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
A d-gem is a {+, -, }-circuit having very few -gates and computing from {x} Z a univariate polynomial of degree d having d distinct integer roots. We introduce d-gems because they offer the remote possibility of being helpful for factoring integers and because their existence for infinitely many d would disprove a form of the Blum-Cucker-Shub-Smale conjecture (strengthened to allow arbitrary constants). A natural step towards a better understanding of the BCSS conjecture would thus be to construct d-gems or to rule out their existence. Ruling out d-gems for large d is currently totally out of reach. Here the best we can do towards that goal is to prove that skew 2 n -gems if they exist require n {+, -}-gates and that skew 2 n -gems for any n 5 would provide new solutions to the Prouhet-Tarry-Escott problem in number theory (skew meaning the further restriction that each {+, -}-gate merely adds an integer to a polynomial). In the opposite direction, here we do manage to construct skew d-gems for several values of d up to 55.
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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 | 0.004 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.009 | 0.002 |
| Research integrity | 0.000 | 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