Bibliographic record
Abstract
. There exists an analogy between the structure of ideals of a cone in a right-ordered group and the structure of ideals of a Dubrovin valuation ring in a simple artinian ring . The structure of ideals of rank one cones and rank one Dubrovin valuation rings can be described completely. One sided versions of this problem are considered in [5] where the ideal theory of right cones is developed and a classification of prime segments is given. The description of the two-sided ideals in this case mirrors the results for cones and Dubrovin valuation rings. However , it remains open whether additional ideals can occur in one particular situation. 1 Prime segments in cones of a right-ordered group Let G be a group with a positive cone P , i.e., PP ` P; P [ P \\Gamma1 = G: If in addition P " P \\Gamma1 = feg, the cone P is called a principal cone of G. The right order " r " defined by a r b if and only if ba \\Gamma1 2 P for a; b 2 G is also a left order if and only if aPa \\Gam...
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.024 | 0.004 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".