Connecting scalar amplitudes using the positive tropical Grassmannian
Bibliographic record
Abstract
A bstract The biadjoint scalar partial amplitude, $$ {m}_n\left(\mathbbm{I},\mathbbm{I}\right) $$ m n I I , can be expressed as a single integral over the positive tropical Grassmannian thus producing a Global Schwinger Parameterization . The first result in this work is an extension to all partial amplitudes m n ( α , β ) using a limiting procedure on kinematic invariants that produces indicator functions in the integrand. The same limiting procedure leads to an integral representation of ϕ 4 amplitudes where indicator functions turn into Dirac delta functions. Their support decomposes into C n /2−1 regions, with C q the q th -Catalan number. The contribution from each region is identified with a m n /2+1 ( α , $$ \mathbbm{I} $$ I ) amplitude. We provide a combinatorial description of the regions in terms of non-crossing chord diagrams and propose a general formula for ϕ 4 amplitudes using the Lagrange inversion construction. We start the exploration of ϕ p theories, finding that their regions are encoded in non-crossing ( p – 2)-chord diagrams. The structure of the expansion of ϕ p amplitudes in terms of ϕ 3 amplitudes is the same as that of Green functions in terms of connected Green functions in the planar limit of Φ p− 1 matrix models. We also discuss possible connections to recent constructions based on Stokes polytopes and accordiohedra.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
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".