Author-once plan protocol: single mermaid plan_init + derived statuses + live quiz nodeId validation

- plan_init is now the ONLY plan tool: a mermaid 'graph TD' block parsed by a
  constrained-subset parser (mermaid-plan.ts) with line-precise errors; the
  seven mutation/tracking tools are gone by design (2026-09-03 design pass).
- Re-call plan_init = sanctioned wholesale rewrite; slugs are permanent.
- derivePlanStatuses (contracts/plan.ts): done = passed check tagged with a
  quiz nodeId; current = open check's node else first topo-ready node — the
  tracking the teacher no longer declares by hand.
- questionToolsFor(ctx) (tools.ts): the quiz schema chains a dynamic plan-
  nodeId validation against the LIVE record — an invalid nodeId is rejected
  at the call boundary and the teacher retries mid-turn, before any UI.
  Static questionTools stay validator-less for the default path.
- Prompts rewritten for mermaid authoring + derived position.
- Out-of-lane surgical touches (flagged for master review):
  src/core/question-core.ts (quizInputObject export + nodeId description),
  src/core/contracts/plan.ts (derivePlanStatuses + doc).

src/agent/prompts/30-phases.md

@@ -12,7 +12,7 @@ The moment you call `plan_init`, a quiet divider appears in the learner's transc
 
 - **Teach first, check second — in that order, in the transcript.** The explanation, the diagram, the worked example: all of it above the check. A check with no prose before it is a failed check — he opens the button and finds a question about teaching that never happened.
 - **Finish the thought before you fire.** Never call a check mid-explanation. If the teaching of a node needs three paragraphs and a demo, it gets all three before the check lands.
-- **One node, one check.** `plan_set_current` when you start teaching the node, teach it completely, then check it (`nodeId` set, so the outcome lands on the graph).
+- **One node, one check.** Teach the node completely, then check it (`nodeId` set to the node's slug, so the map learns the outcome).
 - **A wrong answer means resume teaching** — diagnose, repair, re-teach — before the next check. The button is a gate, not a quiz-show buzzer.
 
 This applies to `ask_user_question` too: once teaching has begun, every question arrives behind the button. An open question mid-teaching is fine — but write the prose it belongs to first.