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/core/layout-settle.ts

@@ -1,5 +1,6 @@
-import type { EmbeddingsLedger, GraphEdge, GraphNode } from "./contracts.ts";
+import type { GraphEdge, GraphNode } from "./contracts.ts";
 import { incrementalLayout } from "./layout.ts";
+import { birthSessionPartition } from "./session-clusters.ts";
 import type { Position } from "./contracts.ts";
 
 /**
@@ -11,17 +12,16 @@ import type { Position } from "./contracts.ts";
  * finish before the next /api/graph fetch reflects the change.
  *
  * SPLIT FROM layout.ts deliberately (2026-09-13): layout.ts is in the
- * browser barrel, and the settle needs the Louvain partition for the
- * cluster centroid pull — the heavy deps must not ship in the client
- * bundle. Server code imports this module DIRECTLY; it is never
- * re-exported through src/core/index.ts.
+ * browser barrel, and the settle needs the cluster partition for the
+ * cluster centroid pull — this module must not ship in the client bundle.
+ * Server code imports it DIRECTLY; it is never re-exported through
+ * src/core/index.ts.
  */
 export function settleGraphLayout(graphStore: {
 	readNodes(): GraphNode[];
 	readEdges(): GraphEdge[];
 	readPositions(): Record<string, Position>;
 	writePositions(positions: Record<string, Position>): void;
-	readEmbeddings(): EmbeddingsLedger;
 }): void {
 	const nodes = graphStore.readNodes();
 	if (nodes.length === 0) return;
@@ -34,11 +34,12 @@ export function settleGraphLayout(graphStore: {
 	});
 	const edges = graphStore.readEdges();
 	const previous = new Map(Object.entries(graphStore.readPositions()));
-	// The cluster partition for the centroid pull: the SAME persisted
-	// semantic topics the snapshot renders (computed by the embedder
-	// once per batch, stored in the embedding ledger) — one cluster
-	// concept everywhere.
-	const communities = graphStore.readEmbeddings().clusters;
+	// The cluster partition for the centroid pull: the SAME birth-session
+	// partition the snapshot renders (derived from provenance on read —
+	// core/session-clusters.ts, wave 7) — one cluster concept everywhere.
+	// The unique list is the deduped set the partition needs (lines may
+	// repeat an id — first defines).
+	const communities = birthSessionPartition(unique);
 	const next = incrementalLayout(unique, edges, previous, { clusters: communities });
 	graphStore.writePositions(Object.fromEntries(next));
 }