Paper Citation Record · LEDGER

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning

As of 8 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2509.03129.

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

pith.paper-citation-record.v1
2509.03129 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T11:15:14.835272Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

26 of 26 outbound references displayed

verified exact3
verified fuzzy13
unresolved9
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f394213d-27ed-42a9-a8f4-48842bddc1dc · outbound

This paper cites Babei, B.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Babei, B

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:19.134810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e086239e-a248-4c9b-8ae4-8f584af18c6e · outbound

This paper cites Balakrishnan, W.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Balakrishnan, W

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:18.994875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 559d6072-202a-4712-b6b9-68a594f46ea4 · outbound

This paper cites Bhargava and A.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Bhargava and A

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:18.824816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 981351c2-a4ab-4575-bc1c-b79ad62f25b0 · outbound

This paper cites an unresolved cited work.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:15:18.679618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 411db786-46d0-48a8-9913-ca513da49a5d · outbound

This paper cites Bosma, J.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Bosma, J

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-05T11:15:13.124743Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b555c2b-8ef3-4b4d-a4d4-709efb819dbc · outbound

This paper cites Davies, P.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Davies, P

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:18.394440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7a151136-dd53-4e81-aec8-e45289906495 · outbound

This paper cites Delaunay.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Delaunay

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:18.237457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ac99291a-906e-49a7-a62b-9d34ccb105cf · outbound

This paper cites Delaunay.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Delaunay

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:18.084877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 14f59e23-15f7-406a-95ce-1ef2ffcda1ee · outbound

This paper cites Mathematical Data Science.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Mathematical Data Science

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-05T11:15:13.804801Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c023e15-8b5e-4ccd-a2db-cf6b6d441912 · outbound

This paper cites Goldfeld.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Goldfeld

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:17.924741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 820c70b4-2c35-4861-ab69-8786d3a7f062 · outbound

This paper cites Hastie, R.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Hastie, R

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:17.774742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 09443e0f-2094-4650-ab93-1454d779538e · outbound

This paper cites an unresolved cited work.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:15:17.591509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation eb7a9db4-460f-43fc-ba7d-b58b7dae92e4 · outbound

This paper cites an unresolved cited work.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:15:17.415566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dfc156c1-b6e3-4453-82ca-a6fd31a0d96c · outbound

This paper cites Heath-Brown.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Heath-Brown

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:17.272727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 57d81a8c-1877-4303-87b6-2023184fae4f · outbound

This paper cites Heath-Brown.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Heath-Brown

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:17.094748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ac1a9771-50f5-4e84-b5dc-3a8e9ed659fc · outbound

This paper cites James, D.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning James, D

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:16.955136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c887fa66-fc4c-4c52-b678-190fabeed662 · outbound

This paper cites The L-functions and modular forms database.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning The L-functions and modular forms database

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:16.812194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2435de5a-fad1-48ab-be76-26f722ea2d9c · outbound

This paper cites Poonen and E.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Poonen and E

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:15:16.504751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 83de081a-072a-4126-b3fd-e85b61d01855 · outbound

This paper cites an unresolved cited work.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:15:16.403018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 40ec49d6-0e31-4b02-b712-eafba5ad6c0f · outbound

This paper cites The congruent numbers have positive natural density.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning The congruent numbers have positive natural density

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-05T11:15:15.604743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d9d6c0b1-11ca-41ca-b162-d432ff27afe6 · outbound

This paper cites $2^\infty$-Selmer groups, $2^\infty$-class groups, and Goldfeld's conjecture.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning $2^\infty$-Selmer groups, $2^\infty$-class groups, and Goldfeld's conjecture

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-05T11:15:15.372378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 24a8736f-05de-4d44-8c7e-3dfd6f6c0ac1 · outbound

This paper cites Sagemath, the Sage Mathematics Software System (Version 10.6).

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Sagemath, the Sage Mathematics Software System (Version 10.6)

Reference 22

Resolution: malformed identifier; raw_fallback, observed 2026-08-05T11:15:16.214745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 69c36e72-56b6-4762-8a5b-85c12325c377 · outbound

This paper cites Genus Periods, Genus Points and Congruent Number Problem.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Genus Periods, Genus Points and Congruent Number Problem

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-05T11:15:15.139877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 01624847-b6fb-4366-8a3d-c1a9bcff8f93 · outbound

This paper cites an unresolved cited work.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:15:16.069833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3b9abae0-88a7-4474-a8d4-9cb4c020ada2 · outbound

This paper cites an unresolved cited work.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:15:15.945046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation efcc71ac-2f91-4b0c-950a-c1ae73767f94 · outbound

This paper cites an unresolved cited work.

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning Unresolved cited work

Reference 2025

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:15:16.690454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.