Paper Citation Record · LEDGER

Violation of the third law of black hole mechanics in vacuum gravity

As of 9 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 2 inbound Pith citation observations for arXiv:2601.20955.

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

pith.paper-citation-record.v1
2601.20955 v2

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T07:22:10.568593Z

measured 23 of 23 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T23:26:53.636812Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T23:24:10.405101Z

Reference resolution

21 of 21 outbound references displayed

verified exact2
verified fuzzy0
unresolved17
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a7ff613b-6cfb-40b4-bf7c-97fe77d29f4b · outbound

This paper cites an unresolved cited work.

Violation of the third law of black hole mechanics in vacuum gravity Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.510996Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 954cb612-8c49-4887-8274-24e42c4b4ca1 · outbound

This paper cites Israel, Phys.

Violation of the third law of black hole mechanics in vacuum gravity Israel, Phys

Reference 2

Resolution: verified exact; doi, observed 2026-08-03T07:23:44.142314Z

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.

Observation 23af7523-1215-4f41-a4b4-b6bd67f46645 · outbound

This paper cites de la Cruz and W.

Violation of the third law of black hole mechanics in vacuum gravity de la Cruz and W

Reference 3

Resolution: verified exact; doi, observed 2026-08-03T07:23:43.887964Z

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.

Observation 9b1e7d2c-a08f-4783-b3a0-367df841d705 · outbound

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

Violation of the third law of black hole mechanics in vacuum gravity Gravitational collapse to extremal black holes and the third law of black hole thermodynamics

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.520741Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32079492-b828-41a8-ac52-b6f804ee6a8a · outbound

This paper cites Extremal black hole formation as a critical phenomenon.

Violation of the third law of black hole mechanics in vacuum gravity Extremal black hole formation as a critical phenomenon

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.524314Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e1814521-7bab-44e2-aa2f-b9981e26771d · outbound

This paper cites A third law of black hole mechanics for supersymmetric black holes and a quasi-local mass-charge inequality.

Violation of the third law of black hole mechanics in vacuum gravity A third law of black hole mechanics for supersymmetric black holes and a quasi-local mass-charge inequality

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.527525Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce394a4a-aa03-4f41-bd01-78d57c2c1b41 · outbound

This paper cites Kehle and R.

Violation of the third law of black hole mechanics in vacuum gravity Kehle and R

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.530857Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4be0a4d-cf35-45d3-999c-fcf23f267029 · outbound

This paper cites an unresolved cited work.

Violation of the third law of black hole mechanics in vacuum gravity Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.534214Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72f46851-50ad-4d9a-961a-048c8845fea3 · outbound

This paper cites Critical behavior in vacuum gravitational collapse in 4+1 dimensions.

Violation of the third law of black hole mechanics in vacuum gravity Critical behavior in vacuum gravitational collapse in 4+1 dimensions

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.537130Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 126dc7f3-e90f-4216-9692-00979466d3e3 · outbound

This paper cites Dafermos and G.

Violation of the third law of black hole mechanics in vacuum gravity Dafermos and G

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.540032Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72d4ed0b-ef5b-49b3-b8ed-6791225d4ed8 · outbound

This paper cites The characteristic gluing problem for the Einstein equations and applications.

Violation of the third law of black hole mechanics in vacuum gravity The characteristic gluing problem for the Einstein equations and applications

Reference 11

Resolution: malformed identifier; no resolver link, observed 2026-08-03T07:22:10.542840Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55a34b9e-099f-4def-8a8f-1c4518188787 · outbound

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

Violation of the third law of black hole mechanics in vacuum gravity Formation of extremal Reissner-Nordstr\"om black holes: insights from numerics

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.545879Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bdd05aa3-8b60-4d6a-be95-bd911677bc61 · outbound

This paper cites an unresolved cited work.

Violation of the third law of black hole mechanics in vacuum gravity Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.549183Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d759c8f1-bbcb-41a4-8fdc-d340c11ed6be · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Violation of the third law of black hole mechanics in vacuum gravity Adam: A Method for Stochastic Optimization

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.551750Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 02ccd8fd-2725-4905-ab7a-01e3a16eb18f · outbound

This paper cites If this does not exhibit convergence to zero, thepvalues are increased.

Violation of the third law of black hole mechanics in vacuum gravity If this does not exhibit convergence to zero, thepvalues are increased

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.506690Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 305c9d7a-eb57-48d6-9fcf-58daeb9dafdd · outbound

This paper cites an unresolved cited work.

Violation of the third law of black hole mechanics in vacuum gravity Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.554812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6baeae1a-2816-42da-a767-29ccf9032399 · outbound

This paper cites Rivi` ere, Frontiers in Applied Mathematics, Vol.

Violation of the third law of black hole mechanics in vacuum gravity Rivi` ere, Frontiers in Applied Mathematics, Vol

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.557795Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b76bc0d-d7de-43dd-921e-2ef2515422b6 · outbound

This paper cites Cockburn, G.

Violation of the third law of black hole mechanics in vacuum gravity Cockburn, G

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.560370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 107cfb0d-4f23-421a-8a04-51c7531fec74 · outbound

This paper cites Cockburn and C.-W.

Violation of the third law of black hole mechanics in vacuum gravity Cockburn and C.-W

Reference 19

Resolution: malformed identifier; doi_truncated, observed 2026-08-03T07:23:43.657545Z

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.

Observation 04220910-1604-4a5a-aa75-91b47ee3e15b · outbound

This paper cites 8J 2e2B 3r5 + 2re−4B 3 f(e B,|Φ| 2) # ∂V r+ 2r3 Ω2 ( (∂V B)2 + |∂V Φ|2 3(1 +|Φ| 2) + Im( ¯Φ∂V Φ) 2 3(1 +|Φ| 2) ) (−∂U r),(10a) and 8G5 3π ∂U mH =−.

Violation of the third law of black hole mechanics in vacuum gravity 8J 2e2B 3r5 + 2re−4B 3 f(e B,|Φ| 2) # ∂V r+ 2r3 Ω2 ( (∂V B)2 + |∂V Φ|2 3(1 +|Φ| 2) + Im( ¯Φ∂V Φ) 2 3(1 +|Φ| 2) ) (−∂U r),(10a) and 8G5 3π ∂U mH =−

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.565774Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c08e50a-1cbf-4e39-a1e6-f801e0833360 · outbound

This paper cites One can convert to coordinates regular at the horizon using standard methods.

Violation of the third law of black hole mechanics in vacuum gravity One can convert to coordinates regular at the horizon using standard methods

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T07:22:10.568593Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 2524cd2f-2ff3-40b9-bc9f-c292893cd2e6 · inbound

Information-Theoretic Black Hole Entropy I: Beyond the Area Law cites this paper.

Information-Theoretic Black Hole Entropy I: Beyond the Area Law Violation of the third law of black hole mechanics in vacuum gravity

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T23:26:53.636812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 771fe0b3-a10d-40cb-b897-f1a253ef663a · inbound

Information--Theoretic Black Hole Entropy II: Infrared Gravity and Charged/Rotating Extensions cites this paper.

Information--Theoretic Black Hole Entropy II: Infrared Gravity and Charged/Rotating Extensions Violation of the third law of black hole mechanics in vacuum gravity

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-07T23:24:10.410215Z

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.