Twin <i>Sudoku</i> Puzzles and Triplet Solid <i>Sudoku</i> Cubes From Strongly Mutually Distinct Twin <i>Sudoku</i> Tables
Bibliographic record
Abstract
A new class of twinSudokutables (TSTs) is presented. These tables can be divided into both$s \times d$and$d \times s$subtables. They are constructed using the cyclotomic cosets of$Z_n$via two distinct vectors of cyclotomic coset elements and their Kronecker product. We prove that it is possible to generate$m$TSTs that are strongly mutually distinct (SMD), i.e., for every$0\leq i, j \leq m-1$, the$(i,j)$th entry of the tables contains different symbols. We also provide a method to construct$m$different TSTs that can be converted into twin solidSudokutables (TSSTs) as a perfect set of SMD TSSTs in order to make triplet solidSudokucubes (TSSCs). These TSSCs are symmetric cubes so that a cut from any of the six faces is a TSST. As a result, new twinSudokupuzzles (TSPs) and SMDTSPs are obtained that can be used to design new types ofSudokugames.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.060 | 0.008 |
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".