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Record W2972669434 · doi:10.48550/arxiv.1909.05291

A Soft Theorem for the Tropical Grassmannian

2019· preprint· en· W2972669434 on OpenAlexaff
Diego García Sepúlveda, Alfredo Guevara

Bibliographic record

VenuearXiv (Cornell University) · 2019
Typepreprint
Languageen
FieldPhysics and Astronomy
TopicNonlinear Waves and Solitons
Canadian institutionsPerimeter Institute
Fundersnot available
KeywordsGrassmannianMathematicsFactorizationAmplitudeScalar (mathematics)Mathematical physicsCombinatoricsGeneralizationScattering amplitudePhysicsMathematical analysisQuantum mechanicsGeometry

Abstract

fetched live from OpenAlex

We study the soft limit of a recently proposed generalization of the biadjoint scalar amplitudes $m^{(k)}_{n}$, which have been conjectured to have a relation to the tropical Grassmannian $\text{Tr G}(k,n)$. Using the CHY formulation along with the Global Residue Theorem, we prove the soft factorization for $m^{(k)}_{n}$ amplitudes for arbitrary $k$ and $n$. We find that the soft factors are in direct correspondence to vertices of the associahedron $\mathcal{A}_{k-1}$, and hence take the form of $m^{(2)}_{n}$ amplitudes. This entails that all scattering amplitudes of the ordinary biadjoint scalar theory can be interpreted as an infinite family of soft factors. Additionally, Grassmannian duality reveals that generalized amplitudes $m^{(k)}_{n}$ with $k>2$ satisfy not only a soft theorem, but also a non-trivial "hard" theorem. We perform numerical checks of our theorems against previous results for $\text{Tr G}(4,7)$ and $\text{Tr G}(5,8)$, thereby providing strong evidence of their relation with the CHY formulation.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.002
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.005
Threshold uncertainty score0.018

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0010.000
Science and technology studies0.0010.003
Scholarly communication0.0010.002
Open science0.0010.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0050.001

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.

Opus teacher head0.049
GPT teacher head0.203
Teacher spread0.154 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations14
Published2019
Admission routes1
Has abstractyes

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