Paper Citation Record · LEDGER

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins

As of 20 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2506.14304.

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

pith.paper-citation-record.v1
2506.14304 v2

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T00:26:58.391592Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:37:44.019900Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T19:37:44.422626Z

Reference resolution

16 of 16 outbound references displayed

verified exact7
verified fuzzy4
unresolved4
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f33a23cf-624c-43cf-a1b4-08b8a76b6fb6 · outbound

This paper cites Aschbacher, R.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Aschbacher, R

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:26:58.684799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 15d0fc66-8c9a-4130-bca7-1ea18d928c95 · outbound

This paper cites An extension theory for partial groups.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins An extension theory for partial groups

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T00:26:58.345988Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 681651d1-2425-40c9-8fef-369ba1e17e9b · outbound

This paper cites Chermak, Fusion systems and localities, Acta Math.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Chermak, Fusion systems and localities, Acta Math

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T00:26:58.350293Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7dd48ac-bc6a-4408-8adf-fae609d8374a · outbound

This paper cites Chermak, Finite localities I, Forum Math.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Chermak, Finite localities I, Forum Math

Reference 4

Resolution: verified exact; doi, observed 2026-08-07T00:26:58.458718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e0a25051-cb4f-4dfc-8825-8f1466291c5c · outbound

This paper cites Finite Localities III.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Finite Localities III

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-07T00:26:58.615203Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 57ed9096-17bf-439a-935d-3395b8444094 · outbound

This paper cites An extension theory for partial groups and localities.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins An extension theory for partial groups and localities

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T00:26:58.360313Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17667537-3951-4d4c-aa42-806baeac3d53 · outbound

This paper cites Semidirect Products and Wreath Products of Localities.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Semidirect Products and Wreath Products of Localities

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-07T00:26:58.587733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b9c92b28-e47d-4271-930e-81f66d163bb0 · outbound

This paper cites Hackney, Higher Segal spaces and partial groups, in Homotopical Al- gebra and Higher Structures, edited by M.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Hackney, Higher Segal spaces and partial groups, in Homotopical Al- gebra and Higher Structures, edited by M

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:26:58.672489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 572609fc-6f99-49c3-9bce-123cf474e280 · outbound

This paper cites Hackney, J.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Hackney, J

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T00:26:58.373369Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73a3ae7f-2cc5-404e-809f-0cef9af06891 · outbound

This paper cites Hayashi, Partial group symmetry in figures II, in preparation.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Hayashi, Partial group symmetry in figures II, in preparation

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:26:58.661464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1304348b-59a5-4cc1-b500-8db09240d0f4 · outbound

This paper cites Howie, Fundamentals of semigroup theory, Lond.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Howie, Fundamentals of semigroup theory, Lond

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:26:58.650114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e770d35e-60ad-466e-8ae5-9e871df31428 · outbound

This paper cites Lynd, Partial groups and higher Segal conditions, in Finite Groups, Fusion Systems and Applications , edited by I.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Lynd, Partial groups and higher Segal conditions, in Finite Groups, Fusion Systems and Applications , edited by I

Reference 12

Resolution: verified exact; doi, observed 2026-08-07T00:26:58.435440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3d894af4-db48-40b8-a705-62f84a2cf4e5 · outbound

This paper cites Martino, S.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Martino, S

Reference 13

Resolution: verified exact; doi, observed 2026-08-07T00:26:58.423180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6f1fac91-7eea-47ef-a1d7-2bcda4e5c1bc · outbound

This paper cites Simplicial effects and weakly associative partial groups.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Simplicial effects and weakly associative partial groups

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-07T00:26:58.483438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 413d6000-3794-4c39-b038-ab22892119cf · outbound

This paper cites Salati, Limits and colimits, generators and relations of partial groups, J.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Salati, Limits and colimits, generators and relations of partial groups, J

Reference 15

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T00:26:58.638310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 79aba6ba-7064-4414-afc4-b2024ee3cc19 · outbound

This paper cites an unresolved cited work.

Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Unresolved cited work

Reference 2294

Resolution: verified exact; doi, observed 2026-08-07T00:26:58.446959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation e25a98b7-5c23-439f-a7e0-f50f669d7db1 · inbound

Higher Segal spaces and partial groups cites this paper.

Higher Segal spaces and partial groups Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:37:44.428452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.