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Natural models of theories of green points

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Juan Diego Caycedo, Boris Zilber

Logic · Submitted 14 Jan 2014

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

The authors' main claim We explicitly present expansions of the complex field which are models of the theories of green points in the multiplicative group case and in the case of an elliptic curve without complex multiplication defined over $\mathbb{R}$.

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arXiv ID1401.3326 (version 1)
Pith IDUEJP5K7H, Pith's permanent record of this paper and its review
CitationBoris Zilber, Juan Diego Caycedo. "Natural models of theories of green points." arXiv:1401.3326 (2014). https://pith.science/paper/UEJP5K7H
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,019 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.93 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We explicitly present expansions of the complex field which are models of the theories of green points in the multiplicative group case and in the case of an elliptic curve without complex multiplication defined over $\mathbb{R}$. In fact, in both cases we give families of structures depending on parameters and prove that they are all models of the theories, provided certain instances of Schanuel's conjecture or an analogous conjecture for the exponential map of the elliptic curve hold. In the multiplicative group case, however, the results are unconditional for generic choices of the parameters.

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 explicitly present expansions of the complex field which are models of the theories of green points in the multiplicative group case and in the case of an elliptic curve without complex multiplication defined over $\mathbb{R}$. contribution 0.86 0.95 0.59 asserted 1.00
s1 In fact, in both cases we give families of structures depending on parameters and prove that they are all models of the theories, provided certain instances of Schanuel's conjecture or an analogous conjecture for the exponential map of the elliptic curve hold. limitation 0.40 0.93 0.27 asserted 0.85
s2 In the multiplicative group case, however, the results are unconditional for generic choices of the parameters. result 0.87 0.89 0.16 asserted 1.00

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

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  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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 explicitly present expansions of the complex field which are models of the theories of green points in the multiplicative group case and in the case of an elliptic curve without complex multiplication defined over $\mathbb{R}$. In fact, in both cases we give families of structures depending on parameters and prove that they are all models of the theories, provided certain instances of Schanuel's conjecture or an analogous conjecture for the exponential map of the elliptic curve hold. In the multiplicative group case, however, the results are unconditional for generic choices of the parameters.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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