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/store/chats.ts

@@ -12,9 +12,10 @@ import * as path from "node:path";
 import { PATHS } from "../../config.ts";
 import type { ChatStore } from "../core/ports.ts";
 import type { ChatRecord, ChatSettings, ChatSummary, ExtractionRunUsage, PlanTree, TurnUsage } from "../core/contracts.ts";
-import type { UIMessage } from "ai";
+import type { LhMessage } from "../core/native-messages.ts";
 import { findPendingToolCall } from "../core/pending.ts";
 import { phaseAt3 } from "../core/phases.ts";
+import { projectNative } from "../core/projection.ts";
 
 function chatFile(id: string): string {
 	if (!/^[A-Za-z0-9_-]+$/.test(id)) throw new Error(`Invalid chat id: ${id}`);
@@ -51,28 +52,43 @@ function listChats(): ChatSummary[] {
 			.filter((f) => f.endsWith(".json"))
 			.map((f) => getChat(f.slice(0, -5)))
 			.filter((r): r is ChatRecord => r !== null)
-			.map(({ messages, tree, turns, extractions, ...summary }) => ({
-				// turns and extractions stay out of the list payload (list =
-				// summaries; usage aggregates ride the full record, the picker
-				// never needs them).
-				...summary,
-				messageCount: messages.length,
-				// Record-derived status for the session picker: phase from the
-				// transcript's explicit markers (probe_done / plan_init — the
-				// event-driven phases, docs/probe-teach-split.md §4), pending
-				// question from the last unanswered quiz/ask part. Liveness (busy)
-				// is NOT record-derived — the API route merges it (ChatListItem).
-				phase: phaseAt3(messages),
-				pendingQuestion: findPendingToolCall(messages) !== null,
-			}))
+			.map(({ messages, tree, turns, extractions, ...summary }) => {
+				// Per-record isolation (Wave B): a record whose messages fail the
+				// projection (e.g. pre-Wave-B UIMessage-format scratch — the
+				// zero-back-compat wipe makes these "corrupt") must not blank the
+				// whole sidebar — same isolation getChat's per-file catch gives.
+				try {
+					const projected = projectNative(messages);
+					return {
+						// turns and extractions stay out of the list payload (list =
+						// summaries; usage aggregates ride the full record, the picker
+						// never needs them).
+						...summary,
+						messageCount: messages.length,
+						// Record-derived status for the session picker: phase from the
+						// transcript's explicit markers (probe_done / plan_init — the
+						// event-driven phases, docs/probe-teach-split.md §4), pending
+						// question from the last unanswered quiz/ask part — both read
+						// through the one-way projection. Liveness (busy) is NOT
+						// record-derived — the API route merges it (ChatListItem).
+						phase: phaseAt3(projected),
+						pendingQuestion: findPendingToolCall(projected) !== null,
+					};
+				} catch (err) {
+					console.error(`[chat ${summary.id}] summary projection failed:`, err);
+					return null;
+				}
+			})
+			.filter((s): s is ChatSummary => s !== null)
 			.sort((a, b) => b.updatedAt.localeCompare(a.updatedAt));
 	} catch {
 		return [];
 	}
 }
 
-/** Persist the full message list (client state + new response) after a turn. */
-function saveMessages(id: string, messages: UIMessage[]): void {
+/** Persist the full native message list (the record IS the agent state —
+ *  Wave B: replay is state.messages = record.messages). */
+function saveMessages(id: string, messages: LhMessage[]): void {
 	const record = getChat(id);
 	if (!record) throw new Error(`Chat not found: ${id}`);
 	record.messages = messages;