Modularity of a certain "rank-2 attractor" Calabi-Yau threefold

Neil Dummigan

RECORD

Modularity of a certain "rank-2 attractor" Calabi-Yau threefold

Neil Dummigan

Number Theory · Submitted 21 Feb 2026

abstract compiled · 2026-09-25 · no language-model review

The authors' main claim We attempt to prove that the 4-dimensional Galois representations associated with a certain Calabi-Yau threefold are reducible, with 2-dimensional composition factors coming from specific modular forms of weights 2 and 4, both level 14.

how it is stated · asserted 0.48 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

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, 2026-09-25: 1 request, 3,650 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.93 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.53 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We attempt to prove that the 4-dimensional Galois representations associated with a certain Calabi-Yau threefold are reducible, with 2-dimensional composition factors coming from specific modular forms of weights 2 and 4, both level 14. This was essentially conjectured by Meyer and Verrill. It was revisited in its present form by Candelas, de la Ossa, Elmi and van Straten, whose computations of Euler factors in a whole pencil of Calabi-Yau threefolds highlighted this fibre as one of three overwhelmingly likely to be ``rank-2 attractors''. Unfortunately there is an error in Section 7.

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	We attempt to prove that the 4-dimensional Galois representations associated with a certain Calabi-Yau threefold are reducible, with 2-dimensional composition factors coming from specific modular forms of weights 2 and 4, both level 14.	contribution 0.95	0.65	0.31	asserted 0.48
s1	This was essentially conjectured by Meyer and Verrill.	background 1.00	0.03	0.04	asserted 0.67
s2	It was revisited in its present form by Candelas, de la Ossa, Elmi and van Straten, whose computations of Euler factors in a whole pencil of Calabi-Yau threefolds highlighted this fibre as one of three overwhelmingly likely to be ``rank-2 attractors''.	background 1.00	0.06	0.04	hedged possibility 0.55
s3	Unfortunately there is an error in Section 7.	limitation 1.00	0.70	0.02	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.72 · evidence from proof or derivation 0.40.

What was examined, and what was not

sources read

arXiv listing abstract v2

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 attempt to prove that the 4-dimensional Galois representations associated with a certain Calabi-Yau threefold are reducible, with 2-dimensional composition factors coming from specific modular forms of weights 2 and 4, both level 14. This was essentially conjectured by Meyer and Verrill. It was revisited in its present form by Candelas, de la Ossa, Elmi and van Straten, whose computations of Euler factors in a whole pencil of Calabi-Yau threefolds highlighted this fibre as one of three overwhelmingly likely to be ``rank-2 attractors''. Unfortunately there is an error in Section 7.

Human review

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

References

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

What it cites · 8 sentences without a confident label

Uses the method or tool of 1 paper

Using a $p$-adic method described in [ref] , which employs the Picard-Fuchs differential equation for the periods of the one-parameter family $X_ϕ$, they determined the characteristic polynomial of Frobenius on $H^3_ét(X_ϕ,, _ℓ)$, for the first thousand primes $p≥5$.

Local Zeta Functions From Calabi-Yau Differential Equations · Introduction · 0.94

Uses data or values from 1 paper

Those for $αp$ and $β$ are derived from [ref] , so depend upon the validity of their method of computation, i.e. the conjecture in [ref] .

Local Zeta Functions From Calabi-Yau Differential Equations · Identifying a $2$-dimensional mod $5$ Galois representation · 0.90

Cites as background 1 paper

I thank also Kilian Bönisch for referring me to [ref] , and Marc Mezzarobba for his helpful response to an enquiry.

Time reversal and $\boldsymbol{CP}$ invariance in Calabi-Yau compactifications · The final result · 0.83

Discussion

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