Why this work is in the frame
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Bibliographic record
Abstract
In this work we study the one-dimensional stochastic Kimura equation t u (z, t) = z 2 z u (z, t)+u (z, t) (z, t) for z > 0 and t 0, equipped with constant initial data and the Dirichlet boundary condition at 0, with being a Gaussian space-time noise.This equation can be seen as a degenerate analog of the parabolic Anderson model.We combine the Wiener chaos theory from the Malliavin calculus, the Duhamel perturbation technique from PDEs, and the kernel analysis of (deterministic) degenerate diffusion equations to develop a solution theory for the stochastic Kimura equation.We establish results on existence, uniqueness, moments, and continuity for the solution u (z, t).In particular, we investigate how the stochastic potential and the degeneracy in the diffusion operator jointly affect the properties of u (z, t) near the boundary.We also derive explicit estimates on the comparison under the L 2 -norm between u (z, t) and its deterministic counterpart for (z, t) from a proper range.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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