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
Let q be a prime and χ be a non-principal character modulo q. Let f x t ( z ) : = ∑ n = 0 q - 1 χ ( n + t ) z n where 1 ⩽ t ⩽ q is the character polynomial associated to χ (cyclically permuted t places). The principal result is that for any non-principal and non-real character χ modulo q and 1 ⩽ t ⩽ q, ‖ f χ t ( z ) ‖ 4 4 = 4 3 q 2 + O ( q 3 / 2 log 2 q ) where the implicit constant is independent of t and q. Here ∥·∥4 denotes the L4 norm on the unit circle. It follows from this that all cyclically permuted character polynomials associated with non-principal and non-real characters have merit factors that approach 3. This complements and completes results of Golay, Høholdt and Jensen, and Turyn (and others). These results show that the merit factors of cyclically permuted character polynomials associated with non-principal real characters vary asymptotically between 3/2 and 6. The averages of the L4 norms are also computed. Let q be a prime number. Then ∑ χ ( mod q ) ‖ f χ t ‖ 4 4 = ( 2 q - 3 ) ( q - 1 ) 2 where the summation is over all characters modulo q.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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