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
<p>onsidering regions in a map to be adjacent when they have nonempty intersection (as opposed to the traditional view requiring intersection in a linear segment) leads to the concept of a <em>facially complete</em> graph: a plane graph that becomes complete when edges are added between every two vertices that lie on a face. Here we present a complete catalog of facially complete graphs: they fall into seven types. A consequence is that if <span class="math inline">\(q\)</span> is the size of the largest face in a plane graph <span class="math inline">\(G\)</span> that is facially complete, then <span class="math inline">\(G\)</span> has at most <span class="math inline">\(\left\lfloor 3q/2\right\rfloor\)</span> vertices. This bound was known, but our proof is completely different from the 1998 approach of Chen, Grigni, and Papadimitriou (Planar map graphs, <em>Proc. 30th ACM Symp. Th. of Computing</em>, 514–523). Our method also yields a count of the 2-connected facially complete graphs with <span class="math inline">\(n\)</span> vertices. We also show that if a plane graph has at most two faces of size 4 and no larger face, then the addition of both diagonals to each 4-face leads to a graph that is 5-colorable.</p>
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.000 |
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