docs: Add article "UCP Translates AP2 Requirements into Reality"

docs/index.md

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     [:octicons-arrow-right-24: Overview](topics/what-is-ap2.md)<br>
     [:octicons-arrow-right-24: Core Concepts](topics/core-concepts.md)<br>
+    [:octicons-arrow-right-24: AP2 and UCP](topics/ap2-and-ucp.md)<br>
     [:octicons-arrow-right-24: AP2, A2A and MCP](topics/ap2-a2a-and-mcp.md)<br>
     [:octicons-arrow-right-24: AP2 and x402](topics/ap2-and-x402.md)<br>
     [:octicons-arrow-right-24: Privacy and Security](topics/privacy-and-security.md)<br>

docs/topics/ap2-and-ucp.md

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+# UCP Translates AP2 Requirements into Reality
+
+UCP is fully compatible with Agent Payments Protocol (AP2) via its
+[**AP2 Mandates Extension**](https://ucp.dev/specification/ap2-mandates/). When
+this extension is enabled, it captures strong cryptographic evidence of the
+user’s consent to purchase.
+
+This article aims to help bridge the gap between UCP and AP2 terminology, to
+help readers of both protocols understand exactly how UCP is fully
+AP2-compliant.
+
+## The Checkout Object: UCP’s Implementation of the AP2 CartMandate
+
+At the center of every UCP checkout session is the
+[**Checkout Object**](https://ucp.dev/specification/ap2-mandates/#step-1-checkout-creation-signing),
+which serves as the functional equivalent of the **AP2 CartMandate**. Both
+structures exist to formalize the merchant’s offer to the user.
+
+Aligning fully with the AP2 protocol, the UCP Checkout object encapsulates:
+
+*   A clear list of the items being purchased.
+*   A total price breakdown, including tax and shipping.
+*   The merchant’s cryptographic signature ensuring the merchant’s offer remains
+    non-repudiable.
+
+## Proof of User Authorization: From Checkout to Payment Mandate
+
+To finalize a purchase, AP2 requires verifiable proof of user authorization for
+both the purchase and the payment method. UCP implements this by generating and
+signing two distinct cryptographic objects during the checkout flow:
+
+1.  **The CheckoutMandate:** This represents the user's signed authorization of
+    the Checkout object. It provides the merchant with non-repudiable proof of
+    what the user agreed to buy.
+2.  **The PaymentMandate:** This captures the user's authorization of a specific
+    Payment Credential. It serves as proof for the payment network, issuer, and
+    credential vault that the user has sanctioned the use of their credentials
+    for this specific transaction.
+
+Both mandates are provided to the merchant via UCP’s
+[`/complete_checkout`](https://ucp.dev/specification/checkout/#complete-checkout)
+API, with the expectation that the **PaymentMandate** is passed along by the
+merchant to their PSP.