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/subagents/researcher.ts

@@ -1,6 +1,9 @@
-import { ToolLoopAgent, stepCountIs, type LanguageModel } from "ai";
+import type { AgentTool } from "@earendil-works/pi-agent-core";
+import type { Usage } from "@earendil-works/pi-ai";
 import { webTools } from "../tools/web.ts";
-import { modelFor } from "../models.ts";
+import { toPiTools } from "../lh-tool.ts";
+import type { PiEngine } from "../models.ts";
+import { runSubagent } from "./pi-run.ts";
 
 /**
  * The researcher sub-agent (vision §2.5): a SEPARATE ToolLoopAgent instance
@@ -9,7 +12,7 @@ import { modelFor } from "../models.ts";
  *
  * System prompt adapted from the pi researcher agent
  * (~/.pi/agent/extensions/interactive-subagents/agents/researcher.md).
- * The model is injectable so tests run the loop with a MockLanguageModelV4.
+ * The engine is injectable so tests run the loop with a scripted faux engine.
  */
 
 const INSTRUCTIONS = `You are a research specialist. You work for a teacher agent inside a learning
@@ -57,13 +60,29 @@ Numbered findings with inline source citations:
 ## Gaps
 What couldn't be answered. Suggested next steps.`;
 
-export function createResearcherAgent(model?: LanguageModel) {
-	return new ToolLoopAgent({
-		model: model ?? modelFor("researcher"),
-		instructions: INSTRUCTIONS,
-		tools: webTools,
-		stopWhen: stepCountIs(12),
-	});
+export interface ResearcherRunOptions {
+	engine?: PiEngine;
+	abortSignal?: AbortSignal;
+	onUsage?: (usage: Usage) => void;
+	onToolStart?: (toolName: string, args: unknown) => void;
 }
 
-export type ResearcherAgent = ReturnType<typeof createResearcherAgent>;
+/**
+ * Run the researcher to completion: isolated context, web tools only, final
+ * text = the brief. The engine is injectable so tests run the loop scripted.
+ */
+export async function runResearcherAgent(prompt: string, opts: ResearcherRunOptions = {}): Promise<string> {
+	const { text } = await runSubagent(toPiTools(webTools) as AgentTool<any, any>[], {
+		role: "researcher",
+		prompt,
+		engine: opts.engine,
+		systemPrompt: INSTRUCTIONS,
+		maxTurns: 12,
+		abortSignal: opts.abortSignal,
+		onUsage: opts.onUsage,
+		onToolStart: opts.onToolStart,
+	});
+	return text;
+}
+
+export type ResearcherAgent = ReturnType<typeof runResearcherAgent>;