Paper Citation Record · LEDGER

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

As of 12 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 5 inbound Pith citation observations for arXiv:2501.18774.

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

pith.paper-citation-record.v1
2501.18774 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T22:47:21.185538Z

measured 36 of 36 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 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T21:53:16.233482Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T05:12:12.299682Z

Reference resolution

31 of 31 outbound references displayed

verified exact0
verified fuzzy13
unresolved18
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ee3e8f34-890d-4a68-946d-0bdd422888ff · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.637882Z

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 e827532e-9e04-40d7-a140-18597b5a2251 · outbound

This paper cites Denef, Hilbert's tenth problem for quadratic rings, Proc.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Denef, Hilbert's tenth problem for quadratic rings, Proc

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.628738Z

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 db7347d2-cc49-4f5a-b959-d617d7c2398f · outbound

This paper cites II , Trans.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field II , Trans

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.618449Z

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 daaed00a-5ace-4ce9-a291-1ab0b6fe1d4d · outbound

This paper cites Denef and L.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Denef and L

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.609192Z

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 05ec4769-ef23-445a-b16b-3837df45c805 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.599869Z

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 e596719d-02ec-4a1e-8458-fc0cb65224c1 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.589479Z

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 b7314a5b-9769-4783-a70a-4b178dc8c1b4 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.580126Z

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 2182b2a4-afa0-40e5-a25c-46ede0da2ea4 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.570541Z

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 9d280649-60ed-480c-9d81-80a5dea33439 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-09T22:47:21.110330Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47aae00b-2796-40f0-b921-ff1da797ca7e · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.561083Z

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 f9dd4b10-53b1-46c4-8b11-8e6f2b7adff5 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-09T22:47:21.117569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5964ca4e-337c-41f4-bb9b-26f6742e1c93 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.551849Z

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 f817dc73-c1af-45c8-80b0-e5ffbf6776bf · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.542565Z

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 9b6153c5-2c9c-45a4-996d-fc4bdad09b16 · outbound

This paper cites I , II , J.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field I , II , J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.533634Z

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 9732b109-1351-4e29-a1a5-0270551e459b · outbound

This paper cites Ram Murty and Hector Pasten, Elliptic curves, L -functions, and H ilbert's tenth problem , J.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Ram Murty and Hector Pasten, Elliptic curves, L -functions, and H ilbert's tenth problem , J

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.523897Z

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 65a4abd0-a21a-44fb-8b23-d00199d67e32 · outbound

This paper cites Mazur and K.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Mazur and K

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.514131Z

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 2ef68412-df7f-472b-a7c0-dc874ddfbc36 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.505087Z

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 045927a5-0368-4840-a399-05143bda9a0d · outbound

This paper cites Number Theory 254 (2024), 1--64.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Number Theory 254 (2024), 1--64

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.495374Z

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 216f9d1b-8675-405e-926e-7dbb47f0a701 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.486296Z

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 1d84fd50-1b81-4ba7-b9eb-239de46e9cca · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.477064Z

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 9395a3cf-5b75-4e88-807e-f1de52afd844 · outbound

This paper cites Sci., vol.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Sci., vol

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.466046Z

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 8ae486b9-a5dd-444b-bbd6-5d869e580ab0 · outbound

This paper cites Schaefer, Explicit descent for J acobians of cyclic covers of the projective line , J.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Schaefer, Explicit descent for J acobians of cyclic covers of the projective line , J

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.455379Z

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 4918ed51-1458-4b97-8238-fa381a471482 · outbound

This paper cites Pure Appl.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Pure Appl

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.445381Z

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 72a753ca-f3d6-4f59-813d-6f497fc754b6 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.435456Z

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 c72cd499-e7b1-474f-8009-6a482bfb7d65 · outbound

This paper cites Shapiro and Alexandra Shlapentokh, Diophantine relationships between algebraic number fields, Comm.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Shapiro and Alexandra Shlapentokh, Diophantine relationships between algebraic number fields, Comm

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.425880Z

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 6c71af5b-d930-4941-812f-0e446352da12 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.414624Z

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 916c90e9-5641-45fc-ab46-1453e277fcb1 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.403716Z

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 43593603-cab9-456c-bf4c-17b69d509b0b · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.393911Z

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 c0c30df2-a867-4ff9-bb4a-21428df39a73 · outbound

This paper cites Colecao Atas 16 (1989), 95--108.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Colecao Atas 16 (1989), 95--108

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.384226Z

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 2214255d-9283-4a75-839f-7b8fcd15b101 · outbound

This paper cites an unresolved cited work.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:47:21.374183Z

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 4cf7e8dc-c028-4431-956d-49e3d26f4437 · outbound

This paper cites Number Theory 160 (2016), 148--185.

Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field Number Theory 160 (2016), 148--185

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:47:21.363314Z

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

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

Hilbert's 10th Problem via Mordell curves cites this paper.

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 8a89b105-edf9-4e9b-a009-8740cb20fa1d · inbound

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

Elliptic curves of rank one over number fields 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 2026-08-07T14:58:05.844254Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d5a21e8-fbfc-4881-9337-2300d9c8305e · inbound

Rank one elliptic curves and rank stability cites this paper.

Rank one elliptic curves and rank stability 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 2026-08-07T15:05:02.044849Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 45a1576a-bdc3-4155-8eee-21c49cbe18b0 · inbound

Mazur's growth number conjecture and congruences cites this paper.

Mazur's growth number conjecture and congruences 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 2026-08-07T14:24:24.489658Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84fdd3e0-b376-44d8-b497-5bbee64db2ab · inbound

Martin Davis: An Overview of his Work in Logic, Computer Science, and Philosophy cites this paper.

Martin Davis: An Overview of his Work in Logic, Computer Science, and Philosophy Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:12:12.307521Z

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.