MVP M6: live Socrates dock — LLM gateway + persisted thread + reply loop

The dock now talks to a real LLM. On first load it asks Socrates for an
opening turn that's grounded in the project's actual SysML model + active
validation issues. User replies and option-picks send turns through the
same channel. Thread + every message persist in SQLite so refresh keeps
the conversation.

apps/web/lib/llm
- gateway.ts: LLMGateway interface (chat + ChatOptions). Two adapters:
    - lmstudio: OpenAI SDK against LMSTUDIO_BASE_URL (default
      http://localhost:1234/v1)
    - anthropic: @anthropic-ai/sdk against claude-sonnet-4-6 (set
      ANTHROPIC_API_KEY when LLM_PROVIDER=anthropic)
  Provider chosen via LLM_PROVIDER env (default: lmstudio).
- chatJSON(): JSON-mode helper with parse-error repair-retry — the same
  defensive pattern proven against gemma-4-e4b in Phase 0.
- prompts.ts: server-only loader that caches .md prompts.
- prompts/socrates/character.md + review.md: ported verbatim from
  phase-0/src/prompts/ (Phase 0 corpus validated these 10/10).
- socrates.ts: sendUserTurn() — builds the system prompt (character +
  review + project context with trimmed model + active issues), runs
  chatJSON against the gateway, persists user + assistant turns,
  returns the structured turn. SocratesTurn schema is { text, options? }
  with up to 3 numbered options matching the prototype.

apps/web/prisma
- SocratesThread + SocratesMessage tables. Auto-create one open thread
  per project on first load.

apps/web/app/api/projects/[projectId]/socrates
- GET: returns active thread + parsed messages.
- POST: body { text }. Empty text triggers an opening turn. Persists user
  + assistant turns, returns assistant turn + provider metadata.

apps/web/components/socrates/SocratesDock.tsx
- Replaces the static thread prop with a projectId. Loads from API on
  mount, auto-triggers an opening turn if the thread is empty, sends
  user replies via POST. Numbered options click-to-pick or 1–3 keyboard
  shortcut (skipped when focus is in an input). Status line shows the
  active provider + model. Optimistic-local: user message appears
  instantly, "thinking…" placeholder shows while the LLM works, errors
  surface inline.

apps/web/.env.example + .env.local
- LLM_PROVIDER, LMSTUDIO_BASE_URL/MODEL/API_KEY, ANTHROPIC_API_KEY/MODEL.
- .env.local committed only with the local default (no real secrets);
  user supplies their own per-machine.

What's not yet here (next iterations):
- Streaming responses (currently waits for full response, ~5-15s)
- Multi-thread switcher (one auto-thread per project)
- Socrates-proposes-ops flow (M7)

apps/web/lib/db/repo.ts

@@ -133,5 +133,38 @@ async function ensureSeeded(projectId: string): Promise<{ projectId: string }> {
       json: JSON.stringify(seedModel),
     },
   });
+
+  // Auto-create an opening Socrates thread so the dock has somewhere to talk.
+  // Socrates' opening turn is generated lazily on first GET (so we don't
+  // pin a model selection to seed time).
+  await prisma.socratesThread.create({
+    data: {
+      projectId,
+      title: "Active thread · " + aristotleFixture.project.name,
+      status: "open",
+    },
+  });
+
   return { projectId };
 }
+
+// ─── Socrates threads ────────────────────────────────────────────────────
+
+export async function getActiveThread(projectId: string): Promise<{ id: string; title: string | null; messages: Array<{ id: string; role: string; content: string; createdAt: Date }> } | null> {
+  const thread = await prisma.socratesThread.findFirst({
+    where: { projectId, status: "open" },
+    orderBy: { updatedAt: "desc" },
+    include: { messages: { orderBy: { createdAt: "asc" } } },
+  });
+  if (!thread) return null;
+  return {
+    id: thread.id,
+    title: thread.title,
+    messages: thread.messages.map(m => ({
+      id: m.id,
+      role: m.role,
+      content: m.content,
+      createdAt: m.createdAt,
+    })),
+  };
+}