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Paper Citation Record · LEDGER

Free Circle Actions on the Product of Three Spheres

As of 24 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2505.21993.

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

pith.paper-citation-record.v1
2505.21993 v2

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:30:22.048279Z

measured 19 of 19 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 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

19 of 19 outbound references displayed

  • verified exact0
  • verified fuzzy7
  • unresolved12
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 764fe0da-2669-4ba5-9afd-fbd60b80c320 · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:26.564752Z

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.

source=pdf_text observed=2026-08-07T13:30:19.844758Z digest=sha256:fe2f4a6cac6b5ffaca2b3fb882c40f83b221ad54a5bd4602a02827ff7c36d853

Observation cc9b5a97-bc1a-4ab0-ac18-a4dc7483bbc0 · outbound

This paper cites Borel, Sur la cohomologie des espaces fibr` es principaux et des espaces homog` enes de groupes de Lie compacts , Ann.

Free Circle Actions on the Product of Three Spheres Borel, Sur la cohomologie des espaces fibr` es principaux et des espaces homog` enes de groupes de Lie compacts , Ann

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:30:26.254745Z

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.

source=pdf_text observed=2026-08-07T13:30:19.994889Z digest=sha256:69e0b3639db5ff26318655dc55ab15a79467b1c5e1f2c603e43e65de29b5f48f

Observation edee6bf6-034b-4e40-ac04-453af19d4b7a · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:25.934975Z

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.

source=pdf_text observed=2026-08-07T13:30:20.092094Z digest=sha256:7f6190b44941e1aff9d27fde66ec22b78cb2d63602aae2e43b422bc4575eb354

Observation 9b837858-0b15-4d55-82a7-f69666ce3c30 · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:25.674752Z

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.

source=pdf_text observed=2026-08-07T13:30:20.246208Z digest=sha256:c72043883661c5851c951d60ffbcd7821720a9b4702608be65c726192ae766c2

Observation 3bd445f7-01b7-4e12-8eca-6d7a6aa2a46f · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:25.293703Z

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.

source=pdf_text observed=2026-08-07T13:30:20.370936Z digest=sha256:961085357e3fba340e9feaeb2f1cdfd9e2557b0bda2cbbd024ee80f8cdfa8b5d

Observation 820b48a9-f987-4250-a71e-349263505805 · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:24.985238Z

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.

source=pdf_text observed=2026-08-07T13:30:20.492678Z digest=sha256:3fbc23823fb6d624781b9017ccd9245ef8295bdbd40251ae4c3a4278d364ae06

Observation 5398a2c1-fba8-494f-9801-33fb2a7d567c · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:24.734904Z

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.

source=pdf_text observed=2026-08-07T13:30:20.634753Z digest=sha256:cfa5228f43caae68aad09cdf76756301e0c3f4740e523317a74b9373decf927a

Observation 56a975da-fe9a-4bd2-965d-7e54f154f26e · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:24.376658Z

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.

source=pdf_text observed=2026-08-07T13:30:20.844771Z digest=sha256:56f18bb0634a89a760678f1159e2a051b5f3d73b134ec35b4f76dbce7b591de9

Observation 2ad5b066-48f7-48c2-86db-c89d2ed0f09c · outbound

This paper cites Kumari, H.

Free Circle Actions on the Product of Three Spheres Kumari, H

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:30:24.213218Z

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.

source=pdf_text observed=2026-08-07T13:30:20.962836Z digest=sha256:21311707f3c9645eef1be137ef2e61c140192f2032112fd70a8ebec43c3c7461

Observation df07cb0d-f063-481f-b579-ada4de658cd0 · outbound

This paper cites McCleary, A user’s guide to spectral sequences, Cambridge Studies in Advanced Mathematics, Cambridge University Press, IInd edition, 58 (2001).

Free Circle Actions on the Product of Three Spheres McCleary, A user’s guide to spectral sequences, Cambridge Studies in Advanced Mathematics, Cambridge University Press, IInd edition, 58 (2001)

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:30:24.084838Z

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.

source=pdf_text observed=2026-08-07T13:30:21.101976Z digest=sha256:36a75be5cc158f5b7df75f42c575de9e4f434da46ea16855a32f7838bc2cb49e

Observation 1e3a6f9e-6813-45fd-8cf2-23ab5b38f505 · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:23.962470Z

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.

source=pdf_text observed=2026-08-07T13:30:21.174751Z digest=sha256:316d2f0cbf521043fc8dfee65a5a53509812d7c403554a1a39ed559baf82aae8

Observation e4f357ff-1a9b-4475-b472-93fb38ed8942 · outbound

This paper cites Singh, Orbit spaces of free involutions on the product of two projective spaces, Results Math., 57(1) (2010), 53-67.

Free Circle Actions on the Product of Three Spheres Singh, Orbit spaces of free involutions on the product of two projective spaces, Results Math., 57(1) (2010), 53-67

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:30:23.813625Z

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.

source=pdf_text observed=2026-08-07T13:30:21.294837Z digest=sha256:f098bfe74eb571409d0b75a854ced352e084b18a73af0e051663eea1d9aa0a9c

Observation a0dac469-1ad8-4e57-9105-b6a021547a59 · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:23.584765Z

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.

source=pdf_text observed=2026-08-07T13:30:21.404425Z digest=sha256:46e662307e9333998568822e84fe7935fa65b20233bdda335a4d231e3684092d

Observation 8a32ac60-df83-43d0-8b53-9f0042dd743f · outbound

This paper cites Ozeki, F.

Free Circle Actions on the Product of Three Spheres Ozeki, F

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:30:23.314777Z

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.

source=pdf_text observed=2026-08-07T13:30:21.491827Z digest=sha256:a6c6ef86097724fedb28e856c9b0d59c6a7fc6a8b89f03add81cb8c3e2d1152d

Observation ed20c824-7b54-4550-9e01-f9838a94f77a · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:23.089066Z

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.

source=pdf_text observed=2026-08-07T13:30:21.615072Z digest=sha256:d89d3fd41599307d39874fd1c3dc8ddf59608b95b51ee8fac1b5c6783107d04b

Observation 471ca958-c5a6-4f22-adba-8028dab830b9 · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:22.854135Z

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.

source=pdf_text observed=2026-08-07T13:30:21.692630Z digest=sha256:d10fd6d4744edbc4e08a8e200cb39b3e40f8ccb2d62c07f94e4c7c993f49b103

Observation 75b406d6-75f2-45d2-9302-9799c2bea77e · outbound

This paper cites an unresolved cited work.

Free Circle Actions on the Product of Three Spheres Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:30:22.672100Z

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.

source=pdf_text observed=2026-08-07T13:30:21.790257Z digest=sha256:947be325bac327c4d8a5b5573c39b75c3d21f02d2438c9becea49195e7b3b0bc

Observation 4b368cdd-53c5-4194-81ab-90b997f6d4d7 · outbound

This paper cites Math., 14 (1962), 145-152.

Free Circle Actions on the Product of Three Spheres Math., 14 (1962), 145-152

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:30:22.445305Z

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.

source=pdf_text observed=2026-08-07T13:30:21.935126Z digest=sha256:e5c349946a4a15e996c5fe91d9d10869958c3a56d8330b4d8648863e9734fbb6

Observation 6820f679-3e7d-4c44-b9e3-53b0d110e623 · outbound

This paper cites Volovikov, On the index of G-spaces, Sb.

Free Circle Actions on the Product of Three Spheres Volovikov, On the index of G-spaces, Sb

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:30:22.248309Z

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.

source=pdf_text observed=2026-08-07T13:30:22.048279Z digest=sha256:65c4959da1c2eed1bdb7b886f5dce42e4cc0fb82050faba90f9beb19febf0244

Pith citing papers

No inbound Pith citation observations are available.