An efficient search strategy for hidden ideals in pointed partially ordered sets
Why this work is in the frame
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Bibliographic record
Abstract
<p>We consider a combinatorial question about searching for an unknown ideal <span class="math inline">\(\mu\)</span> within a known pointed poset <span class="math inline">\(\lambda\)</span>. Elements of <span class="math inline">\(\lambda\)</span> may be queried for membership in <span class="math inline">\(\mu\)</span>, but at most <span class="math inline">\(k\)</span> positive queries are permitted. We provide a general search strategy for this problem, and establish new bounds (based on <span class="math inline">\(k\)</span> and the degree and height of <span class="math inline">\(\lambda\)</span>) for the total number of queries required to identify <span class="math inline">\(\mu\)</span>. We show that this strategy performs asymptotically optimally on the family of complete <span class="math inline">\(\ell\)</span>-ary trees as the height grows.</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 | 0.023 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.000 |
| 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