Bibliographic record
Abstract
In this article we determine all fusions of the association scheme $\mathcal{A} \otimes \mathcal{A}$, where $\mathcal{A}$ is the symmetric rank $3$ association scheme corresponding to a strongly regular graph. This includes both guaranteed fusions, which are fusions for all symmetric rank $3$ association schemes $\mathcal{A}$, and specific case fusions, which exist only under restrictions on the parameters of the association scheme. Along the sections we will determine the fusions of wreath products of strongly regular graphs and the fusions of the tensor square of a symmetric rank $3$ table algebra. This is an extension to the recent work of the authors and Meagher, where we solved the same problem for the generalized Hamming scheme $H(2,\mathcal{A})$ of the association scheme obtained from a strongly regular graph. The main results of this article prove that the families of strongly regular graphs for which $\mathcal{A} \otimes \mathcal{A}$ has a special case fusion are the same families for which $H(2,\mathcal{A})$ has a special case fusion; and that the imprimitive strongly regular graphs are the only family of strongly regular graphs for which the wreath product $\mathcal{A} \wr \mathcal{A}$ has a special case fusion.
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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 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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".