Planar matrices and arrays of Feynman diagrams
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Bibliographic record
Abstract
Abstract Recently, planar collections of Feynman diagrams were proposed by Borges and one of the authors as the natural generalization of Feynman diagrams for the computation of k = 3 biadjoint amplitudes. Planar collections are one-dimensional arrays of metric trees satisfying an induced planarity and compatibility condition. In this work, we introduce planar matrices of Feynman diagrams as the objects that compute k = 4 biadjoint amplitudes. These are symmetric matrices of metric trees satisfying compatibility conditions. We introduce two notions of combinatorial bootstrap techniques for finding collections from Feynman diagrams and matrices from collections. As applications of the first, we find all 693, 13 612 and 346 710 collections for ( k , n ) = (3, 7), (3, 8) and (3, 9), respectively. As applications of the second kind, we find all 90 608 and 30 659 424 planar matrices that compute ( k , n ) = (4, 8) and (4, 9) biadjoint amplitudes, respectively. As an example of the evaluation of matrices of Feynman diagrams, we present the complete form of the (4, 8) and (4, 9) biadjoint amplitudes. We also start a study of higher-dimensional arrays of Feynman diagrams, including the combinatorial version of the duality between ( k , n ) and ( n − k , n ) objects.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 it