Paper Citation Record · LEDGER

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$

As of 8 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2506.01315.

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

pith.paper-citation-record.v1
2506.01315 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:54:26.694894Z

measured 25 of 25 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

25 of 25 outbound references displayed

verified exact1
verified fuzzy20
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 12a77472-a050-4058-8884-9ee6b9f0ca6b · outbound

This paper cites Agarwal and B.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Agarwal and B

Reference 1

Resolution: verified exact; raw_fallback, observed 2026-08-07T11:54:26.991409Z

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 a68a08a5-10e2-48f4-acfa-35d04dd94a6f · outbound

This paper cites Basak, Regular genus and gem-complexity of some mapping tori, Rev.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Basak, Regular genus and gem-complexity of some mapping tori, Rev

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:31.888155Z

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 2a1a76d0-1f14-4cd0-bb17-30191f0b3ed4 · outbound

This paper cites Basak, Genus-minimal crystallizations of PL 4-manifolds, Beitr.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Basak, Genus-minimal crystallizations of PL 4-manifolds, Beitr

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:31.641482Z

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 ad884247-5c8c-460f-b66a-b3f81801e94b · outbound

This paper cites Basak and M.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Basak and M

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:31.431949Z

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 25ce3b78-f761-4edc-b0f1-44a3b2557dcb · outbound

This paper cites Basak and M.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Basak and M

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:31.245852Z

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 a3bc64aa-f6d2-43d1-80f3-8be9bf8c3539 · outbound

This paper cites Basak and J.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Basak and J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:31.047024Z

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 1d7d6ccb-6142-45c2-9c8e-7d7a9ab613fb · outbound

This paper cites Bj¨ orner, Posets, regular CW complexes and Bruhat order, European J.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Bj¨ orner, Posets, regular CW complexes and Bruhat order, European J

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:30.864150Z

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 5efe8956-98cf-4f65-9cb4-2dbe2e30e999 · outbound

This paper cites an unresolved cited work.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:54:30.668406Z

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 29eb1201-5b63-4ed8-802d-35f102f30c74 · outbound

This paper cites an unresolved cited work.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:54:30.469055Z

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 6bf72f10-ec6f-44af-8213-e777b9d52e8f · outbound

This paper cites an unresolved cited work.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:54:30.225271Z

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 f7fe4a8d-ce71-4117-bbd2-3f21f8f70901 · outbound

This paper cites Cavicchioli, On the genus of smooth 4-manifolds, Trans.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Cavicchioli, On the genus of smooth 4-manifolds, Trans

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:30.017292Z

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 7bf13927-5d81-47e4-ab82-375aeea3d8a8 · outbound

This paper cites Cavicchioli, A combinatorial characterization of S3 × S1 among closed 4–manifolds, Proc.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Cavicchioli, A combinatorial characterization of S3 × S1 among closed 4–manifolds, Proc

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:29.782049Z

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 7c0481c5-7eb4-458c-b719-de5ce2433f9f · outbound

This paper cites Cavicchioli and F.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Cavicchioli and F

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:29.555355Z

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 48bfbec0-1b43-4905-ae3a-52db81ef62bb · outbound

This paper cites Cavicchioli and F.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Cavicchioli and F

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:29.346279Z

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 9b8a6789-6cea-468d-ac59-5822e5eea5b0 · outbound

This paper cites Choi, The number of small covers over cubes, Algebr.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Choi, The number of small covers over cubes, Algebr

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:29.152617Z

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 cc91791b-572a-41f0-b980-663818540602 · outbound

This paper cites Davis and T.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Davis and T

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:28.967913Z

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 ce37aa32-49a1-4bc5-afe8-1153f6b05e4c · outbound

This paper cites Ferri and C.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Ferri and C

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:28.764497Z

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 b100cdfc-519b-4cc3-bc82-17b02d80578a · outbound

This paper cites Ferri and C.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Ferri and C

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:28.584732Z

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 c168d0f2-5a4b-4af3-a3b8-402828f13588 · outbound

This paper cites Ferri and C.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Ferri and C

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:28.421666Z

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 cf78b458-6ac6-4f88-b7e0-cb790d2f9435 · outbound

This paper cites Ferri, C.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Ferri, C

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:28.208054Z

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 df1f5ef9-39da-4a67-9e29-a7f86e5b6864 · outbound

This paper cites Gagliardi, On the genus of the complex projective plane, Aequationes Math.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Gagliardi, On the genus of the complex projective plane, Aequationes Math

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:27.979075Z

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 87153854-d41b-43c5-bd70-f2717623a6b8 · outbound

This paper cites Gagliardi, Extending the concept of genus to dimension n, Proc.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Gagliardi, Extending the concept of genus to dimension n, Proc

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:27.778192Z

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 3771c62c-e668-4fd6-be19-a477afd54cb8 · outbound

This paper cites Gagliardi and L.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Gagliardi and L

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:27.583141Z

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 716b5dc6-d8e2-49c4-91da-564354672965 · outbound

This paper cites an unresolved cited work.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:54:27.392022Z

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 bccd96ac-6b1f-44c2-a7d9-85d6940a591f · outbound

This paper cites Spaggiari, On the genus of RP3 × S1, Collect.

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$ Spaggiari, On the genus of RP3 × S1, Collect

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:54:27.168549Z

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.