Paper Overview
Field: Machine Learning Authors: Ren Zhenzhuo arXiv: 2509.00009
Original Abstract
Mathematical communities work with different objects, invariants, and tools, so transferring a problem across them is expensive and often skipped. EULER is a multi-agent system that takes such a transfer—a *bridge*—as its unit of search. Around a fixed conjecture, EULER runs direct, adjacent-domain, and distant-domain routes in competition. A bridge keeps its budget only if it supplies an operation the source representation cannot execute and its target-side evidence returns to the original statement along a checked implication. Six ordered stress tests reject invalid bridges before expensive search begins.
Evaluation
EULER was tested on 120 recent conjectures that were frozen before search, screened for contamination, and drawn from public papers by authors who had recently published in the *Journal of Combinatorial Theory, Series A* (a leading combinatorics journal).
Results
- 10 proofs and 3 disproofs produced
- 45 scoped partial results
- Bridge-specific stress tests reduced false conclusions from 9 to 3
- Combining bridge material with target-native operations yielded a +4.2 positive interaction on solved tasks—an effect neither factor achieved alone
- Domain distance did not reliably predict success; executable operation gain and valid return did
Chinese Abstract (from forum)
The forum post includes a Chinese summary noting that cross-community problem transfer is costly and often skipped, and that EULER treats the bridge as the fundamental search unit with budget retention tied to evidence-checked implication returns.
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*Source: zhichai.net forum post, collected 2026-09-03.*