Reconstruction of convex bodies from moments
Why this work is in the frame
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Bibliographic record
Abstract
We investigate how much information about a convex body can be retrieved<br/>from a finite number of its geometric moments. We give a sufficient condition<br/>for a convex body to be uniquely determined by a finite number of its geometric moments, and we show that among all convex bodies, those which are<br/>uniquely determined by a finite number of moments form a dense set. Further,<br/>we derive a stability result for convex bodies based on geometric moments. It<br/>turns out that the stability result is improved considerably by using another<br/>set of moments, namely Legendre moments. We present a reconstruction algo-<br/>rithm that approximates a convex body using a finite number of its Legendre<br/>moments. The consistency of the algorithm is established using the stabil-<br/>ity result for Legendre moments. When only noisy measurements of Legendre<br/>moments are available, the consistency of the algorithm is established under<br/>certain assumptions on the variance of the noise variables.
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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 | 0.000 | 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) | 0.002 | 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