Bibliographic record
Abstract
Generalizing the concept of convergency to valued fields, Ostrowski in the 1930s introduced pseudo-convergent sequences. In the present paper we classify pseudo-convergent sequences in right chain domains R according to the prime ideal P associated to the breadth I of the sequence using an ideal theory developed for right cones in groups. The ring R is I-compact if every pseudo-convergent sequence in R with breadth I has a limit in R, and we construct right chain domains R which are I-compact only for right ideals I in particular subsets [Formula: see text] of the set of all right ideals of R. Krull's perfect valuation rings and then Ribenboim's notion of a valuation ring complete par étages, where [Formula: see text] is the minimal set containing the completely prime ideals in a commutative valuation ring, is a special case. For a non-discrete right invariant rank-one right chain domain R there are exactly two possibilities for the set [Formula: see text] if the value group of R is the group of real numbers under addition, and there are infinitely many possibilities for [Formula: see text] in all other cases.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".