First-order Definable Retraction Problems for Posets and Reflexive Graphs
Bibliographic record
Abstract
A retraction from a structure P to its substructure Q is a homomorphism from P onto Q that is the identity on Q. We present an algebraic condition which completely characterzies all posets and all reflexive graphs Q such that the class of all posets or reflexive graphs, respectively, that admit a retraction onto Q is first-order definable.
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How this classification was reachedexpand
Direct model labels (unvalidated)
Per-model category and study-design labels from the labeling rounds. They are machine output, unvalidated, and the disagreement between models ships as data. No study design here is MEDLINE-validated yet.
| Model arm | Categories | Study design | Confidence |
|---|---|---|---|
| gemma | no category Domain: not available · Genre: Empirical About the Canadian research system: no · About a Canadian topic: no | Theoretical or conceptual | low |
| gpt | no category Domain: not available · Genre: Empirical About the Canadian research system: no · About a Canadian topic: no | Theoretical or conceptual | high |
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 | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.005 | 0.019 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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, unvalidatedLabeled directly by 2 models reading the full record.
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".