Keep the Chain Alive: Bridge-Survival Compression for Multi-Hop Question Answering

Multi-hop question answering reads long retrieved contexts, so compression governs both the cost and the correctness of that reading. Current compressors, however, drop the bridge entities that connect one hop to the next, making the answer entity in the context unreachable. We propose a dual-paradigm theory of compression that organizes the scattered field into one design space. The quality paradigm attributes every compressor's losses to selection, generation, and arrangement, and identifies bridge survival as the fatal channel for multi-hop questions, one that obeys a product law and collapses exponentially with depth. The overhead paradigm prices compressor, reader, auxiliary, and amortized training, and yields a deployment criterion under which single-call compression is a necessity. We instantiate the theory as ChainPack, a single model trained to keep bridges alive through survival-filtered self-training. Across three full-scale multi-hop benchmarks, one call cuts 90% of the tokens and improves accuracy over the uncompressed context (+3.8 points, full-scale paired), stays within 4 points of the oracle bound on 3-4 hop chains, and on a stronger base model even surpasses this selection ceiling. The theory locates the common failure of existing compressors in bridge survival rather than selection, and the remaining headroom in readers rather than in better compression.