Paper Citation Record · LEDGER

Symbolic Generation and Modular Embedding of High-Quality abc-Triples

As of 12 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2506.10039.

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

pith.paper-citation-record.v1
2506.10039 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:57:18.380047Z

measured 18 of 18 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

18 of 18 outbound references displayed

verified exact0
verified fuzzy16
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 05e4a76c-af0d-43bd-a62c-6503d614b0e8 · outbound

This paper cites an unresolved cited work.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:57:18.569503Z

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 dc0ffb2b-86d2-4f6c-8cb8-44d7521eb488 · outbound

This paper cites th’eorème.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples th’eorème

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.560642Z

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 abd0a5aa-0e36-4508-b9fd-3f763acb1688 · outbound

This paper cites Silverman.The Arithmetic of Elliptic Curves.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Silverman.The Arithmetic of Elliptic Curves

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.552303Z

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 cb829687-876b-445c-89d9-e14f70f34f62 · outbound

This paper cites The abc conjecture implies the mordell conjecture.Expositiones Mathematicae, 24(1):1–9, 2006.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples The abc conjecture implies the mordell conjecture.Expositiones Mathematicae, 24(1):1–9, 2006

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.542714Z

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 29bbe0c3-c358-4606-af98-57d786b8bcc2 · outbound

This paper cites Inter-universal teichm"uller theory i–iv.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Inter-universal teichm"uller theory i–iv

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.534029Z

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 42edeb1c-5f9d-401e-97ab-f653deb03f30 · outbound

This paper cites Browkin and J.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Browkin and J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.525311Z

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 0ca4cab0-5aa2-4ab2-ae98-aba775779a82 · outbound

This paper cites Abc allows us to count squarefrees.International Mathematics Research Notices, (19):991–1009, 1998.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Abc allows us to count squarefrees.International Mathematics Research Notices, (19):991–1009, 1998

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.516461Z

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 fd01aa92-f022-4b75-9813-2c56ea4ee52e · outbound

This paper cites Abc conjecture verified forc< 1018.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Abc conjecture verified forc< 1018

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.505509Z

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 d8855aef-19a4-488c-a0a1-f41216eb21e9 · outbound

This paper cites Contemporary Abstract Algebra.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Contemporary Abstract Algebra

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.495423Z

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 167a6814-4484-4f44-ad9d-bc7d1f43905d · outbound

This paper cites Differential power analysis.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Differential power analysis

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.485489Z

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 d22f662c-8e90-456d-aecb-f76d45a0d361 · outbound

This paper cites Recommendation for the entropy sources used for random bit generation.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Recommendation for the entropy sources used for random bit generation

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.476074Z

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 a41cb62d-5cd2-4a6e-866a-46444df0c9ac · outbound

This paper cites Silverman.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Silverman

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.466972Z

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 19370254-7d22-4ec6-94bf-56df9543a320 · outbound

This paper cites Bos, Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim Lyubashevsky, Jesper M.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Bos, Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim Lyubashevsky, Jesper M

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.456409Z

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 0ac87e2a-dc76-42cd-bd8b-6e292f2cbf71 · outbound

This paper cites Bernstein, Timothy Chou, and Peter Schwabe.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Bernstein, Timothy Chou, and Peter Schwabe

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.445417Z

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 5d8e7181-199a-478f-9ee6-947266d67ce0 · outbound

This paper cites A Course in Number Theory and Cryptography.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples A Course in Number Theory and Cryptography

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.434992Z

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 5ff682ef-637c-4a91-a0da-1cab1864cb48 · outbound

This paper cites Explicit abc-triples of large quality.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Explicit abc-triples of large quality

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.424703Z

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 8ff5e93c-a9d5-478d-9cd8-d4ac565a4cbd · outbound

This paper cites Borwein, Kevin G.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Borwein, Kevin G

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:18.414050Z

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 826ffbce-7c65-4ce9-8f0a-4cc7970c244d · outbound

This paper cites an unresolved cited work.

Symbolic Generation and Modular Embedding of High-Quality abc-Triples Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:57:18.403348Z

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.