Why this work is in the frame
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Bibliographic record
Abstract
The practice of transport phenomena has traditionally been confined to Cartesian, cylindrical, spherical, and bipolar cylindrical. For just the equations of continuity and motion, Dijksman added toroidal coordinates. Our recent work expanded the geometries available for solving transport problems to include eccentric cylindrical. However, this short list of available coordinate systems cannot describe many geometries encountered in transport phenomena. Here, we address this restriction on available geometries for transport phenomena by adding bispherical coordinates to the growing list of coordinate systems for which the equations of change have been developed. Bispherical coordinates allow us to solve transport problems between eccentric spheres or horns, which spherical coordinates cannot handle. We thus develop the equations of change for this coordinate system and provide three worked examples showing how to get new exact solutions to momentum, heat, and mass transfer problems.
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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 | 0.000 | 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) | 0.001 | 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