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.

tests/reattach-transport.test.ts

@@ -18,6 +18,10 @@
 import assert from "node:assert/strict";
 import { afterEach, describe, it } from "node:test";
 import { createReattachingTransport } from "../components/chat-transport.ts";
+import type { ChatInput } from "../src/core/input-events.ts";
+
+/** A no-op input-events stash (the reattach tests never send). */
+const NO_INPUT = { takeInput: () => undefined };
 
 const realFetch = globalThis.fetch;
 afterEach(() => {
@@ -67,7 +71,7 @@ describe("reattach transport (reconnectToStream)", () => {
 			urls.push(String(input));
 			return dripped(sse({ type: "start", messageId: "msg_run_1" }), 8);
 		}) as typeof globalThis.fetch;
-		const transport = createReattachingTransport("chat_x", {});
+		const transport = createReattachingTransport("chat_x", {}, NO_INPUT);
 		await collect((await transport.reconnectToStream(RECONNECT_OPTS))!);
 		assert.deepEqual(urls, ["/api/chats/chat_x/stream"]);
 	});
@@ -76,7 +80,7 @@ describe("reattach transport (reconnectToStream)", () => {
 		globalThis.fetch = (async () =>
 			dripped(sse({ type: "turn-settled" }, "[DONE]"), 8)) as typeof globalThis.fetch;
 		let settled = 0;
-		const transport = createReattachingTransport("chat_x", { onSettled: () => settled++ });
+		const transport = createReattachingTransport("chat_x", { onSettled: () => settled++ }, NO_INPUT);
 		const stream = await transport.reconnectToStream(RECONNECT_OPTS);
 		assert.equal(stream, null);
 		assert.equal(settled, 1);
@@ -86,7 +90,7 @@ describe("reattach transport (reconnectToStream)", () => {
 
 	it("204 (the SDK's native no-stream signal) resolves null untouched", async () => {
 		globalThis.fetch = (async () => new Response(null, { status: 204 })) as typeof globalThis.fetch;
-		const transport = createReattachingTransport("chat_x", {});
+		const transport = createReattachingTransport("chat_x", {}, NO_INPUT);
 		assert.equal(await transport.reconnectToStream(RECONNECT_OPTS), null);
 	});
 
@@ -102,7 +106,7 @@ describe("reattach transport (reconnectToStream)", () => {
 				),
 				13,
 			)) as typeof globalThis.fetch;
-		const transport = createReattachingTransport("chat_x", {});
+		const transport = createReattachingTransport("chat_x", {}, NO_INPUT);
 		const chunks = (await collect((await transport.reconnectToStream(RECONNECT_OPTS))!)) as Array<
 			Record<string, unknown>
 		>;
@@ -120,7 +124,7 @@ describe("reattach transport (reconnectToStream)", () => {
 			)) as typeof globalThis.fetch;
 		const transport = createReattachingTransport("chat_x", {
 			lastMessageId: () => "msg_seed",
-		});
+		}, NO_INPUT);
 		const chunks = (await collect((await transport.reconnectToStream(RECONNECT_OPTS))!)) as Array<
 			Record<string, unknown>
 		>;
@@ -134,7 +138,7 @@ describe("reattach transport (reconnectToStream)", () => {
 	it("survives a body split byte-by-byte across reads", async () => {
 		globalThis.fetch = (async () =>
 			dripped(sse({ type: "start", messageId: "msg_run_1" }, { type: "finish", finishReason: "stop" }), 1)) as typeof globalThis.fetch;
-		const transport = createReattachingTransport("chat_x", {});
+		const transport = createReattachingTransport("chat_x", {}, NO_INPUT);
 		const chunks = (await collect((await transport.reconnectToStream(RECONNECT_OPTS))!)) as Array<
 			Record<string, unknown>
 		>;
@@ -147,7 +151,7 @@ describe("reattach transport (reconnectToStream)", () => {
 
 	it("an unhappy endpoint throws (the SDK surfaces the error banner)", async () => {
 		globalThis.fetch = (async () => new Response("boom", { status: 500 })) as typeof globalThis.fetch;
-		const transport = createReattachingTransport("chat_x", {});
+		const transport = createReattachingTransport("chat_x", {}, NO_INPUT);
 		await assert.rejects(() => transport.reconnectToStream(RECONNECT_OPTS), /boom/);
 	});
 });