THE DYNAMICAL MORDELL-LANG CONJECTURE for ENDOMORPHISMS of SEMIABELIAN VARIETIES DEFINED over FIELDS of POSITIVE CHARACTERISTIC
Bibliographic record
Abstract
Let K be an algebraically closed field of prime characteristic p, let X be a semiabelian variety defined over a finite subfield of K, let Phi : X -> X be a regular self-map defined over K, let V subset of X be a subvariety defined over K, and let alpha is an element of X(K). The dynamical Mordell-Lang conjecture in characteristic p predicts that the set S = {n is an element of N: Phi(n)(alpha) is an element of V} is a union of finitely many arithmetic progressions, along with finitely many p-sets, which are sets of the form {Sigma(m)(i=1) c(i) p(ki ni) : n(i) is an element of N} for some m is an element of N, some rational numbers ci and some non-negative integers ki. We prove that this conjecture is equivalent with some difficult diophantine problem in characteristic 0. In the case X is an algebraic torus, we can prove the conjecture in two cases: either when dim(V) <= 2, or when no iterate of 8 is a group endomorphism which induces the action of a power of the Frobenius on a positive...
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How this classification was reachedexpand
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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".