The continuous wavelet transform in n-dimensions
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Daubechies obtained the [Formula: see text]-dimensional inversion formula for the continuous wavelet transform of spherically symmetric wavelets in [Formula: see text] with convergence interpreted in the [Formula: see text]-norm. From the wavelet [Formula: see text], Daubechies generated a doubly indexed family of wavelets [Formula: see text] by restricting the dilation parameter [Formula: see text] to be a real number greater than zero and the translation parameter [Formula: see text] belonging to [Formula: see text]. We show that [Formula: see text] can be chosen to be in [Formula: see text] with none of the components [Formula: see text] vanishing. Further, we prove that if [Formula: see text] and [Formula: see text] are continuous in [Formula: see text], then the convergence besides being in [Formula: see text] is also pointwise in [Formula: see text]. We advance our theory further to the case when [Formula: see text] and [Formula: see text] both belong to [Formula: see text] then convergence of the wavelet inversion formula is pointwise at all points of continuity of [Formula: see text]. This result significantly enhances the applicability of the wavelet inversion formula to the image processing.
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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 | 0.007 |
| 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