Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Embeddings of graphs on the torus are studied. All 2-cell embeddings of the vertex-transitive graphs on 12 vertices or less are constructed. Their automorphism groups and dual maps are also constructed. A table of embeddings is presented. 1. Toroidal Graphs Let G be a 2-connected graph. The vertex and edge sets of G are V (G) and E(G), respectively. E(G) is a multiset consisting of unordered pairs {u,v}, where u,v 2 V (G), and possibly ordered pairs (v,v), as the graphs G will sometimes have multiple edges and/or loops. We write the pair {u,v} as uv, and the ordered pair (v,v) as vv, which represents a loop on vertex v. If u,v 2 V (G) then u ! v means that u is adjacent to v (and so also v ! u). The reader is referred to Bondy and Murty [2], West [11], or Gross and Tucker [3] for other graph-theoretic terminology. An embedding of a graph on a surface is represented combinatorially by a rotation system [3]. This consists of a cyclic ordering of the incident edges, for each vertex v. Let v be a vertex of G, incident on edges e1,e2,...,ek. We write v ! (e1,e2,...,ek) to indicate the cyclic ordering for v in a rotation system. If some ei is a loop vv, then this loop must appear twice in the cyclic adjacency list (e1,e2,...,ek), because walking around the vertex v along a small circle in the torus will require that a loop vv be crossed twice. Thus, we assume that if ei is a loop vv, there is another e 0 in the list corresponding to the same loop vv. Since every loop must appear twice in the rotation system, a loop contributes two to the degree of a vertex. If ei with endpoints uv is not a loop, then it will appear in the cyclic adjacency list of both vertices u and v. Given ei in the list for u, the corresponding ej in the list for v is given by the rotation sytem. Figure 1 shows an embedding of the complete
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.001 |
| 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it