arXiv:2609.20010v4 Announce Type: replace-cross Abstract: Cross-chain protocols enable applications to exchange messages across blockchains. Under point-to-point configurations, communication depends on a direct connection between the source and destination blockchains, limiting blockchain reachability and requiring additional configurations to connect more blockchains. To quantify this problem, this paper analyzes approximately 25 million mainnet cross-chain transaction events collected from six protocols (Axelar, CCIP, Hyperlane, LayerZero, Relay, and Wormhole) between January and October 2025. The resulting graph covers 286 active blockchains and 11,935 directly connected ordered blockchain pairs. These connections provide a direct reachability of 14.64%, while full direct connectivity would require 81,510 point-to-point configurations. We present XIR, a framework for interoperability across cross-chain protocols based on a verifiable intermediate representation. This representation binds an application message to an ordered record of authenticated cross-chain protocol deliveries, preserving message identity and verification history across protocol boundaries. XIR Gateways and XIR Adapters use this representation to compose existing connections into same-protocol and cross-protocol multi-hop paths. We implement an XIR prototype integrating Hyperlane and LayerZero and evaluate it in local and public-testnet environments. Theoretical analysis and evaluation show that, with correctly configured cross-chain protocol connections, XIR avoids 67,018 additional point-to-point configurations, equivalent to 84.88% of the total required by a point-to-point configuration baseline serving the same reachable pairs, and increases reachability from 14.64% to 96.86% of all ordered blockchain pairs.