docs(x402): define facilitator at first use and add a check-that-it-works step

build/agents/x402.mdx

@@ -31,6 +31,8 @@ Traditional payment systems don't work for AI agents and micropayments:
 
 ## How It Works
 
+A *facilitator* is a service that checks a buyer's signed payment and submits it on-chain on the seller's behalf, so the seller does not run a node or need CELO for gas.
+
 ```mermaid
 sequenceDiagram
     participant Client as Client (Agent)
@@ -177,6 +179,27 @@ If a call to `/settle` fails, the status code tells you why:
 | `402`  | Out of free credits and balance — top up on the dashboard.    |
 | `429`  | Free-tier rate limit reached.                                 |
 
+### Check that it works
+
+Start the server and request the paid route without a payment. This step needs no API key:
+
+```bash
+curl -i http://localhost:3000/premium
+```
+
+The response is `402 Payment Required` with an empty `{}` body. The payment requirements are in the base64-encoded `PAYMENT-REQUIRED` header. To read them:
+
+```bash
+curl -s -o /dev/null -D - http://localhost:3000/premium \
+  | awk -F': ' 'tolower($1)=="payment-required"{print $2}' | tr -d '\r' | base64 -d
+```
+
+The decoded JSON shows the route's price: `10000` base units of USDC, which is $0.01 because USDC has 6 decimals. A `402` with that price means the middleware is wired to the route.
+
+To see a paid response you need a buyer that signs the authorization and retries the request. The simplest way is the `x402` template of Celo Composer, which ships its own seller and buyer wired to Celo Sepolia (see [x402 paid API](/build/quickstart#x402-paid-api)). Run the seller with `pnpm api:dev` and the buyer with `pnpm api:buy`. The buyer pays the template's own route and prints the response and the settlement transaction, so expect that output rather than the `{"data":"paid content"}` from the server above. The buyer wallet needs test USDC on Celo Sepolia and no CELO.
+
+To charge for the server on this page instead, switch it to Celo Sepolia. Change the `network`, `asset` and `payTo` values to the Celo Sepolia ones under [Celo Configuration](#celo-configuration), and change the facilitator `url` to `https://api.x402.sepolia.celo.org`. The mainnet facilitator does not list Celo Sepolia, so the server fails on startup if the URL stays as it is. Settlement needs the key from the previous section. A paid request then returns `200` with `{"data":"paid content"}` and the payment settles on Celo Sepolia for the price above. At that point you have charged an agent $0.01 in test USDC.
+
 ## x402 on Celo
 
 Celo is an ideal network for x402 due to: