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/tools/probe.ts

@@ -1,10 +1,9 @@
 import type { AgentTool } from "@earendil-works/pi-agent-core";
 import { serverExecute } from "../tool-execute.ts";
 import { probeDoneInputSchema, type ProbeDoneResult } from "../../core/contracts.ts";
-import type { UIMessage } from "ai";
-import { findPendingToolCall } from "../../core/pending.ts";
+import { danglingQuestionOf, hasProbeDone, type LhMessage } from "../../core/native-messages.ts";
 import type { ChatStore } from "../../core/ports.ts";
-import { buildProbeHandoffSteer, type ProbeHandoffSteerMessage } from "../../core/contracts.ts";
+import { buildProbeHandoffSteer, type SteerMessage } from "../../core/contracts.ts";
 
 /** What the probe_done tool closes over. */
 export interface ProbeDoneContext {
@@ -13,15 +12,14 @@ export interface ProbeDoneContext {
 	chatStore: ChatStore;
 	/** Queue the handoff steer (the wake pipeline — src/server/jobs.ts).
 	 *  Injected so this module never imports the server seam. */
-	deliver: (steer: ProbeHandoffSteerMessage) => void;
+	deliver: (steer: SteerMessage) => void;
 }
 
-/** Does the transcript already carry a concluded probe (any state)? */
-function probeConcluded(messages: UIMessage[]): boolean {
-	for (const m of messages) {
-		if (m.parts.some((p) => p.type === "tool-probe_done")) return true;
-	}
-	return false;
+/** Does the transcript already carry a concluded probe (any state)?
+ *  Wave B: the native scan (any probe_done tool call, any state) — same
+ *  semantics the UIMessage part scan had. */
+function probeConcluded(messages: readonly LhMessage[]): boolean {
+	return hasProbeDone(messages);
 }
 
 /**
@@ -64,7 +62,7 @@ export function probeDoneTool(ctx: ProbeDoneContext): Record<string, AgentTool<a
 				const record = ctx.chatStore.getChat(ctx.chatId);
 				if (!record) return { ok: false, error: `Chat not found: ${ctx.chatId}` };
 
-				if (findPendingToolCall(record.messages) !== null) {
+				if (danglingQuestionOf(record.messages) !== null) {
 					return {
 						ok: false,
 						error: