FLOWEDIT: Information-Theoretic Set-Valued Mathematical Reasoning under Conflicting Conditions

Conflicting conditions can turn a mathematical problem from a point-valued task into a set of maximal admissible resolutions. Prompted language models often solve one resolution correctly but omit the rest. We introduce FlowEdit, a training framework for recovering all resolution-conditioned answers in one autoregressive response. Structural boundaries expose the shared analysis, branch hypotheses, and branch answers; dual conditional-information objectives increase hypothesis--answer sufficiency and reduce residual dependence among sibling hypotheses. An $\epsilon$-sufficiency result motivates conditioning separation on the analysis rather than the prompt. On $5{,}000$ synthesized and verified problems across three domains and K* ∈ {1, 2, 3, 4}, FlowEdit-Qwen3-4B reaches $0.47$ exact-set match and $0.51$ information recovery, versus $0.28/0.41$ for the strongest prompted proprietary baseline. On Qwen2.5-3B, matched ablations show that structured SFT, either flow objective alone, and prompt-only conditioning are weaker than the full method.