Описание скрученных линейных рекуррент максимального периода в терминах мультипликаторов
Bibliographic record
Abstract
Let P = GF(q) be a field, F = GF(q n ) be an extension of P .We construct a wide class of skew MP-polynomials over F by the description of multipliers of skew MP LRS.For P -skew MP LRS v over F we call linear transformation ψ (generalized) multiplier if there exists a number l ≥ 0 such that ψ(v(i)) = v(i + l), i ≥ 0. Denote by M(v) * the set of all multipliers of a skew MP LRS v, andis a field and M(v) ∼ = F if and only if v is linearized.Sufficient conditions for M(v) ∼ = P are given.It is proved that for any P -skew MP LRS v there exists a transformation ψ such that the sequence ψ(v) is M(v)-skew MP LRS of the same order, and for any field K < F there exists MP LRS v such that M(v) ∼ = K.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.015 | 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".