On characterizing the long-root geometries
Why this work is in the frame
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Bibliographic record
Abstract
Abstract The long-root geometries of symplectic rank at least three are the polar Grassmannians of lines, the metasymplectic spaces, and three Lie incidence geometries of exceptional Lie type. These geometries were characterized as a class of parapolar spaces of symplectic rank at least three satisfying four axioms (see Theorem 1 below). In this note, it is shown that one can dispense with two of the axioms, if one adds to the set of conclusion geometries all strong parapolar spaces of point-diameter 2 for which x ⊥ ∩ S is never a point for any point-symplecton pair ( x , S ). Connections with root filtration spaces are discussed.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it