Counting functions of magic labelings
Bibliographic record
Abstract
A magic labelling of a set system is a labelling of its points by distinct positive \nintegers so that every set of the system has the same sum, the magic sum. The \nmost famous class of examples are magic squares (the sets are the rows, columns, \nand diagonals of a matrix). It follows from a recent paper by Matthias Beck and \nThomas Zaslavky that the number of n by n magic labellings is a quasipolynomial function of the magic sum, and also of an upper bound on the entries in the square. \nThe contribution of this thesis is to develop software that allows computation of a \nlarge class of examples of generating functions for such counting functions. \nThe software will utilize previously developed programs THAC (developed at \nSFSU) and Latte (developed at UC Davis) to compute intermediate results required \nby the overall computation. The symbolic algebra program Maple (developed at \nthe University of Waterloo, Canada) will be used for final algebraic manipulation \nto achieve the final result which is the generating function of a counting function. \nWhile there are other methods to compute these types of counting functions, \nit is believed that the approach used in this thesis is novel and no such software \nexists.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 0.002 |
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".