizer, strict settings-body parser, passthrough resolution,
  and graphToolsEnabled(effective) = graph.enabled && toggle for Teacher's
  registry wiring.

Gates: tsc clean, eslint clean, 923/923 tests, next build compiles.
Live-verified on the worktree dev data: 10 nodes → 2 clusters labeled
with their chat titles; session index + propositions carry levels and
their own timestamps.

src/server/settings-body.ts

@@ -195,6 +195,18 @@ export function parseAgentSettingsBody(body: unknown): SettingsBodyResult<AgentS
 			settings.search = { engine: search.engine };
 		}
 	}
+	// Prober graph tools (wave 7, owner ruling 2026-09-23): an agent-section
+	// subsection, not a tool-toggles key — the mechanism is agent capability
+	// (tool registration), the subject is the graph. Strict write side:
+	// object shape only; `enabled` boolean when present. Absent = ON.
+	if (raw.graphTools !== undefined) {
+		const graphTools = asRecord(raw.graphTools);
+		if (!graphTools) return { ok: false, error: "graphTools must be an object" };
+		if (graphTools.enabled !== undefined && typeof graphTools.enabled !== "boolean") {
+			return { ok: false, error: "graphTools.enabled must be a boolean" };
+		}
+		settings.graphTools = graphTools.enabled === undefined ? {} : { enabled: graphTools.enabled };
+	}
 	return { ok: true, settings };
 }