An alternative a pproach to the classification of the regular near hexagons with parameters (s, t, t 2 ) = (2, 11, 1).
Bibliographic record
Abstract
Based on some results of Shult and Yanushka [7], Brouwer [1] proved that there exists a unique regular near hexagon with parameters (s,t, t(2)) = (2, 11, 1), namely the one related to the extended ternary Golay code. His proof relies on the uniqueness of the Witt design S(5, 6,12), Pless's characterization of the extended ternary Golay code G(12) and some properties of S(5, 6,12) and G(12). It is possible to avoid all this machinery and to give an alternative more elementary and self-contained proof for the uniqueness. It was only observed recently by the author that such an alternative proof is implicit in the literature: it can be obtained by combining some results from the papers [1], [4] and [7]. This survey paper has the aim to bring this fact to the attention of the mathematical community. We describe the parts of the above papers which are relevant for this alternative proof of the classification. The alternative proof also requires that we prove a number of extra facts which are not explicitly contained in any of the three above papers. The present paper can also been seen as an addendum to Section 6.5 of the book [3] where the uniqueness of the near hexagon was not proved.
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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 | 0.004 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.009 | 0.004 |
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".