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.

tests/settings-body.test.ts

@@ -77,6 +77,18 @@ describe("parseAgentSettingsBody", () => {
 		assert.equal(parseAgentSettingsBody({ search: { engine: 1 } }).ok, false);
 	});
 
+	it("graphTools: strict object subsection, enabled boolean when present — wave 7, 2026-09-23", () => {
+		const off = parseAgentSettingsBody({ graphTools: { enabled: false } });
+		assert.ok(off.ok);
+		assert.deepEqual(off.settings.graphTools, { enabled: false });
+		const bare = parseAgentSettingsBody({ graphTools: {} });
+		assert.ok(bare.ok);
+		assert.deepEqual(bare.settings.graphTools, {}, "explicit subsection with no key = the default ON");
+		assert.equal(parseAgentSettingsBody({ graphTools: "off" }).ok, false, "graphTools must be an object");
+		assert.equal(parseAgentSettingsBody({ graphTools: { enabled: "yes" } }).ok, false, "enabled must be a boolean");
+		assert.equal(parseAgentSettingsBody({ graphTools: null }).ok, false);
+	});
+
 	it("an empty {} agent section parses to {} (replace-whole clear)", () => {
 		const r = parseAgentSettingsBody({});
 		assert.ok(r.ok);