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Paper Citation Record · LEDGER

Thermodynamic stability in an Einstein universe

As of 13 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2512.23838.

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

pith.paper-citation-record.v1
2512.23838 v3

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-16T18:44:08.466009Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T01:24:47.155435Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

34 of 34 outbound references displayed

  • verified exact0
  • verified fuzzy12
  • unresolved22
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 76bfd977-626c-4f13-a2cc-582e0aca2c7a · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:51:12.785025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:aeff013d5e7f3f0e7fdb21d0702c6bb1e03a5f500fcb15c2f764ce25aa6ae979

Observation 4cb26855-c284-45c4-9dae-b1c8c0ec3431 · outbound

This paper cites Parker, Quantized Fields and Particle Creation in Expanding Universes.

Thermodynamic stability in an Einstein universe Parker, Quantized Fields and Particle Creation in Expanding Universes

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:51:12.779986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:ee608f1faa2de783adc87b86891a37bbecd4bab3c1dc55aee273ad25be2368da

Observation ffe96d10-02c0-4c81-b800-fbd6d6bc14f2 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:51:12.770796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 8fb2b25c-1c7a-448f-be20-c7d1db7ced1b · outbound

This paper cites Schr¨ odinger,Eigenschwingungen des sph¨ arischen Raumes, Comment.

Thermodynamic stability in an Einstein universe Schr¨ odinger,Eigenschwingungen des sph¨ arischen Raumes, Comment

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:51:12.774023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:a2bb024354b4c9d9538acdf8c7e849bd258a88ffb7d3aaab00c7c7563a3a408d

Observation 64974314-cbad-4a66-9c13-6902f0655b91 · outbound

This paper cites Streeruwitz, Vacuum fluctuations of a scalar field in an Einstein universe, Phys.

Thermodynamic stability in an Einstein universe Streeruwitz, Vacuum fluctuations of a scalar field in an Einstein universe, Phys

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:51:12.776967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:fe5e7bf6daeb32b17256282f281e77e729f0926efc39092db1bd6a1c9d9469b3

Observation fcebbf76-5f0e-4e07-a2ff-81d7e7ae9aeb · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.193266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:538a9b6423359fb32efcb839198dfad00beac56eebbc170d66210c8407ded595

Observation 3ce5006f-5a3d-4f2c-8962-492bce469e9b · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.195024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:d59d83dc0ecc286254b8c97c8824e7b0875283b7d08ca9010ef870c635f49e60

Observation 5daa13e3-db91-4aff-981b-2f5dfb9a77f1 · outbound

This paper cites ¨Ozcan, Casimir energy density for spherical universes inn-dimensional spacetime, Class.

Thermodynamic stability in an Einstein universe ¨Ozcan, Casimir energy density for spherical universes inn-dimensional spacetime, Class

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:51:12.764811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation e5c31958-e2d5-41e4-8616-10bdc66c8221 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.184261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 95ac529b-ea48-4960-af2f-2c74ea83a908 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.186062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 39686730-3c20-4161-9d57-2812c08bee4d · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.180403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation a497fb4a-b04a-49ff-ba2c-e67cb0ff1bab · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.178693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:e551752d1c6c8991cc7fe41c96d77927b95bdbdf7eb7203360baf9400e8ef1eb

Observation 79cc735c-40bf-45e0-a704-a1008ead62ed · outbound

This paper cites Huang,Statistical Mechanics, John Wiley & Sons, U.S.A.

Thermodynamic stability in an Einstein universe Huang,Statistical Mechanics, John Wiley & Sons, U.S.A

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:48:18.182383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 3a7db683-80bc-4850-b267-03e891820c0f · outbound

This paper cites Brevik, K.

Thermodynamic stability in an Einstein universe Brevik, K

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:48:18.187956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation ebc6b12c-54da-490e-967d-6669f2f73fdf · outbound

This paper cites Elizalde and A.

Thermodynamic stability in an Einstein universe Elizalde and A

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:48:18.189738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation d571533f-6b9f-44ed-91d8-6918410c3f50 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.173475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 974ffa14-8bf2-4eb0-aa4c-bdbfa4b5d448 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.175240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation b0dbf41d-b101-4d74-8287-07df0162a31b · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.169958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation cd592cde-3be0-40bc-b598-e4bd66d04ca9 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.168180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 4eaa1fac-5699-4399-9d03-a30a268b4d01 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.177017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:a76b017a50336873c0faad40f0ad6e2af483380dcfdf52c87116571eda7d754d

Observation d8707da4-6398-4ac7-82ff-f2621734cfd3 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.162728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:470bd270396db0a8d2b00a9599a4a401f18fc7bcdda6c5f06576ddf194eb609b

Observation bd48c5a8-6616-4088-81ff-2a980772ba1b · outbound

This paper cites Arfken,Mathematical Methods for Physicists, Academic Press, USA (1985).

Thermodynamic stability in an Einstein universe Arfken,Mathematical Methods for Physicists, Academic Press, USA (1985)

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:48:18.164644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:95c8725b5545e2da44f5c6613f071ea3c517ff17cee6e6f808318dcdae65c820

Observation 4edc059a-6dc5-4dfb-89c0-3664dcce12f6 · outbound

This paper cites Abramowitz and I.

Thermodynamic stability in an Einstein universe Abramowitz and I

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:48:18.159258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 8abf30e9-eb6d-447f-912e-84968428ef16 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.157305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:9de1e7e27038ada3ebc93e05391e035a7c32df9bf1d748a00de0b3dec28696ca

Observation ed9e259d-be65-4902-a84c-b19d45597051 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.160993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 7058be80-e2f4-4a64-b233-5efa80a64c76 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.166413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:696bec54d91bae039f30ed6b25985588ee38723a45becda7251e5925e53eb53e

Observation 2c48af93-baa7-4044-8e98-b1d0958fe6bb · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:48:18.171648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 724d50c4-5929-433d-9ac3-cac7435e156e · outbound

This paper cites Medina and E.

Thermodynamic stability in an Einstein universe Medina and E

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:48:18.191526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:0fad8ccc463a6f36511bcb5bf9b0a7cd90ef5872596a9c51e9f573a553c1fc42

Observation e12028f7-9ade-4ab2-bb85-ba3e004e7a98 · outbound

This paper cites Zhuk and H.

Thermodynamic stability in an Einstein universe Zhuk and H

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:48:18.196910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:f6498f18d522a303176c5646150bb5c68bb77a1205e1984b02e6183911648f93

Observation e2a39d80-5a00-4409-8587-73f7bf5e37a9 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:51:12.767690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation a1ce73fd-2cd1-4bbb-b4bd-8f6216624da1 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:51:12.755777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:3fe7c692dcc565dcff3a6f37fd17102df28243d0e00fe4d74f67fb4d8bef8a2a

Observation a6d609c5-5dc1-4aae-af2e-ea54055f30b0 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:51:12.758604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:731daa1b6171be7f4f1eafc635299a8029872311884e84ccc3cf241f2987e8d0

Observation d1c7c950-5ad0-4f7f-a62a-b04961f0cc2e · outbound

This paper cites Deutsch and P.

Thermodynamic stability in an Einstein universe Deutsch and P

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T18:51:12.752551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:d6d66975ee1ffe6f9e840cfa51a879081cb823d0450d48d72d0602194acee5d9

Observation 6da19fe0-e229-4f32-a92d-93403a540565 · outbound

This paper cites an unresolved cited work.

Thermodynamic stability in an Einstein universe Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-05-16T18:51:12.761773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-16T18:44:08.466009Z digest=sha256:537e10e701c30ee565336cc94b489f0faeac94ef464331104657680db08f3181

Pith citing papers

Observation 1e812059-8c9e-4e22-a9ab-bfbc82cbfe56 · inbound

Accelerated expansion of the universe purely driven by scalar field fluctuations cites this paper.

Accelerated expansion of the universe purely driven by scalar field fluctuations Thermodynamic stability in an Einstein universe

Reference 58

Resolution
unresolved
no resolver link, observed 2026-08-03T01:24:47.155435Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-03T01:24:47.155435Z digest=sha256:41f958a2d99f4101b9c345aa2430556104a2f2257488179a3c4bc31e6d51a192