Mathematical communities work with different objects, invariants, and tools, making cross‑domain problem transfer costly and often omitted. EULER treats such a transfer—a “bridge”—as the unit of search. Around a fixed conjecture, it runs direct, adjacent‑domain, and distant‑domain routes in parallel; a bridge retains its budget only if it supplies an operation the source representation cannot execute and its target‑side evidence returns to the original statement via a checked implication. Six ordered stress tests reject invalid bridges before expensive search begins. We evaluated EULER on 120 recent conjectures that were frozen prior to search, screened for contamination, and drawn from recent papers in the Journal of Combinatorial Theory, Series A. EULER produced 10 proofs, 3 refutations, and 45 scoped partial results. Ablation studies showed two mechanisms that held up: bridge‑specific stress tests cut incorrect conclusions from 9 to 3, and the combination of bridge material with a target‑native operation yielded a +4.2 increase in resolved tasks, a benefit not seen when either factor was used alone. Domain distance did not reliably predict success; the gain from executable operations and a valid return were the decisive factors.
Review