Paper Citation Record · LEDGER

Hilbert's 10th Problem via Mordell curves

As of 13 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2412.04253.

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

pith.paper-citation-record.v1
2412.04253 v2

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T21:53:16.334340Z

measured 22 of 22 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

22 of 22 outbound references displayed

verified exact0
verified fuzzy3
unresolved19
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 95f31f90-79ef-4abe-af6e-180e1a41ea96 · outbound

This paper cites Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field.

Hilbert's 10th Problem via Mordell curves Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T21:53:16.233482Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9a744bd-91f2-474f-88a2-81d2330581f2 · outbound

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

Hilbert's 10th Problem via Mordell curves Integers expressible as the sum of two rational cubes

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-11T21:53:16.239253Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eede168f-7d04-478b-b62d-2aafccb82bb4 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.738070Z

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 540048b7-9734-4ce6-9c8c-d0b6c7e501fe · outbound

This paper cites London Math.

Hilbert's 10th Problem via Mordell curves London Math

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:53:16.725179Z

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 162cc7d4-95b6-4fe8-8b52-d2b371d112fd · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.712282Z

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 bf6c8447-e30e-4f8e-b3af-d1c455815985 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.699661Z

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 8a564e85-d246-4d05-ac48-363c782350e3 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.685733Z

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 f742f7c4-1b77-4a0d-a82c-e3ae5758a2b0 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.673013Z

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 b3aed0ab-0d65-4499-8fd8-3abf04892476 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.659893Z

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 920eea1a-e076-4972-a655-7c3aea8bca41 · outbound

This paper cites $3$-Selmer group, ideal class groups and cube sum problem.

Hilbert's 10th Problem via Mordell curves $3$-Selmer group, ideal class groups and cube sum problem

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T21:53:16.281099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5955ae59-417f-4ae3-bc66-57d80dee8d04 · outbound

This paper cites Binary Cubic Forms and Rational Cube Sum Problem.

Hilbert's 10th Problem via Mordell curves Binary Cubic Forms and Rational Cube Sum Problem

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T21:53:16.286254Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe8ac3b5-081b-4412-8845-1d9727fd7632 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.645976Z

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 d68c75ec-b5c8-4943-bd9b-ef90ed784faa · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T21:53:16.295868Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 31888d81-e974-4631-80a8-603723b052e1 · outbound

This paper cites Dokl., vol.

Hilbert's 10th Problem via Mordell curves Dokl., vol

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:53:16.632670Z

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 716274ea-632b-4139-aa7f-364bf063f868 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.619441Z

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 bd2e04a4-2e9e-4860-9a9f-9394db75f3f0 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.605896Z

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 b65f7140-a8a9-477e-a8e5-0b5bdbccd035 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.591253Z

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 c9c1ba3f-4989-413a-a039-7b3551418d1a · outbound

This paper cites Perelli and J.

Hilbert's 10th Problem via Mordell curves Perelli and J

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:53:16.576293Z

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 30c02815-d181-4a92-b72d-a53ed5bc0368 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.562038Z

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 c2cd549e-bb19-445c-9c58-adf29828a272 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.547923Z

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 b7862091-67c5-4618-8500-0dbd61108256 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.533757Z

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 982f5c99-6619-425a-93cd-c90a89afc208 · outbound

This paper cites an unresolved cited work.

Hilbert's 10th Problem via Mordell curves Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:53:16.519146Z

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.