On the formal analysis of Gaussian optical systems in HOL
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Optics technology is being increasingly used in mainstream industrial and research domains such as terrestrial telescopes, biomedical imaging and optical communication. One of the most widely used modeling approaches for such systems is Gaussian optics, which describes light as a beam. In this paper, we propose to use higher-order-logic theorem proving for the analysis of Gaussian optical systems. In particular, we present the formalization of Gaussian beams and verify the corresponding properties such as beam transformation, beam waist radius and location. Consequently, we build formal reasoning support for the analysis of quasi-optical systems. In order to demonstrate the effectiveness of our approach, we present a case study about the receiver module of a real-world Atacama Pathfinder Experiment (APEX) telescope.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| 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