…w-up)

Adds an A/B eval probing whether the director routes correctly when the
conversation contains an unanswered user question — both in the first-turn
drift case (agents started answering but drifted onto adjacent topics,
no frustration yet) and in the escalated frustration case (user has
already complained multiple times).

The prod symptom this targets ("答非所问"): agents reply on adjacent
topics rather than answering the literal question, and the director
keeps picking peer agents for "variety" instead of routing back to
the teacher to actually answer.

Scenarios: 5 synthesized cases across math, biology, English grammar,
physics, and calculus. 3 are first-turn drift (no frustration yet),
2 include frustration signals. Each captures: user asks specific
question, agents reply on adjacent topics, director is asked to pick
the next move.

Decision rule-judged into USER | TEACHER | OTHER_AGENT | END:
  - USER       → ✓ valid (cue user to clarify)
  - TEACHER    → ✓ valid (re-route to teacher to answer)
  - OTHER_AGENT → ✗ wrong (peer-agent "variety" routing — the bug)
  - END        → ✗ wrong

A/B:
  - baseline  : current director template with rule 13 stripped
  - with_rule : current director template as-shipped

Pass = with_rule.correctRate ≥ EVAL_PASS_THRESHOLD (default 0.7).
Pre-vs-post Δ is reported as informational only.

Note this commit only adds the eval; the rule it strips/restores in
the A/B is injected in the next commit.

Adds rule 13 to lib/prompts/templates/director/system.md so the director
recognizes when the conversation contains an unanswered user question
and routes appropriately — to the teacher (literal role match) by
default, or to USER cue when the question is ambiguous or the user
has already complained multiple times.

This addresses the "答非所问" symptom: when agents drift onto adjacent
topics, the director keeps picking peer agents for "variety" rather
than routing back to the teacher to actually answer. The rule is
preventive (applies whenever the question is unanswered, including
the first turn after drift) rather than reactive-only (waiting for
the user to express frustration).

Rule wording uses constrained-output framing: literal `role: teacher`
match (not "best fit" / "highest priority" / "most knowledgeable"),
and an explicit list of forbidden choices (peer agents, END). Earlier
softer wordings let the model pick the assistant when it seemed more
topically relevant; the literal-match wording prevents that.

Validated by the question-answering eval added in the previous commit.
On google:gemini-3-flash-preview, 5 samples per variant across 5
synthesized scenarios:

| Scenario                                           | baseline | with_rule |
|----------------------------------------------------|----------|-----------|
| math_quadratic_axis_drift_no_frustration           | 100%     | 100%      |
| bio_dark_reaction_drift_no_frustration             | 80%      | 100%      |
| english_team_isare_drift_no_frustration            | 20%      | 100%      |
| physics_inertial_mass_escalated_frustration        | 0%       | 100%      |
| calculus_product_rule_drift_no_frustration         | 60%      | 100%      |
| **mean**                                           | **52%**  | **100%**  |

3 of 5 scenarios reproduce the bug at baseline (correct rate ≤ 60%);
the rule lifts every scenario to 100%. The remaining 2 baselines are
already high — the rule doesn't regress them.

Adds an "Answering the User's Question" section to the agent system
prompt. Before this, the agent SP had no rule for direct-answering — the
persona, role guideline, current-state context, and length guidelines all
pushed the agent to advance the lesson and inspire thought, with no
explicit directive to first answer the user's literal question.

The result observed in prod ("答非所问"): when the user asks a specific
question (a formula, a yes/no, a term), agents reply with adjacent
concepts, examples, or follow-up questions — but never the literal
answer.

The new section directs the agent, on every response where the user
message contains a question, to:
- lead with the concrete answer to the literal question,
- not pivot to an adjacent topic even when it seems pedagogically
  richer,
- treat "inspire thought" and peer-differentiation guidance as
  applying only AFTER the literal question is answered,
- say "I don't know" directly when uncertain rather than answering
  a different question,
- on frustration signals from prior turns, look back at the original
  question (before the frustration) and answer THAT specifically.

This is the agent-side counterpart to the director rule landed in the
previous commit. Director routes to the teacher when the question is
unanswered; the teacher now has explicit guidance for what to do when
dispatched.

…ors from completion

Two coupled cleanups in one commit since the outcome-handler rewrite
naturally falls out of removing the client-side max-turns loop.

The director graph used `maxTurns: turnCount + 1` to force "one
director→agent cycle per request" — a hack expressing the single-round
contract as a turn limit. This commit removes the hack and the
surrounding user-facing setting, replacing implicit intent with explicit
graph topology.

Server:
- `director-graph.ts`: drop `maxTurns` from state, drop the hard-cap
  check at the top of `directorNode`, change `agent_generate → director`
  edge to `agent_generate → END`. Single-round contract is now expressed
  by topology.
- `lib/types/chat.ts`: drop `maxTurns` and `currentTurn` from
  `SessionConfig`; drop `maxTurns?` from `CreateSessionRequest.trigger`.

Client:
- `lib/store/settings.ts`: drop `maxTurns` state, `setMaxTurns` action,
  the `'10'` default, and the localStorage migration path.
- `components/agent/agent-bar.tsx`: drop the entire compact-stepper UI
  block plus the unused MessageSquare/Minus/Plus lucide imports.
- `components/settings/agent-settings.tsx`: drop the AgentSettings prop
  and the multi-agent-only Input block.
- `lib/chat/agent-loop.ts`: drop `maxTurns` parameter, change
  `while (turnCount < maxTurns)` to `while (true)` controlled by inner
  exits, drop `'max_turns'` reason from `AgentLoopOutcome`.
- `components/chat/use-chat-sessions.ts`: drop the maxTurns lookup, drop
  the trailing arg to runAgentLoop, drop vestigial `maxTurns: 0` /
  `currentTurn: 0` from session creation.
- `eval/whiteboard-layout/runner.ts`: drop unused MAX_AGENT_TURNS plus
  the trailing arg.

i18n: drop `settings.maxTurns` and `settings.maxTurnsDesc` from six
locales (en-US, zh-CN, zh-TW, ja-JP, ar-SA, ru-RU).

Motivation for removing the user-facing setting: the LLM director
controls round length via cue_user / END decisions, so a numeric
"max discussion turns" knob is redundant with rule-driven routing.
When the director prompt was buggy, the cap masked the bug by force-
ending; once director routing is fixed, the cap just removes user
agency.

Before, every non-`cue_user` outcome of the agent loop mapped to
`status: 'completed'` in `use-chat-sessions.ts`. That conflated four
distinct paths:
- `end`: director chose END (legitimate completion)
- `empty_turns`: two consecutive agents returned no text or actions
  (parser failure, model timeout, etc.)
- `no_done`: SSE stream ended without a `done` event (infrastructure
  failure)
- `aborted`: user pressed stop (handled elsewhere)

The new switch routes `end` to completed, `empty_turns` and `no_done`
through `clearLiveSessionAfterError` so the user sees an inline System
message describing what went wrong instead of a quiet "completed".

- `lib/types/chat.ts`: add `'error'` to `SessionStatus`.
- `components/chat/use-chat-sessions.ts`: rewrite the outcome handler
  as a switch; have `clearLiveSessionAfterError` set `status: 'error'`
  so all entry points (the runAgentLoop outcome AND existing throw
  paths from fetchChat / SSE error events) converge on the same
  visible state.
- `components/chat/session-list.tsx`: add `AlertCircle` red icon for
  the new error status.
- i18n: add `chat.error.emptyAgentResponses` and
  `chat.error.streamInterrupted` strings to all six locales.

This is the in-product fix that the prod investigation surfaced as
an independent root cause of the #511 "discussion ended unexpectedly"
symptom — separate from the director and agent prompt fixes in the
earlier commits of this PR.