Paper Citation Record · LEDGER

Open case for a closed universe

As of 5 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 5 inbound Pith citation observations for arXiv:2510.13971.

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

pith.paper-citation-record.v1
2510.13971 v2

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-18T06:51:51.473461Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T03:03:01.173988Z

measured 1 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T02:28:24.338817Z

Reference resolution

28 of 28 outbound references displayed

verified exact18
verified fuzzy6
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

0
pith, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 08f128a9-6086-41f7-b888-24dcdfeced14 · outbound

This paper cites Closedcoshbounce.The same scale factor in ak= +1 FRW spacetime corresponds to global de Sitter.

Open case for a closed universe Closedcoshbounce.The same scale factor in ak= +1 FRW spacetime corresponds to global de Sitter

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T06:52:26.225235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation ba5eda60-b8d6-46e3-8b54-42f9359c22cc · outbound

This paper cites Penrose, Gravitational collapse and space-time singu- larities, Phys.

Open case for a closed universe Penrose, Gravitational collapse and space-time singu- larities, Phys

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T06:52:26.216323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation b362e3e0-2b4e-4833-9ec1-d9874014ba34 · outbound

This paper cites Hawking, The Occurrence of singularities in cosmol- ogy, Proc.

Open case for a closed universe Hawking, The Occurrence of singularities in cosmol- ogy, Proc

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T06:52:26.233553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation c2ef05ef-5cb6-4c9b-b625-f03592f5c5ac · outbound

This paper cites Hawking, The Occurrence of singularities in cosmol- ogy.

Open case for a closed universe Hawking, The Occurrence of singularities in cosmol- ogy

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T06:52:26.237054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 463abe3a-3da6-446d-af57-04961fa44541 · outbound

This paper cites Hawking, The occurrence of singularities in cosmology.

Open case for a closed universe Hawking, The occurrence of singularities in cosmology

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T06:52:26.243310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 1de4b3a8-3cd2-4ff1-b7ca-c83397f06d77 · outbound

This paper cites an unresolved cited work.

Open case for a closed universe Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-05-18T06:52:26.212573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 509047ac-af14-41f6-8d94-ee01ce353b75 · outbound

This paper cites an unresolved cited work.

Open case for a closed universe Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-05-18T06:52:26.229117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation fc3d90a0-0ef6-41b7-8e6c-41ee346551b9 · outbound

This paper cites Inflationary spacetimes are not past-complete.

Open case for a closed universe Inflationary spacetimes are not past-complete

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.148371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 01f546a2-69cd-481a-a9f1-d1ed14721065 · outbound

This paper cites The Borde-Guth-Vilenkin Theorem in extended de Sitter spaces.

Open case for a closed universe The Borde-Guth-Vilenkin Theorem in extended de Sitter spaces

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-18T06:52:26.120648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 0668c29a-a7e1-45f1-8a65-4a05f250cff0 · outbound

This paper cites On the initial singularity and extendibility of flat quasi-de Sitter spacetimes.

Open case for a closed universe On the initial singularity and extendibility of flat quasi-de Sitter spacetimes

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-18T06:52:26.166410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 5a3030be-8747-46a4-9396-7dad871ceee0 · outbound

This paper cites The Emergent Universe: inflationary cosmology with no singularity.

Open case for a closed universe The Emergent Universe: inflationary cosmology with no singularity

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.197727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation ad8108c5-f45f-40a0-bc8f-0470d56773a5 · outbound

This paper cites The Emergent Universe: An Explicit Construction.

Open case for a closed universe The Emergent Universe: An Explicit Construction

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.134328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 32939836-4fc6-406a-9ab0-327c8471da3f · outbound

This paper cites On the past-completeness of inflationary spacetimes.

Open case for a closed universe On the past-completeness of inflationary spacetimes

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-18T06:52:26.180811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 06da3977-0506-408f-8e20-bf3016ad6cf1 · outbound

This paper cites Inflationary resolution of the initial singularity,.

Open case for a closed universe Inflationary resolution of the initial singularity,

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-18T06:52:26.154757Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation c6a348d0-6ae1-43b5-b406-070d63dc0173 · outbound

This paper cites Eternal Universes.

Open case for a closed universe Eternal Universes

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-18T06:52:26.176055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 2da21d0b-583d-40f3-95b4-a7200c76bcc6 · outbound

This paper cites an unresolved cited work.

Open case for a closed universe Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-05-18T06:52:26.240211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 922ad56c-0243-494f-ae70-c2f5c624d031 · outbound

This paper cites Averaged null energy condition in spacetimes with boundaries.

Open case for a closed universe Averaged null energy condition in spacetimes with boundaries

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.123837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 3f8c9bf2-4e7e-4f6a-bc86-ad93cf46e152 · outbound

This paper cites Achronal averaged null energy condition.

Open case for a closed universe Achronal averaged null energy condition

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.119387Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 9ae12bcf-5271-4200-8787-9c0985c8f911 · outbound

This paper cites Proving the Achronal Averaged Null Energy Condition from the Generalized Second Law.

Open case for a closed universe Proving the Achronal Averaged Null Energy Condition from the Generalized Second Law

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.102588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 76e4d4ed-2f5f-4c84-b21a-d44caf1f5804 · outbound

This paper cites Averaged Null Energy Condition from Causality.

Open case for a closed universe Averaged Null Energy Condition from Causality

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.139125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 25d70da3-ef36-4046-9cce-fbc1d9547101 · outbound

This paper cites Burwig and D.

Open case for a closed universe Burwig and D

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-18T06:52:26.220916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 05a4d4d3-e417-4d9d-8fe0-1018c7c2163c · outbound

This paper cites DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints.

Open case for a closed universe DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

Reference 22

Resolution: metadata mismatch; local_arxiv, observed 2026-05-18T06:52:26.143722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation c3e58033-04f9-447b-afbc-c5a7121fcbeb · outbound

This paper cites Planck 2018 results. VI. Cosmological parameters.

Open case for a closed universe Planck 2018 results. VI. Cosmological parameters

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.129122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation a3033bac-42e3-4888-96c7-8b44dc282edc · outbound

This paper cites A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state.

Open case for a closed universe A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.185887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 89f635a3-a02f-46de-a06b-0e5f22fe2892 · outbound

This paper cites Phantom Energy and Cosmic Doomsday.

Open case for a closed universe Phantom Energy and Cosmic Doomsday

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.191394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 6b577027-886d-4615-bbba-795d35a3362d · outbound

This paper cites Can the dark energy equation-of-state parameterw be less than −1?.

Open case for a closed universe Can the dark energy equation-of-state parameterw be less than −1?

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-18T06:52:26.160420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation c8af4a80-166c-4cf4-bcce-36255ba86c76 · outbound

This paper cites Can dark energy evolve to the Phantom?.

Open case for a closed universe Can dark energy evolve to the Phantom?

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.171562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation bf667f3f-444a-4caa-bccb-0ab1917877c7 · outbound

This paper cites Dynamical Dark Energy or Simply Cosmic Curvature?.

Open case for a closed universe Dynamical Dark Energy or Simply Cosmic Curvature?

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-05-18T06:52:26.114767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Pith citing papers

Observation a01be91d-9f49-4ad7-8742-47764ba18d35 · inbound

Geodesically Complete Curvature-Bounce Inflation cites this paper.

Geodesically Complete Curvature-Bounce Inflation Open case for a closed universe

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-05-12T09:56:26.905405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation a0013929-9b91-40cd-af29-b3cb1c1ff28f · inbound

Affine ANEC selects the closed FRW branch for geodesically complete cosmology cites this paper.

Affine ANEC selects the closed FRW branch for geodesically complete cosmology Open case for a closed universe

Reference 40

Resolution: verified exact; local_arxiv, observed 2026-05-20T09:13:10.208603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 21d15d72-f8ac-452f-bf4d-9910b7baeac0 · inbound

Obstructions to Minimal Regular Black Hole Cosmologies cites this paper.

Obstructions to Minimal Regular Black Hole Cosmologies Open case for a closed universe

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-06-25T22:08:31.618113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation b3654144-a700-47fc-9439-b53e36b0c347 · inbound

Obstructions to Minimal Regular Black Hole Cosmologies cites this paper.

Obstructions to Minimal Regular Black Hole Cosmologies Open case for a closed universe

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T10:27:41.450261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 858d7013-4876-4484-9f2e-0b1d61e2be24 · inbound

Obstructions to Minimal Regular Black Hole Cosmologies cites this paper.

Obstructions to Minimal Regular Black Hole Cosmologies Open case for a closed universe

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T03:03:01.173988Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.