Errors in the Introduction of Isometric Coordinates and Violation of the Property of Conformality of the Triaxial Ellipsoid Projections
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Bibliographic record
Abstract
The purpose of this study is to show that some coordinate systems previously described as isometric are in fact not isometric, and as a consequence, map projections derived from them do not show the expected characteristics, especially conformality. Definitions and methods of the mathematical theory of surfaces are used. The article discusses two methods of specifying coordinate systems on the surface of the triaxial ellipsoid, erroneously called isometric. A consistent mathematical study of each of them based on the initial definition of isometric coordinates showed that in the first method, the corresponding coordinate system is not orthogonal, much less isometric. In the second method, the coordinates are determined using integration, and the result of the integration depends on the path of this integration. This ambiguity shows that this method is also incorrect. The considered coordinate systems allow the creation of new projections, but these projections are not conformal. As a result of the study, errors in determining isometric coordinates were shown and proven, which in earlier studies led to a violation of the properties of projections. This analysis should lead to the development of truly conformal projections of triaxial ellipsoids. For clarity maps and cartographic grids are presented.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| 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 it