k4-e supermagic labeling of triangular ladders
Why this work is in the frame
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Bibliographic record
Abstract
<p>A graph <span class="math inline">\(G=(V,E)\)</span> is <span class="math inline">\(H\)</span>-supermagic if there exists a bijection <span class="math inline">\(f\)</span> from the set <span class="math inline">\(V\cup E\)</span> to the set of integers <span class="math inline">\(\{1,2,3,\dots,|V|+|E|\}\)</span>, called <span class="math inline">\(H\)</span>-supermagic labeling such that the sum of labels of all elements of every induced subgraph of <span class="math inline">\(G\)</span> isomorphic to <span class="math inline">\(H\)</span> is equal to the same integer and all vertex labels are in <span class="math inline">\(\{1,2,3,\dots,|V|\}\)</span>. We present a <span class="math inline">\((K_4-e)\)</span>-supermagic labeling of the triangular ladder <span class="math inline">\(TL_{2n}\)</span> for any <span class="math inline">\(n\geq2\)</span>.</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 | 0.006 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 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