Paper Citation Record · LEDGER

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations

As of 20 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2606.26993.

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

pith.paper-citation-record.v1
2606.26993 v2

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-01T07:08:11.787292Z

measured 19 of 19 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 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

19 of 19 outbound references displayed

verified exact2
verified fuzzy13
unresolved1
parse uncertain0
malformed identifier1
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4717bb2b-704e-4923-b2c1-86f1ca169a52 · outbound

This paper cites IACR Cryptology ePrint Archive2016, 1157 (2016),http://eprint.iacr.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations IACR Cryptology ePrint Archive2016, 1157 (2016),http://eprint.iacr

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.227364Z

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 e3b345f3-f1d1-4ff2-9c02-a679d0dec37b · outbound

This paper cites Journal de theorie des nombres de Bordeaux16(1), 19–63 (2004).https://doi.org/10.5802/jtnb.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations Journal de theorie des nombres de Bordeaux16(1), 19–63 (2004).https://doi.org/10.5802/jtnb

Reference 2

Resolution: malformed identifier; doi_truncated, observed 2026-07-01T07:15:29.354731Z

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 8bc80c22-4eac-4f90-954d-83955d30d764 · outbound

This paper cites In: EuroS&P.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations In: EuroS&P

Reference 3

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T07:15:29.358677Z

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 2a228700-9eb0-4678-bf3c-7600483df86e · outbound

This paper cites Springer-Verlag (1993).

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations Springer-Verlag (1993)

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.247235Z

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 7a11bbf7-548d-4bcc-ac62-617769ea59f2 · outbound

This paper cites Graduate Texts in Mathematics, Springer New York (2012) 14.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations Graduate Texts in Mathematics, Springer New York (2012) 14

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.251983Z

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 99152275-e7f8-4895-8daa-5f3634207588 · outbound

This paper cites Abhandlungen der Koniglichen Gesellschaft der Wissenschaften in Gottingen23, 3–38 (1878),http://eudml.org/doc/135827.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations Abhandlungen der Koniglichen Gesellschaft der Wissenschaften in Gottingen23, 3–38 (1878),http://eudml.org/doc/135827

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.241050Z

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 31349cec-5aa5-430b-8937-7d93120e51dc · outbound

This paper cites In: Algorithmic Number Theory.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations In: Algorithmic Number Theory

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.249043Z

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 6cbe46aa-7c3e-472c-8b3b-a53df4a2dce9 · outbound

This paper cites Dedekind on Higher Congruences and Index Divisors, 1871 and 1878.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations Dedekind on Higher Congruences and Index Divisors, 1871 and 1878

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-07-01T08:45:35.609482Z

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 15a4200b-378a-4cad-9c15-573f888ebad0 · outbound

This paper cites Foundations of Computational Mathematics13(5), 729–762 (2013).

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations Foundations of Computational Mathematics13(5), 729–762 (2013)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.248139Z

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 21ddb003-4ef0-43c3-b234-dca9f731c48b · outbound

This paper cites Oxford, sixth edn.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations Oxford, sixth edn

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.246436Z

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 f9996ac6-1b4e-4427-a6df-a19b772476ec · outbound

This paper cites In: Algorithmic Number Theory, Third International Symposium, ANTS-III.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations In: Algorithmic Number Theory, Third International Symposium, ANTS-III

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.235002Z

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 5f0a59e4-f9f9-48b3-8a26-e249d1d7748f · outbound

This paper cites an unresolved cited work.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-07-06T16:22:39.239094Z

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 6a4c6c72-5e42-4c67-8e5e-b30e44044ed3 · outbound

This paper cites IACR Cryptology ePrint Archive2018, 1009 (2018),https://eprint.iacr.org/2018/1009.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations IACR Cryptology ePrint Archive2018, 1009 (2018),https://eprint.iacr.org/2018/1009

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.245520Z

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 02123fee-64af-4c99-a4f5-d1fe60cf5414 · outbound

This paper cites In: Advances in Cryptology - EUROCRYPT.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations In: Advances in Cryptology - EUROCRYPT

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.242795Z

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 d867f5e5-8e3a-4171-852f-42f49e50adc5 · outbound

This paper cites In: Proc.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations In: Proc

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.244650Z

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 7ef8f882-1347-4791-a21c-d6895b4ff990 · outbound

This paper cites In: Advances in Cryptology – ASIACRYPT 2021.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations In: Advances in Cryptology – ASIACRYPT 2021

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.231407Z

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 ed5d0cad-80fa-4805-8c12-0a5acc1de97e · outbound

This paper cites Journal fur die reine und angewandte Mathe- matik1985(361), 50–72 (1985).https://doi.org/doi:10.1515/crll.1985.361.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations Journal fur die reine und angewandte Mathe- matik1985(361), 50–72 (1985).https://doi.org/doi:10.1515/crll.1985.361

Reference 17

Resolution: verified exact; doi, observed 2026-07-01T07:15:29.362695Z

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 abdb5512-629e-4304-b62a-254efdd81deb · outbound

This paper cites In: 35th Annual Symposium on Foundations of Computer Science - FOCS.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations In: 35th Annual Symposium on Foundations of Computer Science - FOCS

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T16:22:39.233253Z

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 e7acc456-01f9-4f9a-9c4d-157bcceeee38 · outbound

This paper cites multiplicatively perturbed.

Deterministic and Efficient Ideal Arithmetic via Two-Element Representations multiplicatively perturbed

Reference 19

Resolution: metadata mismatch; doi, observed 2026-07-01T07:15:29.371395Z

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

No inbound Pith citation observations are available.