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Statistical Topology of Real Polynomials. I: Two Variables

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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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George Khimshiashvili, Alexander Ushveridze

High Energy Physics - Theory · Submitted 21 Aug 1996

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

The authors' main claim In particular, for polynomials of two variables, asymptotics of the average gradient degree for large values of n is determined.

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arXiv IDhep-th/9608146 (version 1)
Pith IDU6NTP5T6, Pith's permanent record of this paper and its review
CitationAlexander Ushveridze, George Khimshiashvili. "Statistical Topology of Real Polynomials. I: Two Variables." arXiv:hep-th/9608146 (1996). https://pith.science/paper/U6NTP5T6
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,229 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.02 · states quantitative result 0.26 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We investigate average gradient degree of normal random polynomials of fixed algebraic degree n. In particular, for polynomials of two variables, asymptotics of the average gradient degree for large values of n is determined.

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 investigate average gradient degree of normal random polynomials of fixed algebraic degree n. contribution 0.99 0.91 0.09 asserted 0.75
s1 In particular, for polynomials of two variables, asymptotics of the average gradient degree for large values of n is determined. result 0.94 0.92 0.70 asserted 1.00

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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not examined
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  • T body sentences
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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 investigate average gradient degree of normal random polynomials of fixed algebraic degree n. In particular, for polynomials of two variables, asymptotics of the average gradient degree for large values of n is determined.

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