Progress in invariant and preserving transforms for the ratio of collinear points in the desargues affine plane skew field
Bibliographic record
Abstract
This paper introduces invariant transforms that preserve the ratio of either two or three points collinear in the Desargues affine plane skew field. The results given here have a clean, geometric presentation based based Desargues affine plan axiomatics and definitions with skew field properties. The main results in this paper, are (1) ratio of two and three points is \emph{Invariant} under transforms: Inversion, Natural Translation, Natural Dilation, Mobi\us Transform, in a line of Desargues affine plane. (2) parallel projection of a pair of lines in the Desargues affine plane preserves the ratio of two and three points, (3) translations in the Desargues affine plane preserve the ratio of 2 and 3 points and (4) dilation in the Desargues affine plane preserve the ratio of 2 and 3 points.
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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 | 0.001 | 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".