Paper Citation Record · LEDGER

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics

As of 18 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:2411.17938.

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

pith.paper-citation-record.v1
2411.17938 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T11:49:58.763042Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T17:23:50.748618Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

38 of 38 outbound references displayed

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verified fuzzy16
unresolved21
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External citation measurements

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Outbound references

Observation a41f0455-7d8f-4101-a210-129f4d5ca2c3 · outbound

This paper cites Nernst’s theorem.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Nernst’s theorem

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:59.182657Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2a6ccce5-3a5a-4a45-ab75-f56a4118e35e · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:59.172503Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 605b1957-5b24-4f0e-af5a-4b3105402fbb · outbound

This paper cites This occurs when, for some horizon r+, we have f (r+) = f ′(r+) = 0.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics This occurs when, for some horizon r+, we have f (r+) = f ′(r+) = 0

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:59.162087Z

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Observation 186e60d9-c94e-44a3-a426-60e8aca7d989 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:59.151767Z

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Observation 3cda121d-8354-4c83-8cb0-d617f2a54ad3 · outbound

This paper cites It is notated DR,k dS (DR,k AdS).6 Deﬁnition 4.2 : de Sitter-Schwarzschild data.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics It is notated DR,k dS (DR,k AdS).6 Deﬁnition 4.2 : de Sitter-Schwarzschild data

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:59.132141Z

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Observation c333ea67-0ede-4640-87b3-79557d718fe0 · outbound

This paper cites Let k ∈ N, and 0 ≤ r′ sch ≤ R, where r′ sch is the apparent horizon of a SAdS black hole with parameters Λ , M.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Let k ∈ N, and 0 ≤ r′ sch ≤ R, where r′ sch is the apparent horizon of a SAdS black hole with parameters Λ , M

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:59.122148Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 64e23dbd-ffd9-4e3b-b6ba-8794f14a78f2 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:59.142127Z

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Observation dd9aea2b-047b-468f-8f0b-7f6261c71203 · outbound

This paper cites 5 is the Schwarzschild Anti-de Sitter sphere data set of mass M and co smological constant Λ < 0, notated DR,k,M SAdS Deﬁnition 4.4 : RNAdS data.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics 5 is the Schwarzschild Anti-de Sitter sphere data set of mass M and co smological constant Λ < 0, notated DR,k,M SAdS Deﬁnition 4.4 : RNAdS data

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:59.112235Z

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Observation 8cb443df-406e-4545-8fcf-ca910358d4a4 · outbound

This paper cites If D ∈ Dk satisﬁes (for all 1 ≤ i ≤ k):.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics If D ∈ Dk satisﬁes (for all 1 ≤ i ≤ k):

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:59.101845Z

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Observation 77360c29-716a-438c-ad13-65fcc17dbb82 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 12

Resolution: parse uncertain; raw_fallback, observed 2026-08-12T11:49:59.091896Z

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Observation 7f9dead2-eff9-4727-a0ee-30e8211688e0 · outbound

This paper cites Similarly, we deﬁne gauge equivalence for DR,k,M RN AdS: Lemma 4.2 : Gauge Transformation for RN AdS: If D ∈ Dk satisﬁes (for all 1 ≤ i ≤ k):.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Similarly, we deﬁne gauge equivalence for DR,k,M RN AdS: Lemma 4.2 : Gauge Transformation for RN AdS: If D ∈ Dk satisﬁes (for all 1 ≤ i ≤ k):

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:59.082022Z

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Observation 12a6971a-9c56-4014-8482-363810854402 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:59.072008Z

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Observation 402e1db6-833f-4510-b424-57b403723caa · outbound

This paper cites We ﬁrst show the cases of gluing DR,k,M dS , DR,k,M AdS to dS/AdS-Schwarzschild Cauchy data sphere sets DR,k,M SdS , DR,k,M SAdS respectively.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics We ﬁrst show the cases of gluing DR,k,M dS , DR,k,M AdS to dS/AdS-Schwarzschild Cauchy data sphere sets DR,k,M SdS , DR,k,M SAdS respectively

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:59.061483Z

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Observation 37edff58-33ea-42df-a671-111cc900af25 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:59.050872Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c7a4a0f3-8c29-43f4-bc26-fa733fd4c43c · outbound

This paper cites Furthermore, 1 − 2Mi r(0; α) ≥ 1 − 4Mi Mf > 0, so ∂ur(0; α) < 0.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Furthermore, 1 − 2Mi r(0; α) ≥ 1 − 4Mi Mf > 0, so ∂ur(0; α) < 0

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:59.040232Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c6673b43-f6c8-413b-9873-ac6f0b67c46c · outbound

This paper cites For the sake of clarity, we reframe the main corollary, and then follow a similar argument to Section 5.3 [Ung22].

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics For the sake of clarity, we reframe the main corollary, and then follow a similar argument to Section 5.3 [Ung22]

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:59.029587Z

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Observation ac38d72a-099d-4cb2-9091-7742326c27db · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:59.008253Z

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Observation 38ef1672-ad71-41c6-8eae-dad474a14306 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.997721Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cb316dc7-7843-4432-9566-634f3503924e · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.987250Z

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Observation 336af7ea-30a5-412a-9ed6-9be6b8c2c6c8 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.976261Z

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Observation a8e58b72-17f7-45be-9b3c-be4ad996eab9 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.965954Z

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Observation 99f52827-248c-4684-bf29-7df120e3b1c9 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.955204Z

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Observation 5b37fe99-a638-4acf-9394-f896765f0e8a · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.944200Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f9b3c368-6548-43c6-9415-861fe6457c4a · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:59.018852Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9dadc82e-b974-467d-8640-8ddd8dbdfb9c · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.933993Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9fad1c4b-02c9-4604-9c33-e9c46b3fb0d3 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.923041Z

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Observation b5f8abe2-cb2d-4861-b5d5-58d1d638cc9e · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.912909Z

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Observation 0f12342c-a1ca-402b-8b9c-3df2930c1bf3 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.903004Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d1162d05-bb12-4d23-b16e-5d6f66c20c50 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.892660Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6afbbcd8-4be7-467d-ac3d-d5f4d586b159 · outbound

This paper cites We begin by gluing an AdS cone to a Schwarzschild-AdS event horizon ( M = 1) along {u = −1}.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics We begin by gluing an AdS cone to a Schwarzschild-AdS event horizon ( M = 1) along {u = −1}

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:58.882595Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 43a790cc-7459-42ac-aaf7-e6ac3c80865f · outbound

This paper cites This is done to ensure that the sign of ∂ur is preserved along v.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics This is done to ensure that the sign of ∂ur is preserved along v

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:58.871615Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 57525d31-275e-4b03-af98-769c79ae19b2 · outbound

This paper cites For stability of tachyonic modes of φ in AdS, we require that the solutions satisfy the Breitenlohner- Freedman bound at conformal inﬁnity in order to be stable.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics For stability of tachyonic modes of φ in AdS, we require that the solutions satisfy the Breitenlohner- Freedman bound at conformal inﬁnity in order to be stable

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:58.860251Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6aa2e174-304f-4f1a-aaa1-db60f3055ef7 · outbound

This paper cites an unresolved cited work.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-12T11:49:58.849480Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 57311feb-712c-473c-8c7e-083415fd7df6 · outbound

This paper cites Thermodynamics and internal dynamics of bla ck holes: Some recent developments.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Thermodynamics and internal dynamics of bla ck holes: Some recent developments

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:58.838665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ff7c5c43-7ac0-4729-be64-20afb87eeddd · outbound

This paper cites The global structure of spherically symmet ric charged scalar ﬁeld spacetimes.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics The global structure of spherically symmet ric charged scalar ﬁeld spacetimes

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:58.827692Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 03c74ea1-b910-4948-8acd-20c1c7a00088 · outbound

This paper cites On continued gravitat ional contraction.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics On continued gravitat ional contraction

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T11:49:58.816834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f46935de-3bbd-45d1-8ffd-51305f13a8c3 · outbound

This paper cites Strong cosmic censorship for the spherically symmetric Einstein-Maxwell-charged-Klein-Gordon system with positive $\Lambda$: stability of the Cauchy horizon and $H^1$ extensions.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Strong cosmic censorship for the spherically symmetric Einstein-Maxwell-charged-Klein-Gordon system with positive $\Lambda$: stability of the Cauchy horizon and $H^1$ extensions

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-12T11:49:58.759283Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 61f6277c-f2d4-4776-930f-5c2689629582 · outbound

This paper cites Gravitational collapse to extremal black holes and the third law of black hole thermodynamics.

$C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics Gravitational collapse to extremal black holes and the third law of black hole thermodynamics

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-12T11:49:58.763042Z

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Unavailable: canonical work link unavailable.

Pith citing papers

Observation d74bf603-b54c-4357-affa-48a2dfd29035 · inbound

Formation of extremal Reissner-Nordstr\"om black holes: insights from numerics cites this paper.

Formation of extremal Reissner-Nordstr\"om black holes: insights from numerics $C^{k}$-regular extremal black holes in maximally-symmetric spacetime and the third law of black hole thermodynamics

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T17:23:50.748618Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.