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>An edge-coloring of a graph <span class="math inline">\(G\)</span> with natural numbers <span class="math inline">\(1,2,\ldots\)</span> is called a sum edge-coloring if the colors of edges incident to any vertex of <span class="math inline">\(G\)</span> are distinct and the sum of the colors of the edges of <span class="math inline">\(G\)</span> is minimum. The edge-chromatic sum of a graph <span class="math inline">\(G\)</span> is the sum of the colors of edges in a sum edge-coloring of <span class="math inline">\(G\)</span>. In general, the problem of finding the edge-chromatic sum of an <span class="math inline">\(r\)</span>-regular (<span class="math inline">\(r\geq 3\)</span>) graph is <span class="math inline">\(NP\)</span>-complete. In this paper we provide some bounds on the edge-chromatic sums of various products of graphs. In particular, we give tight upper bounds on the edge-chromatic sums of tensor, strong tensor, Cartesian, strong products and composition of graphs. We also determine the edge-chromatic sums and edge-strengths of the Cartesian products of regular graphs and paths (cycles) with an even number of vertices. Finally, we determine the edge-chromatic sums and edge-strengths of grids, cylinders, and tori.</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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| 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