Bibliographic record
Abstract
We study EFX orientations of multigraphs with self-loops. In this setting, vertices represent agents, edges represent goods, and a good provides positive utility to an agent only if it is incident to the agent. We focus on the bi-valued symmetric case in which each edge has equal utility to both incident agents, and edges have one of two possible utilities α > β ≥0. In contrast with the case of simple graphs for which bipartiteness implies the existence of an EFX orientation, we show that deciding whether a symmetric multigraph G of any multiplicity q ≥ 2 has an EFX orientation is NP-complete even if G is bipartite, α > qβ, and G contains a structure called a non-trivial odd multitree (NTOM). Moreover, we show that NTOMs are a problematic structure in the sense that even very simple NTOMs can fail to have EFX orientations, and multigraphs that do not contain NTOMs always have EFX orientations that can be found in polynomial-time.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".