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>We introduce the <em>ID-index</em> of a finite simple connected graph. For a graph <span class="math inline">\(G=(V,\ E)\)</span> with diameter <span class="math inline">\(d\)</span>, we let <span class="math inline">\(f:V\longrightarrow \mathbb{Z}\)</span> assign <em>ranks</em> to the vertices. Then under <span class="math inline">\(f\)</span>, each vertex <span class="math inline">\(v\)</span> gets a <em>string</em>, which is a <span class="math inline">\(d\)</span>-vector with the <span class="math inline">\(i\)</span>-th coordinate being the sum of the ranks of the vertices that are of distance <span class="math inline">\(i\)</span> from <span class="math inline">\(v\)</span>. The <em>ID-index</em> of <span class="math inline">\(G\)</span>, denoted by <span class="math inline">\(IDI(G)\)</span>, is defined to be the minimum number <span class="math inline">\(k\)</span> for which there is an <span class="math inline">\(f\)</span> with <span class="math inline">\(|f(V)|=k\)</span>, such that each vertex gets a distinct string under <span class="math inline">\(f\)</span>. We present some relations between ID-graphs, which were defined by Chartrand, Kono, and Zhang, and their ID-indices; give a lower bound on the ID-index of a graph; and determine the ID-indices of paths, grids, cycles, prisms, complete graphs, some complete multipartite graphs, and some caterpillars.</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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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