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E_n Genera

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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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Steven Greg Chadwick, Michael A. Mandell

Algebraic Topology · Submitted 12 Oct 2013

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

The authors' main claim Every map of ring spectra MU to R is represented by a map of E_2 ring spectra.

how it is stated · asserted 1.00 read the record →

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arXiv ID1310.3336 (version 1)
Pith IDPA2UJXIX, Pith's permanent record of this paper and its review
CitationMichael A. Mandell, Steven Greg Chadwick. "E_n Genera." arXiv:1310.3336 (2013). https://pith.science/paper/PA2UJXIX
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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,866 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Let R be an E_2 ring spectrum with zero odd dimensional homotopy groups. Every map of ring spectra MU to R is represented by a map of E_2 ring spectra. If 2 is invertible in pi_0(R), then every map of ring spectra MSO to R is represented by a map of E_2 ring spectra.

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 Let R be an E_2 ring spectrum with zero odd dimensional homotopy groups. background 0.93 0.14 0.03 asserted 0.71
s1 Every map of ring spectra MU to R is represented by a map of E_2 ring spectra. result 0.99 0.74 0.47 asserted 1.00
s2 If 2 is invertible in pi_0(R), then every map of ring spectra MSO to R is represented by a map of E_2 ring spectra. result 0.99 0.71 0.21 asserted 1.00

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 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

Let R be an E_2 ring spectrum with zero odd dimensional homotopy groups. Every map of ring spectra MU to R is represented by a map of E_2 ring spectra. If 2 is invertible in pi_0(R), then every map of ring spectra MSO to R is represented by a map of E_2 ring spectra.

Human review

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How the literature uses it

3 arXiv papers cite this in 9 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 · 3 sentences without a confident label

Builds on it 1 paper
  • The proofs of both of these theorems use the following statement, which is a translation of [ref] to $^Σ()$ with a slight generalization based on [ref] .

    An algebraic model for commutative HZ-algebras · Model structures on algebras over an operad over $^Σ()$ · 0.93

Uses its method or tool 1 paper
Cites it as background 2 papers
  • Other approaches to model structures for commutative monoids in symmetric spectra and rigidification results can be found for instance in work by John Harper [ref] , David White [ref] , and Steven Chadwick and Michael Mandell [ref] .

    An algebraic model for commutative HZ-algebras · Model structures on algebras over an operad over $^Σ()$ · 0.99

  • In light of the recent interest in $E_n$ genera [ref] , the reader may wonder if there are maps $_p→$ that are somewhat compatible with the $E_∞$ multiplications, but not entirely so.

    Commutative S-algebras of prime characteristics and applications to unoriented bordism · Non-existence of Einfty maps · 0.96

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