Geometric optics expansions for quarter-space boundary value problems III: glancing modes and multiple self-interaction
Bibliographic record
Abstract
This article aims to continue the study of geometric optics expansions for hyperbolic boundary value problems in the quarter-space initiated in [2]. The motivations are linked to the range of effective applicability of the theorem establishing the existence of the geometric optics expansions. Compared to [2], we ameliorate the range of applicability by adding two distinct features. The first one is that now we can consider glancing modes in the expansions by using the results of [17]. The second one, which is proper to quarter-space problems, is that we can now consider rather “complicated” self-interaction phenomena. It is a first step in the study of geometric optics expansions in bounded domains. A direct consequence of the first point of amelioration is that no condition on glancing modes is required to intialize the construction of the geometric optics expansion. It seems to indicate that the expected condition characterizing the strong well-posedness of corner problems, established in [14], can be relaxed to the hyperbolic component of the stable subspace only.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".