Paper Citation Record · LEDGER

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two

As of 19 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 1 inbound Pith citation observation for arXiv:2505.22470.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2505.22470 v4

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-19T13:06:11.119310Z

measured 16 of 16 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T08:37:21.571460Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

15 of 15 outbound references displayed

verified exact13
verified fuzzy2
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 38f609ec-9454-4132-8572-33cc9ec8c925 · outbound

This paper cites Integers expressible as the sum of two rational cubes.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two Integers expressible as the sum of two rational cubes

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.141624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 096f7aa0-d660-494f-a866-b1a373651c30 · outbound

This paper cites [BD11] Nils Bruin and Kevin Doerksen.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two [BD11] Nils Bruin and Kevin Doerksen

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T13:07:18.396810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f2aae7ae-55cd-4dc6-9def-94afc93ee297 · outbound

This paper cites Galois module structures and the Hasse principle in twist families via the distribution of Selmer groups.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two Galois module structures and the Hasse principle in twist families via the distribution of Selmer groups

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.170120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ad4bfff8-ef64-4f97-9b6f-9c96574775c5 · outbound

This paper cites Kolyvagin’s work on modular elliptic curves in L-functions and arithmetic (Durham, 1989).London Mathematical Society Lecture Note Series, 153:235–256.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two Kolyvagin’s work on modular elliptic curves in L-functions and arithmetic (Durham, 1989).London Mathematical Society Lecture Note Series, 153:235–256

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T13:07:18.399290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7287ed5d-d2cd-454f-a3bb-8f4df89a4a65 · outbound

This paper cites [KMR14] Zev Klagsbrun, Barry Mazur, and Karl Rubin.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two [KMR14] Zev Klagsbrun, Barry Mazur, and Karl Rubin

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.135722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 05e31e8e-235d-45b9-9625-e0546f41cc92 · outbound

This paper cites [KP25] Peter Koymans and Carlo Pagano.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two [KP25] Peter Koymans and Carlo Pagano

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.187995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3c9ded7e-0ff3-488c-8e43-b422b50235ac · outbound

This paper cites Elliptic curves of rank one over number fields.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two Elliptic curves of rank one over number fields

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.173913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5c4939a9-f7be-49a7-b9e6-5fc0546e0d08 · outbound

This paper cites Sums of rational cubes and the $3$-Selmer group.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two Sums of rational cubes and the $3$-Selmer group

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.148122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5bf6a0bd-441f-4ef7-af9e-f42d0762ee87 · outbound

This paper cites Hasse principle for intersections of two quadrics via Kummer surfaces.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two Hasse principle for intersections of two quadrics via Kummer surfaces

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.177757Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e0c7c525-c9e6-4cb7-b21a-b36b9df02cba · outbound

This paper cites Infinitely many elliptic curves over $\mathbb{Q}(i)$ with rank 2 and $j$-invariant 1728.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two Infinitely many elliptic curves over $\mathbb{Q}(i)$ with rank 2 and $j$-invariant 1728

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.165437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 41122515-e88e-4fbf-a4dd-c5ab9c21362d · outbound

This paper cites The distribution of $\ell^\infty$-Selmer groups in degree $\ell$ twist families I.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two The distribution of $\ell^\infty$-Selmer groups in degree $\ell$ twist families I

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.123826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 589e518c-1884-4c57-88e8-24f530ba3c1b · outbound

This paper cites The distribution of $\ell^{\infty}$-Selmer groups in degree $\ell$ twist families II.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two The distribution of $\ell^{\infty}$-Selmer groups in degree $\ell$ twist families II

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.154871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3b29240c-651e-46f9-8cf9-234a92612b09 · outbound

This paper cites The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.182734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9a33b257-0306-4323-990c-f84243e3d79d · outbound

This paper cites Rank one elliptic curves and rank stability.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two Rank one elliptic curves and rank stability

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.129530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 13f364ad-c0cc-4edb-b8a4-e494d0782b03 · outbound

This paper cites There are infinitely many elliptic curves over the rationals of rank 2.

Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two There are infinitely many elliptic curves over the rationals of rank 2

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-19T13:07:18.160140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation bfe4904c-3789-4f02-afa9-9036d638355e · inbound

Logarithmic Density of Rank $\geq 1$ and Rank $\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography cites this paper.

Logarithmic Density of Rank $\geq 1$ and Rank $\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-03T08:37:21.571460Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.