Swap the server engine to pi-ai/pi-agent-core (Band B+C of docs/pi-engine-swap.md)

The Vercel AI SDK survives only as Band D (useChat client + UIMessage
record types); @openrouter/ai-sdk-provider is uninstalled.

- src/agent/models.ts: PiEngine {model, streamFn} via createModels +
  openrouterProvider subpath; thinkingLevelFor maps config effort none->off
- src/agent/lh-tool.ts: neutral LhTool (zod authoring, optional execute,
  clientQuestion flag); toPiTool converts via z.toJSONSchema and re-runs
  zod inside execute so refinements ride the error-result retry path
- src/server/pi/record-adapter.ts: UIMessage records -> pi Messages
  (dangling tool calls get synthesized interrupted results)
- src/server/pi/ui-stream.ts: SSE bridge emitting AI-SDK-shaped chunks so
  the useChat client parses unchanged (continuation id rule, question
  tools never emit output, tool-input-error for bad authoring)
- teacher-agent.ts: stateless per-turn pi Agents; shouldStopAfterTurn
  stops only when every question-tool call resolved cleanly (errors retry)
- chat-handler.ts: buildAgent(outgoing) factory seam (stateless doctrine);
  assertValidUiMessages owns the retired SDK validation gate
- sub-agents via shared runSubagent (pi-run.ts); extraction stages stop
  after a clean submit; visual-maker keeps its hand-rolled loop over
  direct streamSimple calls; aborted model calls bill no usage
- tests: all model seams ported to pi-ai faux provider (scripted
  FauxResponseSteps, agent factories); handleChatRequest second param
  is now an agent factory

Gates: tsc, lint, build, 305/305. Live GLM smoke (disposable driver,
deleted): prober streaming + persistence, question seam, turn-2
continuation same message id, per-turn real token usage - ALL PASS.
Data wiped at the pivot (chats/graph/jobs, .gitkeeps kept).

src/agent/tools/probe.ts

@@ -1,5 +1,5 @@
-import { tool, type ToolSet } from "ai";
 import { z } from "zod";
+import { lhTool, type LhTool } from "../lh-tool.ts";
 import type { ProbeDoneInput, ProbeDoneResult } from "../../core/contracts.ts";
 import type { UIMessage } from "ai";
 import { findPendingToolCall } from "../../core/pending.ts";
@@ -44,9 +44,10 @@ function probeConcluded(messages: UIMessage[]): boolean {
  * The first probe_done in the transcript is also the construction seam:
  * from that message on, every request builds the TEACHER agent.
  */
-export function probeDoneTool(ctx: ProbeDoneContext): ToolSet {
+export function probeDoneTool(ctx: ProbeDoneContext): Record<string, LhTool<any, any>> {
 	return {
-		probe_done: tool({
+		probe_done: lhTool({
+			name: "probe_done",
 			description:
 				"Conclude the probing phase and hand off to the teaching phase. Call this ONCE, when the probe is " +
 				"complete: every strand the lesson depends on is bracketed (a floor he reliably gets right AND a " +
@@ -55,7 +56,7 @@ export function probeDoneTool(ctx: ProbeDoneContext): ToolSet {
 				"(floor, ceiling, misconceptions, what to build from). It streams to the learner live and becomes " +
 				"the handoff artifact the teacher plans from. Refused while a question is still open, and after " +
 				"the probe is already concluded. After it succeeds, say your closing sentence and end your turn.",
-			inputSchema: z.object({
+			schema: z.object({
 				assessment: z
 					.object({
 						strands: z