Bibliographic record
Abstract
Let a smooth curve (hairline crack) split a planar domain into two pieces. We consider a homeomorphism of the domain (hyperelastic deformation), which is a diffeomorphism on each side of the curve. However, the one-sided derivatives along the curve need not match. The goal is to smooth such a deformation near the curve (welding area) to become a diffeomorphism of the entire domain. Apart from interpretations and relevance to engineering practice (strengthening deformed welds), there is a mathematical interest in this subject, beginning with the work of J. Munkres [J. Munkres, Ann. of Math. (2), 72 (1960), pp. 521--554] on smoothing piecewise-differentiable homeomorphisms, and, most recently, approximation of Sobolev homeomorphisms [T. Iwaniec, L. V. Kovalev, and J. Onninen, Arch. Ration. Mech. Anal., 201 (2011), pp. 1047--1067] and monotone Sobolev mappings with diffeomorphisms [T. Iwaniec and J. Onninen, Arch. Ration. Mech. Anal., to appear].
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".