diff --git a/adapters/adapter-core/package.json b/adapters/adapter-core/package.json
index bdceb7f..b7f4d55 100644
--- a/adapters/adapter-core/package.json
+++ b/adapters/adapter-core/package.json
@@ -27,6 +27,6 @@
  "scripts": {
  "build": "tsc -p tsconfig.json",
  "typecheck": "tsc -p tsconfig.json --noEmit",
- "test": "tsc -p tsconfig.json && node test/static.test.mjs && node test/host.test.mjs && node test/whoami.test.mjs && node test/agent-text.test.mjs && node test/delete-guard.test.mjs"
+ "test": "tsc -p tsconfig.json && node test/static.test.mjs && node test/host.test.mjs && node test/whoami.test.mjs && node test/agent-text.test.mjs && node test/delete-guard.test.mjs && node test/unknown-route.test.mjs"
  }
 }
diff --git a/adapters/adapter-core/src/server.ts b/adapters/adapter-core/src/server.ts
index 195bb47..35e8466 100644
--- a/adapters/adapter-core/src/server.ts
+++ b/adapters/adapter-core/src/server.ts
@@ -61,10 +61,21 @@ const REFERENCE_SCAN_MAX_PAGES = 200;
 const TASK_TIMEOUT_MS = 60_000;
 const TASK_MAX_DELIVERIES = 5;
 const DESCRIBE_PREFIX = "/api/_a2app/describe/";
+/** A miss is usually a guessed route, so it names the routes that answer. */
+const UNKNOWN_ROUTE_MESSAGE =
+  "No such route. Operations are invoked with POST /api/ops/<name>; GET /api/_a2app/describe lists them.";
+/** Path prefixes owned exclusively by the adapter. Keep in step with the router
+ *  in `handle`. */
+const ADAPTER_NAMESPACES = ["/api/_a2app", "/api/ops", "/api/collections"];
+
+function isAdapterNamespace(path: string): boolean {
+  return ADAPTER_NAMESPACES.some((ns) => path === ns || path.startsWith(`${ns}/`));
+}
 
 export interface A2App {
-  /** Route a request. Resolves to a reply, or null if the path is not an A2App
-   *  path (the host app then handles it with its own routes). */
+  /** Route a request. Resolves to a reply, or null if the path is outside the
+   *  adapter's namespaces (the host app then handles it with its own routes). A
+   *  miss inside them is a 404 reply, never null. */
   handle(req: A2AppRequest): Promise<A2AppReply | null>;
   /** The identity document. */
   identity(): Record<string, unknown>;
@@ -1141,6 +1152,11 @@ export function createA2App(binding: Binding, config: A2AppConfig): A2App {
       return handleOperation(req, decodeURIComponent(op[1]!));
     }
 
+    // A miss in the adapter's own namespaces is the adapter's to answer. The rest
+    // of /api/ stays the host's: this is middleware, and a host may mount routes
+    // of its own there.
+    if (isAdapterNamespace(path)) return err(404, "not_found", UNKNOWN_ROUTE_MESSAGE);
+
     return null; // not an A2App path — the host app handles it
   }
 
diff --git a/adapters/adapter-core/src/static.ts b/adapters/adapter-core/src/static.ts
index 2a2c21c..662fe96 100644
--- a/adapters/adapter-core/src/static.ts
+++ b/adapters/adapter-core/src/static.ts
@@ -196,6 +196,14 @@ export function createStaticView(dir: string, options: StaticViewOptions = {}):
   }
 
   function handler(req: IncomingMessage, res: ServerResponse): void {
+    const url = new URL(req.url ?? "/", "http://localhost");
+    const file = resolveFile(url.pathname);
+    // Path before method: 405 is only for a file that exists.
+    if (file === null) {
+      notFound(res);
+      return;
+    }
+
     const method = (req.method ?? "GET").toUpperCase();
     if (method !== "GET" && method !== "HEAD") {
       res.writeHead(405, { "content-type": "application/json", allow: "GET, HEAD" });
@@ -205,13 +213,6 @@ export function createStaticView(dir: string, options: StaticViewOptions = {}):
       return;
     }
 
-    const url = new URL(req.url ?? "/", "http://localhost");
-    const file = resolveFile(url.pathname);
-    if (file === null) {
-      notFound(res);
-      return;
-    }
-
     const body = readFileSync(file);
     const etag = `"${createHash("sha256").update(body).digest("hex").slice(0, 32)}"`;
     const lastModified = statSync(file).mtime;
diff --git a/adapters/adapter-core/test/static.test.mjs b/adapters/adapter-core/test/static.test.mjs
index 5559903..7c6a475 100644
--- a/adapters/adapter-core/test/static.test.mjs
+++ b/adapters/adapter-core/test/static.test.mjs
@@ -136,6 +136,15 @@ await check("static assets are GET-only", async () => {
   assert.equal(res.headers.get("allow"), "GET, HEAD");
 });
 
+await check("a POST to a path that names no file is a 404, not a 405", async () => {
+  // 405 means "right resource, wrong verb" — only true of a file that exists.
+  for (const path of ["/missing.html", "/sub"]) {
+    const res = await get(path, { method: "POST" });
+    assert.equal(res.status, 404, `${path} answered ${res.status}`);
+    assert.equal((await res.json()).code, "not_found");
+  }
+});
+
 /* -------------------------------------------------------------- aliases */
 
 await check("an alias serves a file from outside the View directory", async () => {
diff --git a/adapters/adapter-core/test/unknown-route.test.mjs b/adapters/adapter-core/test/unknown-route.test.mjs
new file mode 100644
index 0000000..b68454b
--- /dev/null
+++ b/adapters/adapter-core/test/unknown-route.test.mjs
@@ -0,0 +1,109 @@
+/**
+ * A miss inside the adapter's namespaces is the adapter's to answer; the rest of
+ * /api/ stays the host's.
+ *
+ * Wired the way a blueprint wires it — the adapter first, the static View as the
+ * fallthrough — because the contract lives in the seam between the two.
+ *
+ * Run: node test/unknown-route.test.mjs
+ */
+import assert from "node:assert/strict";
+import { mkdtempSync, rmSync, writeFileSync } from "node:fs";
+import { createServer } from "node:http";
+import { tmpdir } from "node:os";
+import { join } from "node:path";
+import { createA2App, MemoryBinding, createStaticView } from "../dist/index.js";
+import { a2appMiddleware, createA2AppServer } from "../dist/http.js";
+
+const dir = mkdtempSync(join(tmpdir(), "a2app-unknown-route-"));
+writeFileSync(join(dir, "index.html"), "<!doctype html><p>view</p>");
+
+const app = createA2App(
+  new MemoryBinding({
+    appId: "unknown_route_test",
+    appName: "Unknown Route Test",
+    entities: { notes: { module: "desk", fields: [{ name: "title", type: "string" }], seed: [] } },
+  }),
+  { modules: [{ name: "desk", summary: "notes" }] },
+);
+
+const server = createA2AppServer(app, createStaticView(dir).handler);
+await new Promise((r) => server.listen(0, "127.0.0.1", r));
+const base = `http://127.0.0.1:${server.address().port}`;
+const send = (method, path) =>
+  fetch(`${base}${path}`, {
+    method,
+    headers: { "content-type": "application/json" },
+    ...(method === "GET" ? {} : { body: "{}" }),
+  });
+
+let failures = 0;
+async function check(name, fn) {
+  try {
+    await fn();
+    console.log(`  ok   ${name}`);
+  } catch (err) {
+    failures += 1;
+    console.error(`  FAIL ${name}\n       ${err.message}`);
+  }
+}
+
+await check("POST to an unknown /api/_a2app route is a 404 that names the real routes", async () => {
+  const res = await send("POST", "/api/_a2app/operate");
+  assert.equal(res.status, 404);
+  const body = await res.json();
+  assert.equal(body.code, "not_found");
+  assert.equal(body.ok, false);
+  assert.match(body.message, /POST \/api\/ops\/<name>/);
+  assert.match(body.message, /\/api\/_a2app\/describe/);
+});
+
+await check("the adapter, not the View, answers every miss under its namespaces", async () => {
+  const paths = ["/api/_a2app/does-not-exist", "/api/ops", "/api/ops/a/b", "/api/collections/notes", "/api/collections"];
+  for (const path of paths) {
+    for (const method of ["GET", "POST", "PATCH", "DELETE"]) {
+      const res = await send(method, path);
+      assert.equal(res.status, 404, `${method} ${path} answered ${res.status}`);
+      // The View's 404 has the same code; only the adapter's names the routes.
+      assert.match((await res.json()).message, /\/api\/_a2app\/describe/, `${method} ${path}`);
+    }
+  }
+});
+
+await check("the routes that exist still answer", async () => {
+  assert.equal((await send("GET", "/api/_a2app/describe")).status, 200);
+  assert.equal((await (await send("POST", "/api/ops/nope")).json()).code, "unknown_operation");
+});
+
+await check("a POST to a real static file is still a 405", async () => {
+  const res = await send("POST", "/index.html");
+  assert.equal(res.status, 405);
+  assert.equal(res.headers.get("allow"), "GET, HEAD");
+});
+
+await check("the rest of /api/ is still the host's", async () => {
+  const mw = a2appMiddleware(app);
+  const host = createServer((req, res) =>
+    mw(req, res, () => {
+      res.writeHead(200, { "content-type": "application/json" });
+      res.end(JSON.stringify({ host: true }));
+    }),
+  );
+  await new Promise((r) => host.listen(0, "127.0.0.1", r));
+  try {
+    const res = await fetch(`http://127.0.0.1:${host.address().port}/api/custom`, { method: "POST", body: "{}" });
+    assert.equal(res.status, 200);
+    assert.equal((await res.json()).host, true);
+  } finally {
+    host.close();
+  }
+});
+
+server.close();
+rmSync(dir, { recursive: true, force: true });
+
+if (failures > 0) {
+  console.error(`\nunknown route: ${failures} check(s) failed`);
+  process.exit(1);
+}
+console.log("\nunknown route: all checks passed");
diff --git a/toolkits/blueprint-go-react/template/a2app_adapter.go b/toolkits/blueprint-go-react/template/a2app_adapter.go
index c0e1296..98f5508 100644
--- a/toolkits/blueprint-go-react/template/a2app_adapter.go
+++ b/toolkits/blueprint-go-react/template/a2app_adapter.go
@@ -2454,7 +2454,7 @@ func (a *Adapter) dispatch(method, path string, headers map[string]string, body
 		return a.handleOperation(headers, m[1], body)
 	}
 
-	return errEnv(404, "not_found", "No such route.", nil)
+	return errEnv(404, "not_found", "No such route. Operations are invoked with POST /api/ops/<name>; GET /api/_a2app/describe lists them.", nil)
 }
 
 /* -- records ------------------------------------------------------------------ */
diff --git a/toolkits/blueprint-go-react/template/main.go b/toolkits/blueprint-go-react/template/main.go
index 4ba9a60..0aabcf6 100644
--- a/toolkits/blueprint-go-react/template/main.go
+++ b/toolkits/blueprint-go-react/template/main.go
@@ -379,6 +379,13 @@ func matchesEtag(header, etag string) bool {
 }
 
 func (v *staticView) serveHTTP(w http.ResponseWriter, r *http.Request) {
+	// Path before method: 405 is only for a file that exists.
+	file := v.resolveFile(r.URL.Path)
+	if file == "" {
+		writeJSON(w, 404, M{"a2app": true, "ok": false, "code": "not_found", "message": "No such route."})
+		return
+	}
+
 	method := strings.ToUpper(r.Method)
 	if method != "GET" && method != "HEAD" {
 		w.Header().Set("Allow", "GET, HEAD")
@@ -386,12 +393,6 @@ func (v *staticView) serveHTTP(w http.ResponseWriter, r *http.Request) {
 		return
 	}
 
-	file := v.resolveFile(r.URL.Path)
-	if file == "" {
-		writeJSON(w, 404, M{"a2app": true, "ok": false, "code": "not_found", "message": "No such route."})
-		return
-	}
-
 	body, err := os.ReadFile(file)
 	if err != nil {
 		writeJSON(w, 404, M{"a2app": true, "ok": false, "code": "not_found", "message": "No such route."})
diff --git a/toolkits/blueprint-python-fastapi/template/a2app_adapter.py b/toolkits/blueprint-python-fastapi/template/a2app_adapter.py
index 6961600..9425c40 100644
--- a/toolkits/blueprint-python-fastapi/template/a2app_adapter.py
+++ b/toolkits/blueprint-python-fastapi/template/a2app_adapter.py
@@ -1401,7 +1401,7 @@ def dispatch(self, method: str, path: str, headers: dict, body: Optional[dict],
                 return self._err(405, "usage", "Operations are POST-only.")
             return self._handle_operation(headers, m.group(1), body or {})
 
-        return self._err(404, "not_found", "No such route.")
+        return self._err(404, "not_found", "No such route. Operations are invoked with POST /api/ops/<name>; GET /api/_a2app/describe lists them.")
 
     # -- records ------------------------------------------------------------
     def _references_to(self, entity: str, rec_id: str) -> list[dict]:
diff --git a/toolkits/blueprint-python-fastapi/template/main.py b/toolkits/blueprint-python-fastapi/template/main.py
index 32e3e54..2bb5967 100644
--- a/toolkits/blueprint-python-fastapi/template/main.py
+++ b/toolkits/blueprint-python-fastapi/template/main.py
@@ -110,10 +110,13 @@ async def _read_body(request: Request):
         return {"__unparsed__": raw.decode("utf8", "replace")}, None
 
 
-@app.api_route("/api/{path:path}", methods=["GET", "POST", "PATCH", "DELETE"])
+# Every standard method, so the adapter decides: a method left off this list would get
+# Starlette's own 405, outside the a2app envelope, even on a route that does not
+# exist.
+@app.api_route("/api/{path:path}", methods=["GET", "HEAD", "POST", "PUT", "PATCH", "DELETE", "OPTIONS"])
 async def a2app_route(path: str, request: Request):
     body = None
-    if request.method in ("POST", "PATCH"):
+    if request.method in ("POST", "PUT", "PATCH"):
         body, too_large = await _read_body(request)
         if too_large is not None:
             return JSONResponse(status_code=too_large[0], content=too_large[1])
diff --git a/toolkits/blueprint-rails-vue/template/lib/a2app_adapter.rb b/toolkits/blueprint-rails-vue/template/lib/a2app_adapter.rb
index 7f0a497..763b8ec 100644
--- a/toolkits/blueprint-rails-vue/template/lib/a2app_adapter.rb
+++ b/toolkits/blueprint-rails-vue/template/lib/a2app_adapter.rb
@@ -1431,7 +1431,7 @@ def dispatch(method, path, headers, body, query = nil)
         return handle_operation(headers, m[1], body || {})
       end
 
-      err(404, "not_found", "No such route.")
+      err(404, "not_found", "No such route. Operations are invoked with POST /api/ops/<name>; GET /api/_a2app/describe lists them.")
     end
 
     # -- records ------------------------------------------------------------
diff --git a/toolkits/blueprint-rust-react/template/src/a2app_adapter.rs b/toolkits/blueprint-rust-react/template/src/a2app_adapter.rs
index cd1f9e4..ad88ea7 100644
--- a/toolkits/blueprint-rust-react/template/src/a2app_adapter.rs
+++ b/toolkits/blueprint-rust-react/template/src/a2app_adapter.rs
@@ -2540,7 +2540,7 @@ impl Adapter {
             }
         }
 
-        Self::err(404, "not_found", "No such route.")
+        Self::err(404, "not_found", "No such route. Operations are invoked with POST /api/ops/<name>; GET /api/_a2app/describe lists them.")
     }
 
     // -- records ------------------------------------------------------------
diff --git a/toolkits/blueprint-rust-react/template/src/main.rs b/toolkits/blueprint-rust-react/template/src/main.rs
index c0c7309..0af8534 100644
--- a/toolkits/blueprint-rust-react/template/src/main.rs
+++ b/toolkits/blueprint-rust-react/template/src/main.rs
@@ -600,21 +600,6 @@ fn handle_request(
     }
 
     // ---------------------------------------------------------- static View
-    if method != "GET" && method != "HEAD" {
-        let response = tiny_http::Response::from_string(
-            json!({
-                "a2app": true, "ok": false, "code": "method_not_allowed",
-                "message": "Static assets are GET-only.",
-            })
-            .to_string(),
-        )
-        .with_status_code(405)
-        .with_header(header("Content-Type", "application/json"))
-        .with_header(header("Allow", "GET, HEAD"));
-        let _ = request.respond(response);
-        return 405;
-    }
-
     // Alias before path resolution: the watcher is served from the project
     // root, outside the built tree, so it survives any View rewrite.
     let file = if path == "/_a2app/update.js" {
@@ -626,11 +611,27 @@ fn handle_request(
     } else {
         resolve_static(served_dir, path)
     };
+    // Path before method: 405 is only for a file that exists.
     let file = match file {
         Some(f) => f,
         None => return respond_json(request, 404, &not_found_envelope()),
     };
 
+    if method != "GET" && method != "HEAD" {
+        let response = tiny_http::Response::from_string(
+            json!({
+                "a2app": true, "ok": false, "code": "method_not_allowed",
+                "message": "Static assets are GET-only.",
+            })
+            .to_string(),
+        )
+        .with_status_code(405)
+        .with_header(header("Content-Type", "application/json"))
+        .with_header(header("Allow", "GET, HEAD"));
+        let _ = request.respond(response);
+        return 405;
+    }
+
     let body = match fs::read(&file) {
         Ok(b) => b,
         Err(_) => return respond_json(request, 404, &not_found_envelope()),