Why this work is in the frame
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Bibliographic record
Abstract
The generalized Oberwolfach problem asks for a factorization of the complete graph Kv into prescribed 2-factors and at most a 1-factor. When all 2-factors are pairwise isomorphic and v is odd, we have the classic Oberwolfach problem, which was originally stated as a seating problem: given v attendees at a conference with t circular tables such that the ith table seats ai people and ∑t{i=1} ai = v, find a seating arrangement over the (v-1)/2 days of the conference, so that every person sits next to each other person exactly once. In this paper we introduce the related minisymposium problem, which requires a solution to the generalized Oberwolfach problem on v vertices that contains a subsystem on m vertices. That is, the decomposition restricted to the required m vertices is a solution to the generalized Oberwolfach problem on m vertices. In the seating context above, the larger conference contains a minisymposium of m participants, and we also require that pairs of these m participants be seated next to each other for ⌊(m−1)/2⌋ of the days. When the cycles are as long as possible, i.e. v, m and v − m, a flexible method of Hilton and Johnson provides a solution. We use this result to provide further solutions when v ≡ m ≡ 2 (mod 4) and all cycle lengths are even. In addition, we provide extensive results in the case where all cycle lengths are equal to k, solving all cases when m ∣ v, except possibly when k is odd and v is even.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| 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 | 0.003 |
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 it