PyEuclid: A Versatile Formal Plane Geometry System in Python
Bibliographic record
Abstract
Abstract We introduce , a unified and versatile Python-based formal system for representing and reasoning about plane geometry problems. designs a new formal language that faithfully encodes geometric information, including diagrams, and integrates two complementary components to perform geometric reasoning: (1) a deductive database with an extensive set of inference rules for geometric properties, and (2) an algebraic system for solving diverse equations involving geometric quantities. By seamlessly combining these components, enables human-like reasoning and supports generating concise reasoning steps (proofs), either fully automatically or through interactive guidance. Benchmark evaluations demonstrate that outperforms existing tools, solving a broader range of problems across both proof generation and calculation tasks. Moreover, holds significant potential for educational use and integration with advanced deep learning systems.
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How this classification was reachedexpand
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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.039 | 0.017 |
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 source (direct Gemma or distilled Codex), 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".