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">\(G = (V, E)\)</span> be a graph with vertex set <span class="math inline">\(V\)</span> and edge set <span class="math inline">\(E\)</span>. A vertex set <span class="math inline">\(S \subset V\)</span> is a <span><em>perfect dominating set</em></span> if every vertex in <span class="math inline">\(V - S\)</span> is adjacent to exactly one vertex in <span class="math inline">\(S\)</span>. A perfect dominating set <span class="math inline">\(S\)</span> is furthermore: (i) an <span><em>efficient dominating set</em></span> or a <span><em><span class="math inline">\(1\)</span>-efficient dominating set</em></span> if no two vertices in <span class="math inline">\(S\)</span> are adjacent, (ii) a <span><em>total efficient dominating set</em></span> or a <span><em><span class="math inline">\(2\)</span>-efficient dominating set</em></span> if every vertex in <span class="math inline">\(S\)</span> is adjacent to exactly one other vertex in <span class="math inline">\(S\)</span>, and (iii) a <span><em><span class="math inline">\(1,2\)</span>-efficient dominating set</em></span> if every vertex in <span class="math inline">\(S\)</span> either adjacent to no vertices in <span class="math inline">\(S\)</span> or to exactly one other vertex in <span class="math inline">\(S\)</span>. In this paper we introduce the concept of <span><em><span class="math inline">\(1,2\)</span>-efficiency</em></span> in graphs and apply it to the existence of <span class="math inline">\(1,2\)</span>-efficient sets in <span><em>grid graphs</em></span> <span class="math inline">\(G_{m,n}\)</span>, that is, graphs resembling chessboards having a rectangular array of <span class="math inline">\(m \times n\)</span> vertices arranged into <span class="math inline">\(m\)</span> rows of <span class="math inline">\(n\)</span> vertices, or <span class="math inline">\(n\)</span> columns of <span class="math inline">\(m\)</span> vertices. It is well known that almost no grid graphs are <span class="math inline">\(1\)</span>-efficient, and relatively few grid graphs are <span class="math inline">\(2\)</span>-efficient. However, in this paper, we show that all but a relatively small percentage of grid graphs are <span class="math inline">\(1,2\)</span>-efficient.</p>
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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 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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