Wave B: the native message record — input events, projection, adapter death

The chat record is now pi-native agent history (LhMessage[]), the AI SDK's
UIMessage transcript contract is gone from the server, and every client turn
arrives as ONE explicit input event.

Core (new):
- src/core/native-messages.ts — the LhMessage taxonomy (user/assistant/
  toolResult + lhMarker customs: verdict, probe-handoff, subagent-steer,
  subagent-abort, plan-block), constructors, and toLlmMessages — the single
  model-facing seam (convertToLlm): strips ids, flattens markers to user
  text, drops UI-only plan-blocks, synthesizes INTERRUPTED results for
  dangling aborted calls, never throws.
- src/core/projection.ts — projectNative: the one-way native → UIMessage
  projection (consecutive assistant+toolResult runs group into one
  assistant view message; toolResults attach backward by toolCallId;
  markers project to data parts; plan-blocks splice after the last
  successful plan_init). Every existing consumer reads through it.
- src/core/input-events.ts — the ChatInput union (text/answer/verdict/
  continue), parseChatInput validation, and inputAppends (answer targets
  the dangling question call or 400s; verdict = optional note user
  message + native verdict marker).

Server:
- chat-handler.ts — the turn root takes {chatId, input}; write-ahead
  persists input appends + claimed steers before the turn; claimSteers
  coalesces the whole queue with the handler's steerDelivered filter as
  the dedupe seam; teacher-vs-prober branch on hasProbeDone.
- turn-service.ts — persistTurn stamps ids, drops clean question
  placeholder toolResults (the record ends at the unanswered call),
  emits plan-block markers idempotently (plan-blocks.ts rewrite), and
  persists abort partials.
- ui-stream.ts — PiTurnSpec takes the native base; the wire dialect is
  unchanged. jobs.ts steers are native markers (steer_<jobId> dedup ids);
  waitForIdle reads danglingQuestionOf. teacher-agent.ts wires
  convertToLlm: toLlmMessages. record-adapter.ts DELETED wholesale.
- GET /api/chats/[id] serves messages: projectNative(record.messages).

Client:
- chat-transport.ts — the 409 retry is IDENTITY (re-POST the same event
  body after the turn settles — the event was never persisted
  pre-acceptance; the merge logic is gone). The transport consumes the
  stashed input event via prepareSendMessagesRequest and throws loudly on
  a missing stash.
- chat.tsx — every send call site stashes exactly one ChatInput event
  (text, answer, verdict, continue) before invoking the SDK send.

Tests: full native migration (chat-flow rewritten to input events and
native record pins; jobs/extraction/demos/graph/usage/plan-blocks/
probe-done/reattach-transport converted; record-adapter.test.ts deleted;
chat-transport tests pin the identity retry). 982/982, typecheck, lint,
build all green.

src/agent/teacher-agent.ts

@@ -15,6 +15,7 @@ import {
 } from "./tools.ts";
 import { quizInputObject, quizInputProblems } from "../core/question-core.ts";
 import { QUESTION_TOOLS, type EnabledTools } from "../core/pending.ts";
+import { toLlmMessages } from "../core/native-messages.ts";
 
 /**
  * The two teaching-side agents (docs/probe-teach-split.md): the PROBER and
@@ -89,7 +90,7 @@ export type StepUsageCollector = (usage: Usage) => void;
 export interface AgentBuildOptions {
 	/** Model + stream function — tests inject a scripted faux engine. */
 	engine?: PiEngine;
-	/** The initial transcript, as pi messages (recordToPiMessages). */
+	/** The initial transcript, as pi messages (the record IS agent state). */
 	messages?: AgentMessage[];
 	/** Money channel: one call per model request. */
 	onUsage?: StepUsageCollector;
@@ -164,6 +165,13 @@ function baseAgentOptions(kind: AgentKind, opts: AgentBuildOptions, tools: Agent
 		},
 		streamFn: engine.streamFn,
 		shouldStopAfterTurn: stopper,
+		// Wave B (owner-approved 2026-09-26): the model-facing conversion is
+		// THE app seam — markers flatten to their canonical user text
+		// (verdictText / HANDOFF_TEXT / steer text, all single-sourced),
+		// UI-only markers (plan-block) drop, the app's id fields strip, and
+		// an abort's dangling question call gets its INTERRUPTED result. It
+		// must never throw (pi's convertToLlm contract).
+		convertToLlm: toLlmMessages,
 	});
 	if (opts.onUsage) {
 		agent.subscribe((event: AgentEvent) => {