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Lattices of type $A_n$, $D_n$, $E_n$ and codes

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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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Riku Higa

Number Theory · Submitted 27 Feb 2025

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

The authors' main claim We propose a construction of lattices from codes corresponding to lattices of type $A_n$, $D_n$ and $E_n$.

how it is stated · asserted 0.96 read the record →

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arXiv ID2502.19753 (version 1)
Pith IDWDII3DL3, Pith's permanent record of this paper and its review
CitationRiku Higa. "Lattices of type $A_n$, $D_n$, $E_n$ and codes." arXiv:2502.19753 (2025). https://pith.science/paper/WDII3DL3
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, 2,911 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.78 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We propose a construction of lattices from codes corresponding to lattices of type $A_n$, $D_n$ and $E_n$. This construction is a generalization of construction A of lattices from $p$-ary codes corresponding to a lattice of type $A_{p-1}$. Moreover, we introduce some examples of application of lattices from the construction to Hilbert modular form.

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 propose a construction of lattices from codes corresponding to lattices of type $A_n$, $D_n$ and $E_n$. contribution 0.99 0.93 0.61 asserted 0.96
s1 This construction is a generalization of construction A of lattices from $p$-ary codes corresponding to a lattice of type $A_{p-1}$. contribution 0.47 0.57 0.14 asserted 1.00
s2 Moreover, we introduce some examples of application of lattices from the construction to Hilbert modular form. contribution 0.93 0.91 0.13 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from proof or derivation 0.98.

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

We propose a construction of lattices from codes corresponding to lattices of type $A_n$, $D_n$ and $E_n$. This construction is a generalization of construction A of lattices from $p$-ary codes corresponding to a lattice of type $A_{p-1}$. Moreover, we introduce some examples of application of lattices from the construction to Hilbert modular form.

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