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Integral points on conic log K3 surfaces

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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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Yonatan Harpaz

Algebraic Geometry · Submitted 16 Nov 2015

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

The authors' main claim Adapting a powerful method of Swinnerton-Dyer, we give explicit sufficient conditions for the existence of integral points on certain schemes which are fibered into affine conics.

how it is stated · asserted 1.00 read the record →

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arXiv ID1511.04876 (version 2)
Pith IDFV6OIDWF, Pith's permanent record of this paper and its review
CitationYonatan Harpaz. "Integral points on conic log K3 surfaces." arXiv:1511.04876 (2015). https://pith.science/paper/FV6OIDWF
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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, 2,904 input tokens.

What the abstract itself states, as probabilities: claims first 0.93 · states limitation 0.45 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.67 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Adapting a powerful method of Swinnerton-Dyer, we give explicit sufficient conditions for the existence of integral points on certain schemes which are fibered into affine conics. This includes, in particular, cases where the scheme is geometrically a smooth log K3 surface. To the knowledge of the author, this is the first family of log K3 surfaces for which such conditions are established.

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 Adapting a powerful method of Swinnerton-Dyer, we give explicit sufficient conditions for the existence of integral points on certain schemes which are fibered into affine conics. contribution 0.89 0.95 0.82 asserted 1.00
s1 This includes, in particular, cases where the scheme is geometrically a smooth log K3 surface. interpretation 0.53 0.71 0.13 asserted 0.97
s2 To the knowledge of the author, this is the first family of log K3 surfaces for which such conditions are established. gap 0.56 0.54 0.20 asserted 0.92

What kind of paper the classifier reports this is: theoretical result 0.98 · 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

Adapting a powerful method of Swinnerton-Dyer, we give explicit sufficient conditions for the existence of integral points on certain schemes which are fibered into affine conics. This includes, in particular, cases where the scheme is geometrically a smooth log K3 surface. To the knowledge of the author, this is the first family of log K3 surfaces for which such conditions are established.

Human review

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What this paper does with the arXiv papers it cites

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

What it cites · 2 sentences without a confident label

Cites as background 1 paper

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