Why this work is in the frame
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Bibliographic record
Abstract
We study spectral and scattering properties of the discrete Laplacian H on the half-space [Formula: see text] with boundary condition ψ(n, -1) = V (n) ψ (n, 0). We consider cases where V is a deterministic function and a random process on Z d . Let H 0 be the Dirichlet Laplacian on [Formula: see text]. We show that the wave operators Ω ± (H, H 0 ) exist for all V, and in particular, that σ (H 0 )⊂ σ ac (H). We study when and where the wave operators are complete and the spectrum of H is purely absolutely continuous, and prove some optimal results. In particular, if V is a random process on a probability space (Ω, ℱ, P), such that the random variables V (n) are independent and have densities, we show that the spectrum of H on σ (H 0 ) is purely absolutely continuous P-a.s. If in addition lim |V(n)| = ∞ P-a.s., we show that the wave operators Ω ± (H, H 0 ) are complete on σ (H 0 ) P-a.s.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.009 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.003 |
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