Bibliographic record
Abstract
A bstract A generalization of the scattering equations on X (2 , n ), the configuration space of n points on ℂℙ 1 , to higher dimensional projective spaces was recently introduced by Early, Guevara, Mizera, and one of the authors. One of the new features in X ( k, n ) with k > 2 is the presence of both regular and singular solutions in a soft limit. In this work we study soft limits in X (3 , 7), X (4 , 7), X (3 , 8) and X (5 , 8), find all singular solutions, and show their geometrical configurations. More explicitly, for X (3 , 7) and X (4 , 7) we find 180 and 120 singular solutions which when added to the known number of regular solutions both give rise to 1 272 solutions as it is expected since X (3 , 7) ∼ X (4 , 7). Likewise, for X (3 , 8) and X (5 , 8) we find 59 640 and 58 800 singular solutions which when added to the regular solutions both give rise to 188 112 solutions. We also propose a classification of all configurations that can support singular solutions for general X ( k, n ) and comment on their contribution to soft expansions of generalized biadjoint amplitudes.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".