Bibliographic record
Abstract
The author of [27] proves that the set of post-critically finite (PCF) polynomials of given degree is a set of bounded height, up to PGL_2-conjugacy. This result is extended to show that the set of monic polynomials g(z) with rational coefficients of given degree such that there exists a d ≥ 2 such that g(z^d) is PCF, is also a set of bounded height. Note that by fixing the degree of a polynomial and algebraic degree of its coefficients, the set of such PCF polynomials is in fact finite, and computable. Bounds on the coefficients for quartic PCF polynomials with rational coefficients are computed, and a search of the resulting space yields 16 distinct conjugacy classes. Infinite families of PCF polynomials containing each of these distinct conjugacy classes are found, giving a lower bound on the number of such conjugacy classes in terms of degree 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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".