Zero mean curvature surfaces in Lorentz--Minkowski 3-space which change type across a light-like line
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Bibliographic record
Abstract
It is well-known that space-like maximal surfaces and time-like\nminimal surfaces in Lorentz--Minkowski $3$-space $\\boldsymbol{R}^{3}_{1}$\nhave singularities in general. They are both characterized\nas zero mean curvature surfaces. We are interested in the\ncase where the singular set consists of a light-like line,\nsince this case has not been analyzed before. As a continuation\nof a previous work by the authors, we give the first example\nof a family of such surfaces which change type across a light-like\nline. As a corollary, we also obtain a family of zero mean\ncurvature hypersurfaces in $\\boldsymbol{R}^{n+1}_{1}$ that\nchange type across an ($n-1$)-dimensional light-like plane.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.010 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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