BATTLE for Bitcoin: Capital-Efficient Optimistic Bridges with Large Committees

We present BATTLE for Bitcoin, a DoS-resilient dispute layer that secures optimistic bridges between Bitcoin and rollups or sidechains. Our design adapts the BATTLE tournament protocol to Bitcoin's UTXO model using BitVM-style FLEX components and garbled circuits with on-demand L1 security bonds. Disputes are resolved in logarithmic rounds while recycling rewards, keeping the honest asserter's minimum initial capital constant even under many permissionless challengers. The construction is fully contestable (challengers can supply higher-work counter-proofs) and relies only on standard timelocks and pre-signed transaction DAGs, without new opcodes. For $N$ operators, the protocol requires $O(N^2)$ pre-signed transactions, signatures, and message exchanges, yet remains practical at $N\!\gtrsim\!10^3$, enabling high decentralization.