A general criterion for the Pólya-Carlson dichotomy and application
Bibliographic record
Abstract
We prove a general criterion for an irrational power series f ( z ) = ∑ n = 0 ∞ a n z n f(z)=\sum _{n=0}^{\infty }a_nz^n with coefficients in a number field K K to admit the unit circle as a natural boundary. As an application, let F F be a finite field, let d d be a positive integer, let A ∈ M d ( F [ t ] ) A\in M_d(F[t]) be a d × d d\times d -matrix with entries in F [ t ] F[t] , and let ζ A ( z ) \zeta _A(z) be the Artin-Mazur zeta function associated to the multiplication-by- A A map on the compact abelian group F ( ( 1 / t ) ) d / F [ t ] d F((1/t))^d/F[t]^d
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.028 | 0.005 |
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 source (direct Gemma or distilled Codex), 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".