Paper Citation Record · LEDGER

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces

As of 12 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 0 inbound Pith citation observations for arXiv:2507.16588.

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

pith.paper-citation-record.v1
2507.16588 v3

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measured 53 of 53 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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Reference resolution

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External citation measurements

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Outbound references

Observation cc757e1f-d8e7-483b-a0d5-ea48665f0f07 · outbound

This paper cites an unresolved cited work.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 1

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Observation e5bf91d9-51c7-4157-9936-38b8a26d12bf · outbound

This paper cites an unresolved cited work.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 2

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Observation e86f301a-6beb-48eb-8b65-749ed564d6af · outbound

This paper cites an unresolved cited work.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:17.412075Z

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Observation c21b4bcf-943b-4237-9e0e-66f717554a44 · outbound

This paper cites Bray,On the positive mass, penrose, an zas inequalities in general dimension, surveys in geo- metric analysis and relativity, adv.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Bray,On the positive mass, penrose, an zas inequalities in general dimension, surveys in geo- metric analysis and relativity, adv

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.396330Z

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Observation ff4a9038-3a10-4101-86a2-9a38c01ffd82 · outbound

This paper cites Bray and Jeffrey L.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Bray and Jeffrey L

Reference 5

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Observation 57646c96-1552-4157-9b8f-010a5ac69297 · outbound

This paper cites 1, 175–197.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 1, 175–197

Reference 6

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 7

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:17.336296Z

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Observation 88387bf8-8603-4ba4-9d3c-c56982b2b067 · outbound

This paper cites Math., vol.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Math., vol

Reference 9

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Observation 03ff0f52-7a5a-4ba8-b9b2-de076166c5c2 · outbound

This paper cites 24, 245019.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 24, 245019

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.306718Z

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Observation a0df6739-ea5f-426d-84d8-9b2fc8a1dbcf · outbound

This paper cites 1, 105–160.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 1, 105–160

Reference 11

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Observation 5400dafe-afec-42f0-bad9-983da93a8f7a · outbound

This paper cites 1, 159–186.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 1, 159–186

Reference 12

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Observation 8401d653-6598-48f3-894a-2798b0c4b1c1 · outbound

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:17.262552Z

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:17.247329Z

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Observation c3df45eb-c326-4dd7-b7a7-7f7106dc5c55 · outbound

This paper cites 5, 1725–1732.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 5, 1725–1732

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.232942Z

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Observation 10dd503a-0038-4f43-89c6-ef56cd597e2a · outbound

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:17.216566Z

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Observation f2d7cc9d-c3fd-4e76-abee-88fc3aba606d · outbound

This paper cites Hawking,Gravitational radiation in an expanding universe, J.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Hawking,Gravitational radiation in an expanding universe, J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.199407Z

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Observation 12fb0e15-055c-4a32-beb8-07e9f92e6201 · outbound

This paper cites 3, 307–343.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 3, 307–343

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.182635Z

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Observation bea413f5-b770-4ae5-b147-91bfe45e80a6 · outbound

This paper cites an unresolved cited work.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:17.167782Z

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Observation 5ab45f3b-ab5e-456c-8b5c-18881749af96 · outbound

This paper cites Ann.350(2011), no.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Ann.350(2011), no

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.152584Z

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Observation ab548dd2-b035-4d40-b387-2bd3f46207e3 · outbound

This paper cites Sharp lower bound for the charged Hawking mass in the electrostatic space.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Sharp lower bound for the charged Hawking mass in the electrostatic space

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:19:16.706375Z

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Observation 4473db54-6eaa-44a8-982b-b823418a721c · outbound

This paper cites Modified Hawking mass and rigidity of three-manifolds with boundary.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Modified Hawking mass and rigidity of three-manifolds with boundary

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:19:16.681305Z

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Observation f3e804c9-b031-4e25-afbc-126fc87bd565 · outbound

This paper cites 23, 231102.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 23, 231102

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.138068Z

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Observation ffeadf4d-0a17-4852-8285-3c0e3da844ec · outbound

This paper cites 1, 181–204.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 1, 181–204

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.122073Z

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Observation ba49fee5-8d83-4092-82d2-c71901ab99ad · outbound

This paper cites The Higher Dimensional Positive Mass Theorem I.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces The Higher Dimensional Positive Mass Theorem I

Reference 25

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Observation 1bc18b4c-0306-481b-b997-91f7eeb398e7 · outbound

This paper cites The Higher Dimensional Positive Mass Theorem II.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces The Higher Dimensional Positive Mass Theorem II

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T15:19:16.419622Z

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Observation ab33989a-da11-4549-a0b7-a0231dcd7ea1 · outbound

This paper cites 1, 015007.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 1, 015007

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.106666Z

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Observation 616f9c42-fe27-4951-9ef4-77889fad08ee · outbound

This paper cites 12, 5373–5380.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 12, 5373–5380

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.091689Z

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Observation e39ec2e9-c1a2-464d-a7c0-e890f52095c1 · outbound

This paper cites Differential Geom.77(2007), no.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Differential Geom.77(2007), no

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.076839Z

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Observation b25fd3d0-3c1b-4105-a80f-654dcd90ef07 · outbound

This paper cites 2, 437–459.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 2, 437–459

Reference 30

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Observation d53f1eef-9c32-4b2b-9ea8-a744148ed4b9 · outbound

This paper cites 2, 1323–1354.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 2, 1323–1354

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.048957Z

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:17.033648Z

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:17.019238Z

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Observation ca3e7795-ba70-41d4-ac87-cbcf1ca9d650 · outbound

This paper cites 3, 1844–1896.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 3, 1844–1896

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:17.003308Z

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:16.987512Z

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Observation 31956695-ca35-4b11-8cc0-ac109f9c6478 · outbound

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 36

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Observation f03d0bf6-d91b-434d-b800-ff46084660de · outbound

This paper cites 3, 337–394.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 3, 337–394

Reference 37

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Observation ee9d2e4f-36cb-4bd6-b4db-bc0ce839d78f · outbound

This paper cites 3, 035002.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 3, 035002

Reference 38

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Observation 9976b232-ea23-4435-8888-9b594f20e635 · outbound

This paper cites thesis, Universität Potsdam, 2025.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces thesis, Universität Potsdam, 2025

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:16.928268Z

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Observation 3afadc5e-ff05-40bf-ad02-473b76f02776 · outbound

This paper cites 2, 505–570.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 2, 505–570

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:16.911260Z

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Observation 07e767cd-a249-4491-a74f-12d8990a55fc · outbound

This paper cites 35, American Mathematical Soc., 1972.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 35, American Mathematical Soc., 1972

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:16.894221Z

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Observation 303ece0a-e52d-4700-b796-444a63102efa · outbound

This paper cites 2, 215–220.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 2, 215–220

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:16.877704Z

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Observation 0e2578bf-4295-43e5-9ce0-a7cb1f490196 · outbound

This paper cites Positive Scalar Curvature and Minimal Hypersurface Singularities.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Positive Scalar Curvature and Minimal Hypersurface Singularities

Reference 43

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 22, 7038–7050

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:16.861667Z

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Observation 0b65b900-3172-42d8-92b9-cef5d512b536 · outbound

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:16.845948Z

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Observation 743dc088-3647-43c3-b3a2-d5a16f022bce · outbound

This paper cites 1, 79–125.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 1, 79–125

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-06T15:19:16.523181Z

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Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:16.820037Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 24224284-68a3-482d-a328-353ff5412199 · outbound

This paper cites 4, 419–441.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 4, 419–441

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:16.804966Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0e8136ea-dfc2-4590-8f02-afd0e0b715e2 · outbound

This paper cites an unresolved cited work.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Unresolved cited work

Reference 49

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:19:16.788995Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 800fd929-5422-481a-92cd-1db7cecbb393 · outbound

This paper cites 1, 257–282.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 1, 257–282

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:16.773308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d772829e-e374-4b6f-bc29-53ce66bd8686 · outbound

This paper cites Relativity 7(2004), no.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces Relativity 7(2004), no

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:16.757364Z

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Observation f29dc90f-4eb8-450a-ab97-a462a2f080de · outbound

This paper cites 6, 5837–5853.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces 6, 5837–5853

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:16.742332Z

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Observation 83b641a8-0a1a-47bc-acae-39fa496e3b3a · outbound

This paper cites positivity of quasilocal mass.

Rigidity and positivity of Hawking quasi-local energy on area-constrained critical surfaces positivity of quasilocal mass

Reference 53

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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