Summary on the proof of BAB Conjecture

Yanning Xu

RECORD

Summary on the proof of BAB Conjecture

Yanning Xu

Algebraic Geometry · Submitted 19 Apr 2018

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

The authors' main claim This is a summary of the proof of BAB conjecture.

how it is stated · asserted 0.99 read the record →

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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, 2,793 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.37 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This is a summary of the proof of BAB conjecture.	contribution 0.84	0.33	0.14	asserted 0.99
s1	All material are taken from the two BAB paper in the reference.	limitation 0.39	0.27	0.03	asserted 1.00
s2	The aim of this summary is to help reader to understand the more technical side of the proof of BAB.	contribution 0.78	0.27	0.06	asserted 0.98

What kind of paper the classifier reports this is: review 0.94 · evidence from literature 0.89.

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

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.

Human review

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How the literature uses it

1 arXiv paper cite this in 2 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 · 1 sentence without a confident label

Cites it as background 1 paper

Bounding the number of blowups is hard, and the next few sentences simplify a very complicated argument to the extreme[see [ref] and [ref] for a more realistic account of all that is involved.].

Boundedness results for singular Fano varieties and applications to Cremona groups · Preparation for the proof of Theorem <ref>thm:lct: $ℝ$-linear systems of bounded degrees · 0.84

What it cites · 25 sentences without a confident label

Uses the method or tool of 1 paper

Using Lemma 2.42 in [ref] , the fact that Cartier Index of $E$ is bounded near on codimensional one points of $S$ and $Γ_Y+N_Y-S$ doesn't intersect $S$, we can pick a bounded $l$ such that we following sequence is exact.

Anti-pluricanonical systems on Fano varieties · Lifting Section from Non-klt Centres · 0.95

Cites as background 1 paper

For the definition of a bounded family of varieties or log bounded family of couples, please see [ref] .

Anti-pluricanonical systems on Fano varieties · Bounded Families of Pairs and Subvarieties · 0.98

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