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
1. The Riemann–Lebesgue Lemma. In its usual form, the Riemann– Lebesgue Lemma reads as follows: If f ∈ L 1 and ˆ f(s) = ∫ ∞ − ∞ eisx f(x) dx is its Fourier transform, then ˆ f(s) exists and is finite for each s ∈ R and ˆf(s) → 0 as |s | → ∞ (s ∈ R). This result encompasses Fourier sine and cosine transforms as well as Fourier series coefficients for functions periodic on finite intervals. When the integral is allowed to converge conditionally, the asserted asymptotic behaviour can fail dramatically. In fact, we show that for each sequence an ↑ ∞ we can find a continuous function f such that ˆ f(s) exists for each s ∈ R and ˆ f(n) ≥ an for all integers n ≥ 1. We also work out the asymptotics of a class of Fourier integrals that can have arbitrarily large polynomial growth. Our main tool is the principle of stationary phase. The conditionally convergent integrals we consider in this paper can be thought of as Henstock integrals [1] or as improper Riemann integrals. Two examples of conditionally convergent Fourier transforms that do not tend to zero at infinity can be obtained from [3, 3.691]: and x=0 x=0 2 sin(ax) cos(ax2} cos(sx) dx = 1
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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