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The envelope of lines meeting a fixed line that are tangent to two spheres

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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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Gábor Megyesi (UMIST), Frank Sottile (Texas A&M University)

Algebraic Geometry · Submitted 23 Apr 2003

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

The authors' main claim All such configurations are degenerate.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0304346 (version 2)
Pith IDUM3NBEA6, Pith's permanent record of this paper and its review
CitationFrank Sottile (Texas A&M University), G\'abor Megyesi (UMIST). "The envelope of lines meeting a fixed line that are tangent to two spheres." arXiv:math/0304346 (2003). https://pith.science/paper/UM3NBEA6
Claim paper

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, 2,930 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.31 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.19 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also meet the given line. All such configurations are degenerate. The path to this result involves the interplay of some beautiful and intricate geometry of real surfaces in 3-space, complex algebraic geometry, explicit computation and graphics.

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 study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also meet the given line. contribution 0.98 0.93 0.16 asserted 0.99
s1 All such configurations are degenerate. result 0.99 0.83 0.72 asserted 1.00
s2 The path to this result involves the interplay of some beautiful and intricate geometry of real surfaces in 3-space, complex algebraic geometry, explicit computation and graphics. method 0.99 0.72 0.03 asserted 0.92

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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 study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also meet the given line. All such configurations are degenerate. The path to this result involves the interplay of some beautiful and intricate geometry of real surfaces in 3-space, complex algebraic geometry, explicit computation and graphics.

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