Why this work is in the frame
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Bibliographic record
Abstract
Locus computation is an essential issue in mathematics education, and a traditional feature of Dynamic Geometry software (DGS). The rising of programs merging DGS and Computer Algebra software (CAS) has fostered a combined approach to locus computation, quite performing in standard examples, but demanding an extended theoretical, and the related algorithmic counterpart, able to deal with less conventional situations. Here we formulate—and reflect about, yielding some proposals—on a few pending issues related to the protocols for the computation of parametric families of loci. Then we focus on a different source of difficulties, through the example of the very elementary and classical theorem of Thales. Thus, in the framework of the current development of automated deduction in geometry (ADG) tools, we will show how the automatic discovery of Thales's converse statement might require a locus computation that gives rise to an unexpected family of octic curves. Finally, we will exhibit how the handling (finding the equation, plotting, geometric characterization, etc.) of such curves requires the concourse of DGS and CAS programs, a mixed graphic–symbolic–numeric approach, and human–machine interaction, a cooperation that could be the basis towards achieving the required improvements concerning locus computation software.
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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) | 0.006 | 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 it