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The Degree of a Tropical Root Surface of Type $A$

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Federico Ardila-Mantilla, Mont Cordero-Aguilar

Combinatorics · Submitted 7 Dec 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that the tropical surface of the root system $A_{n-1}$ has degree $\frac{1}{2}n (n-1)(n-2)$.

how it is stated · asserted 1.00 read the record →

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arXiv ID2212.03904 (version 2)
Pith IDCLUNXMIB, Pith's permanent record of this paper and its review
CitationFederico Ardila-Mantilla, Mont Cordero-Aguilar. "The Degree of a Tropical Root Surface of Type $A$." arXiv:2212.03904 (2022). https://pith.science/paper/CLUNXMIB
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,620 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.03 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We prove that the tropical surface of the root system $A_{n-1}$ has degree $\frac{1}{2}n (n-1)(n-2)$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove that the tropical surface of the root system $A_{n-1}$ has degree $\frac{1}{2}n (n-1)(n-2)$. result 0.99 0.95 0.93 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We prove that the tropical surface of the root system $A_{n-1}$ has degree $\frac{1}{2}n (n-1)(n-2)$.

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