Planar matrices and arrays of Feynman diagrams: poles for higher <i>k</i>
Bibliographic record
Abstract
Abstract Planar arrays of tree diagrams were introduced as a generalization of Feynman diagrams that enable the computation of biadjoint amplitudes m n ( k ) for k > 2. In this follow-up work, we investigate the poles of m n ( k ) from the perspective of such arrays. For general k, we characterize the underlying polytope as a Flag Complex and propose a computation of the amplitude-based solely on the knowledge of the poles, whose number is drastically less than the number of the full arrays. As an example, we first provide all the poles for the cases (k, n) = (3, 7), (3, 8), (3, 9), (3, 10), (4, 8) and (4, 9) in terms of their planar arrays of degenerate Feynman diagrams. We then implement simple compatibility criteria together with an addition operation between arrays and recover the full collections/arrays for such cases. Along the way, we implement hard and soft kinematical limits, which provide a map between the poles in kinematic space and their combinatoric arrays. We use the operation to give a proof of a previously conjectured combinatorial duality for arrays in (k, n) and (n − k, n). We also outline the relation to boundary maps of the hypersimplex Δ k,n and rays in the tropical Grassmannian Tr ( k , n ) .
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 0.002 |
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".