A Fast Convergent Error Bound for Gaussian Interpolation
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
It's well known that there is a so-called exponential-type error bound for Gaussian interpolation which is the most powerful error bound hitherto. It's of the formj f (x) s(x)j c1(c2d) c3 dk fk h where f and s are the interpolated and interpolating functions respectively, c1; c2; c3 are positive constants, d is the fill distance which roughly speaking measures the spacing of the data points, andk fkh is the h-norm of f where h is the Gaussian function. The error bound is suitable for x 2 R n ; n 1, and gets small rapidly as d ! 0. The drawback is that the crucial constants c2 and c3 get worse rapidly as n increases in the sense c2! 1 and c3! 0 as n! 1. In this paper we raise an error bound of the form j f (x) s(x)j c 0 (c 0 d) c0 d p dk fk h; where c 0 and c 0 are independent of the dimension n. Moreover, c 0 << c2; c3 << c 0 , and c 0 is only slightly di erent from c1. What's important is that all constants c 0 ; c 0 and c 0 can be computed without slight di culty.
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 | 0.000 | 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) | 0.000 | 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