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Counting rational points on algebraic varieties

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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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T.D. Browning, D.R. Heath-Brown, P. Salberger

Number Theory · Submitted 5 Oct 2004

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

The authors' main claim The bounds obtained are uniform in varieties of fixed degree and fixed dimension, and are essentially best possible for varieties of degree at least six.

how it is stated · asserted 0.99 read the record →

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arXiv IDmath/0410117 (version 4)
Pith IDGU343NXY, Pith's permanent record of this paper and its review
CitationD.R. Heath-Brown, P. Salberger, T.D. Browning. "Counting rational points on algebraic varieties." arXiv:math/0410117 (2004). https://pith.science/paper/GU343NXY
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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, 2,864 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.70 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.46 · compares with prior results 0.30 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

Let $Z$ be a projective geometrically integral algebraic variety. This paper is concerned with estimating the number of rational points on $Z$ which have height at most $B$. The bounds obtained are uniform in varieties of fixed degree and fixed dimension, and are essentially best possible for varieties of degree at least six.

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 Let $Z$ be a projective geometrically integral algebraic variety. background 0.99 0.05 0.02 asserted 0.76
s1 This paper is concerned with estimating the number of rational points on $Z$ which have height at most $B$. contribution 0.68 0.60 0.07 asserted 0.93
s2 The bounds obtained are uniform in varieties of fixed degree and fixed dimension, and are essentially best possible for varieties of degree at least six. result 0.97 0.91 0.80 asserted 0.99

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

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  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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

Let $Z$ be a projective geometrically integral algebraic variety. This paper is concerned with estimating the number of rational points on $Z$ which have height at most $B$. The bounds obtained are uniform in varieties of fixed degree and fixed dimension, and are essentially best possible for varieties of degree at least six.

Human review

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1 arXiv paper cite this in 4 sentences

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

Papers citing it · 3 sentences without a confident label

Uses its method or tool 1 paper
  • Instead, we estimate the number of solutions to the Diophantine system of constraints using a result from the mathematical literature [ref] .

    Counting String Theory Standard Models · Introduction and Summary · 0.98

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