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Paper Citation Record · LEDGER

Free Circle Actions on the Product of Three Spheres

As of 8 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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:19.844758Z digest=sha256:47056696645ef7db60c2a7b1ded65d4efc2c0955f3798f85f93b46bb4eb3b27e

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:19.994889Z digest=sha256:c62baa4c329db655703d7d6c3bc346dd21d010d169962bbbe073c71962ff81fb

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:20.092094Z digest=sha256:d2f4c5816ae583823691a7928d11fe6eff9f533c42e4a602a30f22f4e5fc28ee

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:20.246208Z digest=sha256:b4f9bf6d5f96446d300d64ab5cc966a5dcea7b4d91288cf5369e7287e70dd47c

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:20.370936Z digest=sha256:b2a22220c32e4ed7eac683f82f521e67c77f1c7c4e81a4016272e543dd9abd29

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:20.492678Z digest=sha256:621df337da437e22e43d08a69cf682b5cd89555d6d84a860591b3467f951a576

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:20.634753Z digest=sha256:99e9215b4322307478c4a50f569dff90da38e5b1674068b972a7a209543c7ebe

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:20.844771Z digest=sha256:d6d449d8ddc8648cbdedc01360a5f3ef1fd92194ce2fd68960d24923930be545

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:20.962836Z digest=sha256:0b8c37cbfe5bb4824d65d4c3f30da3aabb6b1797432ec0cb0e8c49f8bbdc3ef4

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:21.101976Z digest=sha256:4937e9bc2d07d90954d0376c051a72a061f8c221d23dfdbaee6ec9fc5c9794eb

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:21.174751Z digest=sha256:8674ad7eafeb3e5f5b4659220f68cfc5f19ce18876a728bbcf5e523f8d2b2515

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:21.294837Z digest=sha256:3ab26fec737749b2d256e8974768b9e667ebea301a259b68ca72bb4d87fa6602

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:21.404425Z digest=sha256:29d74c341d05a8f3afa8ba3ea44a3a60a7d566a1cfeb5e689f92ce18ddc6dfa8

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:21.491827Z digest=sha256:38247d49613ddc38ec26cf4fac73697856a5d65400c7dcb93b67a6d51e6e3060

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:21.615072Z digest=sha256:1aa4d2f236cd86e8ee1948c2633926f5cc01585c8a163fb9605593d5c3459684

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:21.692630Z digest=sha256:e1af0a6e7da7dd596318575357f104210413bd5ed6a85411629c3ae74a4fbbd9

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:21.790257Z digest=sha256:43af05912735cfa22a56c3d758f569480b84a8f9baa58afc49b9ea24859c7ff2

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:21.935126Z digest=sha256:3a6304fc8ef89cc5f66228b8f6e4071d6a37771b00a1fe246efe9663bfc18380

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T13:30:22.048279Z digest=sha256:557110f4f29902671685bc3c2d36920cb36bb2a8ec3c9c3b2a5e02ed5f0b60be

Pith citing papers

No inbound Pith citation observations are available.