Paper Citation Record · LEDGER

Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges

As of 17 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2108.09311.

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

pith.paper-citation-record.v1
2108.09311 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 4 of 4 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:38:01.578186Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T10:06:52.153739Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation e292748d-dc0d-4ab2-bde6-915d2e01bef7 · inbound

A single point as a Calabi-Yau zerofold cites this paper.

A single point as a Calabi-Yau zerofold Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T19:38:01.578186Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c4e609f7-4dbf-469b-93e8-e4078722d80b · inbound

Revisiting the Quantum Geometry of Torus-fibered Calabi-Yau Threefolds cites this paper.

Revisiting the Quantum Geometry of Torus-fibered Calabi-Yau Threefolds Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T07:58:48.285409Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b62656d1-15c7-4890-a78c-ceadea083c5f · inbound

String probes, simple currents, and the no global symmetries conjecture cites this paper.

String probes, simple currents, and the no global symmetries conjecture Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges

Reference 135

Resolution: verified exact; arxiv_id, observed 2026-05-14T20:32:57.162828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c1441310-a438-48b0-8610-7c0de3427623 · inbound

Kaleidoscopes, Waves and the Prepotential cites this paper.

Kaleidoscopes, Waves and the Prepotential Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges

Reference 58

Resolution: verified exact; arxiv_id, observed 2026-07-02T10:06:52.155538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.