feat: probe/teach agent split — explicit phase markers, position-only plan map

Diagnosis (2026-09-11 user testing, minimal-effort GLM): sessions stuck on
'plan' forever. Two causes: (1) the three-phase view read the stored tree's
currentNodeId, which nothing ever writes post author-once (2026-09-03) — a
structural dead seam; (2) the teacher stochastically left quiz.nodeId
untagged, and done-by-quiz-result semantics would have falsely completed
nodes anyway.

The redesign (docs/probe-teach-split.md) abolishes derived occupancy in
favor of explicit events:

- Two agents over one transcript: createProberAgent (quiz without a
  nodeId field, ask, probe_done) and createTeacherAgent (full toolset,
  plan_init onward). The chat-handler construction branch keys on a
  probe_done part in the transcript. MODELS.prober added.
- probe_done: server-side seam tool — carries the learner assessment
  (strands + free-form edge read), refuses while a question is open or
  the probe is already concluded, and queues a handoff steer through the
  generalized wake pipeline (steers now dedupe by id, not jobId; job
  finalization only for job steers). The teacher auto-wakes and authors
  the plan; the learner sees the assessment via the probe-done card.
- phases: probe ends at a concluded probe_done, plan ends at a
  successful plan_init — strictly sequential, no skipping, no legacy
  compatibility (data wiped at the pivot per doctrine).
- Plan map = position, not completion: derivePlanStatuses reads only
  tagged quiz CALLS (state/outcome feed nothing); current = latest
  tagged node with consecutive duplicates collapsed, visited = earlier
  distinct stays (a revisit stays in both — current wins at render).
  PlanTree is structure-only; currentNodeId/doneNodeIds and the dead
  mutation helpers are gone. No fallback current.
- Prompts split per agent (prompts/prober/, prompts/teacher/ over the
  trimmed shared base); graph-context injection removed entirely
  (shelved, docs/probe-teach-split.md §5); knowledge-graph context no
  longer reaches either agent.
- Plan blocks are full-only snapshots at plan_init (neighborhood
  machinery retired; the persistent DAG window is the future UI wave);
  usage capture unchanged.

Gates: tsc clean, 294/294 tests (phases/plan-tree/plan-blocks/question-
tools rewritten to the new semantics; probe-done + handoff-wake tests
added), lint, build. Live GLM smoke PASS: prober concluded with an honest
assessment, teacher auto-woke, authored a 10-node plan with the block
attached, then tagged checks on slope-instinct → secant derived current/
visited exactly as designed; grading honest both ways (driver off-by-one
proved a wrong answer grades false).

src/core/contracts/jobs.ts

@@ -242,7 +242,7 @@ export interface AbortSteerMessage extends UIMessage {
 }
 
 /** Anything the wake pipeline may queue and deliver. */
-export type SteerMessage = SubagentSteerMessage | AbortSteerMessage;
+export type SteerMessage = SubagentSteerMessage | AbortSteerMessage | ProbeHandoffSteerMessage;
 
 /** Whether a result is the failure shape (html/svg empty, failure brief). */
 export function isSubagentFailure(kind: JobKind, result: ResearchResult | DemoResult | VisualResult): boolean {
@@ -326,10 +326,39 @@ function abortText(kind: JobKind): string {
 	return "The figure job was aborted by the learner — no figure is coming. Acknowledge it in one line and teach without it (a re-dispatch is fine if the learner wants it).";
 }
 
-/** True when the transcript already carries this job's steer (idempotent delivery). */
-export function steerDelivered(messages: UIMessage[], jobId: string): boolean {
-	return messages.some(
-		(m) => (m.metadata as { subagentResult?: { jobId?: string } } | undefined)?.subagentResult?.jobId === jobId,
-	);
+// ─── the probe handoff steer (the probe→teach split, docs/probe-teach-split.md §2) ──
+//
+// probe_done's execute queues this through the same wake pipeline; the
+// pump fires it once the prober's turn ends (gates + grace). It carries no
+// artifact — the assessment it references is durable in the transcript as
+// the probe_done tool part. Deterministic id per chat: exactly one
+// handoff, idempotent re-delivery.
+
+export interface ProbeHandoffSteerMessage extends UIMessage {
+	id: `steer_probe_${string}`;
+	role: "user";
+	metadata: { probeHandoff: { chatId: string } };
+	parts: [{ type: "text"; text: string }];
+}
+
+export function buildProbeHandoffSteer(chatId: string): ProbeHandoffSteerMessage {
+	return {
+		id: `steer_probe_${chatId}`,
+		role: "user",
+		metadata: { probeHandoff: { chatId } },
+		parts: [
+			{
+				type: "text",
+				text: "The probe is concluded — the learner assessment is recorded. Author the session's plan map now (call plan_init) and present it, then begin teaching.",
+			},
+		],
+	};
+}
+
+/** True when the transcript already carries this steer — idempotent
+ *  delivery for ANY steer kind: every steer id is deterministic per its
+ *  event (steer_<jobId> for jobs, steer_probe_<chatId> for the handoff). */
+export function steerDelivered(messages: UIMessage[], steerId: string): boolean {
+	return messages.some((m) => m.id === steerId);
 }