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Bibliographic record
Abstract
We introduce an algorithm that samples a set of loop momenta distributed as a given Feynman integrand. The algorithm uses the tropical sampling method and can be applied to evaluate phase-space-type integrals efficiently. We provide an implementation, momtrop , and apply it to a series of relevant integrals from the loop-tree duality framework. Compared to naive sampling methods, we observe convergence speedups by factors of more than 10 6 . Program Title: momtrop CPC Library link to program files: https://doi.org/10.17632/v9mxr9dw2z.1 Developer's repository link: https://github.com/alphal00p/momtrop Licensing provisions: MIT Programming language: Rust Nature of problem: Efficient numerical evaluation of Feynman-type integrals (e.g. phase space or loop-tree duality integrals). Solution method: Efficient sampling of loop momenta distributed as the Feynman measure (i.e. the integrand of a scalar Euclidean Feynman integral) using tropical sampling [1]. The input to the library is the graph associated to the Feynman measure. From the graph a sampler is produced that takes as input a set of uniformly distributed random numbers and returns a (weighted) set of loop momenta. Additional comments including restrictions and unusual features: Memory usage is exponential in the number of propagators of the Feynman integral. There can be numerical instabilities if the parameters are close to a divergent configuration. [1] M. Borinsky, Tropical Monte Carlo quadrature for Feynman integrals, Ann. Inst. H. Poincare D Comb. Phys. Interact. 10 (4) (2023) 635–685. arXiv:2008.12310 , https://doi.org/10.4171/aihpd/158 .
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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 | 0.000 |
| 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 | 0.001 | 0.001 |
| 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