Paper Citation Record · LEDGER

An exact way to verify whether n is a congruent number using Heegner points

As of 12 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2411.14188.

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

pith.paper-citation-record.v1
2411.14188 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T15:35:22.869384Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

17 of 17 outbound references displayed

verified exact0
verified fuzzy12
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 89b5d4e6-c519-47c2-863f-c0b484bf8761 · outbound

This paper cites Milne, Algebraic number theory (v3) , https://www.

An exact way to verify whether n is a congruent number using Heegner points Milne, Algebraic number theory (v3) , https://www

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:23.169560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 00d6c79a-b80e-4db0-be8a-df7e4ddbb8bf · outbound

This paper cites Some remarks on Heegner point computations.

An exact way to verify whether n is a congruent number using Heegner points Some remarks on Heegner point computations

Reference 2

Resolution: metadata mismatch; local_arxiv, observed 2026-08-12T15:35:22.915634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0ee438b5-8090-4dbf-b2bf-93a1636c516b · outbound

This paper cites Buell, Binary quadratic forms - Classical theory and modern comput ations, Springer-Verlag, New York, 1989.

An exact way to verify whether n is a congruent number using Heegner points Buell, Binary quadratic forms - Classical theory and modern comput ations, Springer-Verlag, New York, 1989

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:23.154236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 248a095d-f1c8-4d37-9379-1241f2c7c7b0 · outbound

This paper cites Mordell, On the Riemann hypothesis and imaginary quadratic ﬁelds wit h a given class number , J.

An exact way to verify whether n is a congruent number using Heegner points Mordell, On the Riemann hypothesis and imaginary quadratic ﬁelds wit h a given class number , J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:23.139382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 854476b3-3ab9-44e4-bcc2-263f46b6b68f · outbound

This paper cites an unresolved cited work.

An exact way to verify whether n is a congruent number using Heegner points Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:35:23.123670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3ef17983-ad7b-4538-a3c1-24a8ded70bb5 · outbound

This paper cites Smith, The Congruent Numbers Have Positive Natural Density , https://arxiv.org/pdf/1603.

An exact way to verify whether n is a congruent number using Heegner points Smith, The Congruent Numbers Have Positive Natural Density , https://arxiv.org/pdf/1603

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:23.108279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b3e05568-2f11-46f5-9955-6fcfa85b2059 · outbound

This paper cites Silverman, The arithmetic of elliptic curves , Graduate texts in mathematics 106, Springer- Verlag, New York, 1986.

An exact way to verify whether n is a congruent number using Heegner points Silverman, The arithmetic of elliptic curves , Graduate texts in mathematics 106, Springer- Verlag, New York, 1986

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:23.092806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ef6faa9b-99c2-4a9f-9d51-dd7678fdfe0e · outbound

This paper cites an unresolved cited work.

An exact way to verify whether n is a congruent number using Heegner points Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:35:23.076986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ee52256f-8a4c-4f28-ae1b-c96cb64ac521 · outbound

This paper cites an unresolved cited work.

An exact way to verify whether n is a congruent number using Heegner points Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:35:23.061630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2984abd9-ac9c-4fdd-99a5-2fb2a5aa3f66 · outbound

This paper cites Cohen, A course in computational algebraic number theory , Graduate Texts in Mathematics, Springer-Verlag, New York Inc., 1993.

An exact way to verify whether n is a congruent number using Heegner points Cohen, A course in computational algebraic number theory , Graduate Texts in Mathematics, Springer-Verlag, New York Inc., 1993

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:23.045935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f71ed344-805a-4378-9136-c27aeaa83127 · outbound

This paper cites Diamond and J.

An exact way to verify whether n is a congruent number using Heegner points Diamond and J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:23.030675Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation be0dad8e-cb1c-405b-84df-ce540264fa6b · outbound

This paper cites Gross and D.

An exact way to verify whether n is a congruent number using Heegner points Gross and D

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:23.016232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1800df68-d935-4002-8713-801e4656b6e3 · outbound

This paper cites Buell, Binary quadratic forms-Classical theory and modern comput ations, Springer-Verlag New York Inc., 1989.

An exact way to verify whether n is a congruent number using Heegner points Buell, Binary quadratic forms-Classical theory and modern comput ations, Springer-Verlag New York Inc., 1989

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:22.998944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9771d9aa-cdd7-438a-a4ee-55811e95f258 · outbound

This paper cites Birch and H.P.F Swinnerton-Dyer, Notes on elliptic curves , J.

An exact way to verify whether n is a congruent number using Heegner points Birch and H.P.F Swinnerton-Dyer, Notes on elliptic curves , J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:22.982239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 29bdc80f-c602-445d-8a94-aed2c7ebde40 · outbound

This paper cites an unresolved cited work.

An exact way to verify whether n is a congruent number using Heegner points Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:35:22.966422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 91f8f24f-ea76-424d-a47e-46c48eca942a · outbound

This paper cites Gross, W.

An exact way to verify whether n is a congruent number using Heegner points Gross, W

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:22.949026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4a8396e1-0e85-4140-a491-cdb79ca7ae31 · outbound

This paper cites Knapp, Elliptic curves , Princeton University Press, Princeton, N.J., 1992.

An exact way to verify whether n is a congruent number using Heegner points Knapp, Elliptic curves , Princeton University Press, Princeton, N.J., 1992

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:35:22.932889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

No inbound Pith citation observations are available.