Modern blockchain ecosystems comprise many heterogeneous networks, creating a growing need for interoperability. Cross-chain bridges provide the core infrastructure for this interoperability by enabling verifiable state transitions that move assets and liquidity across chains. While prior work has focused mainly on bridge design and security, the system-level and economic consequences of cross-chain liquidity interoperability remain less understood. We present a large-scale empirical measurement study of cross-chain interoperability using a dataset spanning 20 blockchains and 16 major bridge protocols from 2022 to 2025. We model the multi-chain ecosystem as a time-varying weighted hypergraph and introduce two complementary metrics. Structural interoperability captures connectivity created by deployed bridge infrastructure, reflecting bridge coverage and redundancy independent of user behavior. Active interoperability captures realized cross-chain usage, measured by normalized transfer activity. This decomposition separates infrastructure capacity from actual utilization and yields several findings. The cross-chain network evolves from a sparse hub-and-spoke structure into a denser multi-hub core led by EVM-compatible chains. Bridge expansion and chain growth are uneven: some chains achieve broad structural access but limited realized usage, whereas others concentrate activity through a small set of routes. Overall, interoperability provision and interoperability use diverge substantially, showing that connectivity alone does not imply economically meaningful integration. These results provide a measurement framework for understanding how cross-chain infrastructure reshapes blockchain market structure and liquidity organization.

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