Paper Citation Record · LEDGER

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group

As of 23 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2502.04084.

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

pith.paper-citation-record.v1
2502.04084 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T23:48:30.997733Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T05:09:49.886165Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

30 of 30 outbound references displayed

verified exact0
verified fuzzy17
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1427f2e4-6132-433b-9b04-777e38afa1ec · outbound

This paper cites 9, 1997–2027.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 9, 1997–2027

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.904985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 35ff203a-d31a-4def-9c6d-0c14813cf5df · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.897741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6cbd0b18-1a70-4be0-9301-0138c61c0a55 · outbound

This paper cites 8, 2255–2263.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 8, 2255–2263

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.890621Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d92885b2-b2d6-478d-843d-39b381fbdc10 · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.880838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a9528018-ed5d-4774-bfbd-a4cff4fbf3c0 · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.786022Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f52ea00b-be8d-41c9-b957-38d51c9d9c45 · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.726056Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c480b8f8-f94c-48ad-89c2-3e1ab45ab7d5 · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.718329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 20532a3b-fb3f-43d8-9ea5-d31b24064a91 · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.709993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6cf60c4f-1571-4946-8ec8-7769f9094315 · outbound

This paper cites 1, 3, 3.1, 3.1, 3.2.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 1, 3, 3.1, 3.1, 3.2

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.702105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5b8507d5-061c-4de9-be99-d2066bf62699 · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.693329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9930b4ff-efaa-4bb9-a0a8-f15a907f0fc7 · outbound

This paper cites 2, 149–172.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 2, 149–172

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.684867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f01e51c9-7f86-487b-b40f-992e6bd63cde · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.621847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a57447bb-1257-4fc3-a72d-2224ab800c7e · outbound

This paper cites 1, 33–186.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 1, 33–186

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.453029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4470bb5c-8e8f-4d71-b590-25a3be1d4f41 · outbound

This paper cites 1, 334–350.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 1, 334–350

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.445089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b3e7facd-284c-4a4d-b42f-f48d1cc3eb36 · outbound

This paper cites 3, 373–387.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 3, 373–387

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.437010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 57dbc248-abc3-4bc6-8fb8-c1647e81c960 · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.428672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 91036337-9c50-4b40-860a-1e5a76a75b7c · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.420071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5e21612b-9e2b-458e-b499-ed23d4a071cf · outbound

This paper cites 3, 733–772.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 3, 733–772

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.411204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9921b1d6-7baa-479f-a595-a01c19da4806 · outbound

This paper cites 2, 273–318.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 2, 273–318

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.392946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8d2b223e-2187-424a-9adb-7ef478498b6d · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.310411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation af6a4ff6-f207-4158-b56e-401bce196d70 · outbound

This paper cites 1, Princeton university press,.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 1, Princeton university press,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.241081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f8ae7363-4876-4fcb-9665-48b9773e669f · outbound

This paper cites 2, 348–374.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 2, 348–374

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.232642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2f9e729c-27a9-4e7a-aabc-f5ece053ed32 · outbound

This paper cites 2, 515–549.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 2, 515–549

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.223677Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b225ae44-931e-4494-9858-b255680f3610 · outbound

This paper cites 4, 671–686.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 4, 671–686

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.215324Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9d9acd73-3951-4716-a576-982420d9f585 · outbound

This paper cites 1, 180–213.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 1, 180–213

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.205786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ee7e1693-b3c6-4a22-8a48-7a3160e3de6e · outbound

This paper cites 1, 5, 5, 6.1.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 1, 5, 5, 6.1

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.196301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6547f02d-8d6c-4f97-b0ef-880b8fe04ff3 · outbound

This paper cites 1, 203–228.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 1, 203–228

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.106419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6160fa26-3c00-496d-9d0d-fe0c04ad690f · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.051775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b6240116-be88-4ce6-9c85-931ecab7de7f · outbound

This paper cites an unresolved cited work.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-08T23:48:31.042294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e2f4d4ef-f2e4-4e78-8756-06890785ea6f · outbound

This paper cites 1, 5, 5 Depar tment of Ma thema tics, University College London, Lon don, WC1H 0AY, UK Email address : e.lupoian@ucl.ac.uk 25.

Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group 1, 5, 5 Depar tment of Ma thema tics, University College London, Lon don, WC1H 0AY, UK Email address : e.lupoian@ucl.ac.uk 25

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T23:48:31.031754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

Observation c8bc8488-e1db-4767-85ac-3472196cbebd · inbound

Bernoulli determinants and cuspidal subgroups cites this paper.

Bernoulli determinants and cuspidal subgroups Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T05:09:49.886165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.