Why this work is in the frame
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Bibliographic record
Abstract
Consider A an abelian variety of dimension r defined over Q. Assume that rankQA≥g, where g≥0 is an integer, and let a1,…,ag∈A(Q) be linearly independent points. (So, in particular, a1,…,ag have infinite order, and if g=0, then the set {a1,…,ag} is empty.) For p a rational prime of good reduction for A, let A¯ be the reduction of A at p, let a¯i for i=1,…,g be the reduction of ai (modulo p), and let 〈a¯1,…,a¯g〉 be the subgroup of A¯(Fp) generated by a¯1,…,a¯g. Assume that Q(A[2])=Q and Q(A[2],2−1a1,…,2−1ag)≠Q. (Note that this particular assumption Q(A[2])=Q forces the inequality g≥1, but we can take care of the case g=0, under the right assumptions, also.) Then in this article, in particular, we show that the number of primes p for which A¯(Fp)〈a¯1,…,a¯g〉 has at most (2r−1) cyclic components is infinite. This result is the right generalization of the classical Artin’s primitive root conjecture in the context of general abelian varieties; that is, this result is an unconditional proof of Artin’s conjecture for abelian varieties. Artin’s primitive root conjecture (1927) states that, for any integer a≠±1 or a perfect square, there are infinitely many primes p for which a is a primitive root (modp). (This conjecture is not known for any specific a.)
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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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