Paper Citation Record · LEDGER

Counting Reciprocal Hyperbolic Elements in Hecke Groups

As of 7 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2505.21365.

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

pith.paper-citation-record.v1
2505.21365 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:45:26.721492Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

21 of 21 outbound references displayed

verified exact1
verified fuzzy17
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 93e75353-0628-45fe-a3cd-112a6b3ce6e6 · outbound

This paper cites Basmajian and R.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Basmajian and R

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:29.483863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f7e2ddde-06ad-4a63-8b7e-93e9f659d6c6 · outbound

This paper cites Basmajian and R.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Basmajian and R

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:29.328951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation dfe3a225-71c8-4d8e-ad13-3c41bddee92c · outbound

This paper cites Basmajian and Mingkun Liu, Low lying geodesics on the modular surface and necklaces,Mathematical research letters, to appear.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Basmajian and Mingkun Liu, Low lying geodesics on the modular surface and necklaces,Mathematical research letters, to appear

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:29.170337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f182ac59-9df1-44b4-80e2-c065d8d0fe7f · outbound

This paper cites Bourgain and A.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Bourgain and A

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:29.060941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5cc1e3dd-1c45-4bb7-9f92-cafeccd5ac31 · outbound

This paper cites an unresolved cited work.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:45:28.918923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 84baa284-4b0c-438f-8f53-58e2c4cca009 · outbound

This paper cites Buser, Geometry and spectra of compact Riemann surfaces.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Buser, Geometry and spectra of compact Riemann surfaces

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:28.806967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ab033bc2-2893-4a66-97db-5fc51b8859b8 · outbound

This paper cites Das and K.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Das and K

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:28.644804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 761b0b6c-44f3-4f6c-a729-62d0a496eb9b · outbound

This paper cites Spherical growth of reciprocal classes in the Hecke Groups.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Spherical growth of reciprocal classes in the Hecke Groups

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T13:45:25.885595Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ad6a5fc2-1e30-4ee7-a8ba-abb69f954ed6 · outbound

This paper cites Erlandsson, A remark on the word length in surface groups.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Erlandsson, A remark on the word length in surface groups

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:28.507642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bfa8e8dd-95b0-4494-ab3b-782c6d804f68 · outbound

This paper cites Erlandsson, H.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Erlandsson, H

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:28.381550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6201eff4-fcc5-4848-8798-95c60c112963 · outbound

This paper cites Erlandsson and J.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Erlandsson and J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:28.253829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3cabd379-0712-4b5a-80ea-a3fd5e1eab68 · outbound

This paper cites Counting and equidistribution of reciprocal geodesics and dihedral groups.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Counting and equidistribution of reciprocal geodesics and dihedral groups

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:45:26.879458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bd7c41cb-cb31-4a7b-b69d-925e794c9533 · outbound

This paper cites Flajolet and R.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Flajolet and R

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:28.083036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6eb9acc8-e202-4172-af49-d7fe74d9b2e4 · outbound

This paper cites Lyndon and P.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Lyndon and P

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:27.933994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 91299e94-ea7a-4cb7-840e-aa1cb5b9e9e5 · outbound

This paper cites Magnus, A.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Magnus, A

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:27.784216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2fdba58d-c040-4a26-b07b-cfa2cf266e1e · outbound

This paper cites Marmolejo, Growth of Conjugacy Classes of Reciprocal Words in Triangle Groups.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Marmolejo, Growth of Conjugacy Classes of Reciprocal Words in Triangle Groups

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:27.659179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e5ef3401-8725-4cdd-a4cb-09774246c966 · outbound

This paper cites Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:27.529031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2968e16e-acd4-4ce2-beab-5ce8121ca209 · outbound

This paper cites Rivin, Growth in free groups (and other stories) – twelve years later.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Rivin, Growth in free groups (and other stories) – twelve years later

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:27.408812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c1d7931d-d82c-40f8-be2f-0c5a5a2de27b · outbound

This paper cites Sarnak, Reciprocal geodesics.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Sarnak, Reciprocal geodesics

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:27.279652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c82049db-9841-44e6-bba2-62b9f6c3e964 · outbound

This paper cites Traina, The conjugacy problem of the modular group and the class number of real quadratic number fields.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Traina, The conjugacy problem of the modular group and the class number of real quadratic number fields

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:45:27.169595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 64aa240e-ccc7-48d7-ab9d-f58067227661 · outbound

This paper cites an unresolved cited work.

Counting Reciprocal Hyperbolic Elements in Hecke Groups Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:45:27.032669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

No inbound Pith citation observations are available.