Weak Gabor bi-frames on periodic subsets of the real line
Why this work is in the frame
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Bibliographic record
Abstract
In this paper, we introduce the concept of weak Gabor bi-frame (WGBF) in a general closed subspace [Formula: see text] of [Formula: see text]. It is a generalization of Gabor bi-frame, and is new even if [Formula: see text]. A WGBF for [Formula: see text] contains all information of [Formula: see text] to some extent. Let [Formula: see text], [Formula: see text], and [Formula: see text] be an [Formula: see text]-periodic subset of [Formula: see text] with positive measure. This paper is devoted to characterizing WGBFs for [Formula: see text] of the form [Formula: see text] It is well-known that, if [Formula: see text], the projections of Gabor frames for [Formula: see text] onto [Formula: see text] cannot cover all Gabor frames for [Formula: see text]. This paper presents a Zak transform-domain and a time-domain characterization of WGBFs for [Formula: see text]. These characterizations are new even if [Formula: see text]. Some examples are also provided to illustrate the generality of our theory.
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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) | 0.000 | 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 | 0.001 |
| 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