Pith. Sign in

RECORD

Representing integers as a sum of three cubes

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Jon Grantham, P.G. Walsh

Number Theory · Submitted 22 Nov 2022

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

The authors' main claim In particular, a barrier to solving the case $k=3$, which was outlined in a previous paper of the second author, is overcome.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2211.12149 (version 1)
Pith IDOJK27GWP, Pith's permanent record of this paper and its review
CitationJon Grantham, P.G. Walsh. "Representing integers as a sum of three cubes." arXiv:2211.12149 (2022). https://pith.science/paper/OJK27GWP
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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,491 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.48 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.88 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

In this article we further develop methods for representing integers as a sum of three cubes. In particular, a barrier to solving the case $k=3$, which was outlined in a previous paper of the second author, is overcome. A very recent computation indicates that the method is quite favourable to other methods in terms of time estimates. A hybrid of the method presented here and those in a previous paper is currently underway for unsolved cases.

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 In this article we further develop methods for representing integers as a sum of three cubes. contribution 0.94 0.79 0.11 asserted 0.92
s1 In particular, a barrier to solving the case $k=3$, which was outlined in a previous paper of the second author, is overcome. contribution 0.79 0.69 0.40 asserted 1.00
s2 A very recent computation indicates that the method is quite favourable to other methods in terms of time estimates. result 0.78 0.25 0.09 hedged possibility 0.97
s3 A hybrid of the method presented here and those in a previous paper is currently underway for unsolved cases. future work 1.00 0.62 0.05 asserted 0.98

What kind of paper the classifier reports this is: method or tool 0.97 · evidence from proof or derivation 0.70.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
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

In this article we further develop methods for representing integers as a sum of three cubes. In particular, a barrier to solving the case $k=3$, which was outlined in a previous paper of the second author, is overcome. A very recent computation indicates that the method is quite favourable to other methods in terms of time estimates. A hybrid of the method presented here and those in a previous paper is currently underway for unsolved cases.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

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

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.