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>Let <span class="math inline">\(k\ge 1\)</span> be an integer. Let <span class="math inline">\(G=(V,E)\)</span> be a connected graph with <span class="math inline">\(n\)</span> vertices and <span class="math inline">\(m\)</span> edges. Suppose fires break out at two adjacent vertices. In each round, a firefighter can protect <span class="math inline">\(k\)</span> vertices, and then the fires spread to all unprotected neighbors. For <span class="math inline">\(uv\in E(G)\)</span>, let <span class="math inline">\(sn_{k}(uv)\)</span> denote the maximum number of vertices the firefighter can save when fires break out at the ends of <span class="math inline">\(uv\)</span>. The <span class="math inline">\(k\)</span>-edge surviving rate <span class="math inline">\(\rho&#39;_k(G)\)</span> of <span class="math inline">\(G\)</span> is defined as the average proportion of vertices saved when the starting vertices of the fires are chosen uniformly at random over all eages, i.e., <span class="math inline">\(\rho&#39;_k(G)=\sum\limits_{uv\in E(G)}sn_{k}(uv)/nm\)</span>. In particular, we write <span class="math inline">\(\rho&#39;(G)=\rho&#39;_1(G)\)</span>. For a given class of graphs <span class="math inline">\(\mathcal{G}\)</span> and a constant <span class="math inline">\(\varepsilon>0\)</span>, we seek the minimum value <span class="math inline">\(k\)</span> such that <span class="math inline">\(\rho&#39;_k(G)>\varepsilon\)</span> for all <span class="math inline">\(G\in \mathcal{G}\)</span>. In this paper, we prove that for Halin graphs, this minimum value is exactly 1. Specifically, every Halin graph <span class="math inline">\(G\)</span> satisfies <span class="math inline">\(\rho&#39;(G)> 1/12\)</span>.</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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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