Paper Citation Record · LEDGER

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes

As of 21 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2606.07781.

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

pith.paper-citation-record.v1
2606.07781 v1

Coverage vector

measured 33 of 33 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-06-27T20:56:59.185526Z

measured 33 of 33 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

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Reference resolution

33 of 33 outbound references displayed

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Outbound references

Observation 47cbbe94-b3fb-4074-8cdd-4c6b7c53ae1d · outbound

This paper cites Proof of the Spacetime Penrose Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Proof of the Spacetime Penrose Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-02T20:07:22.075565Z

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Observation 45135bec-bba7-498e-9b6b-6624a7531319 · outbound

This paper cites Anderson, and J.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Anderson, and J

Reference 2

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Observation 20c3875d-c326-4f9d-be76-96c2d6249724 · outbound

This paper cites Andersson, M.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Andersson, M

Reference 3

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Observation f8dc0882-ee15-4470-8cc6-44233d1f5445 · outbound

This paper cites Andersson, M.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Andersson, M

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation fa827e88-79e0-4b8e-b5b3-e66e49374092 · outbound

This paper cites Andersson, M.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Andersson, M

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 9eaddc32-427d-4901-823e-15f2bbacfc8b · outbound

This paper cites Andersson, M.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Andersson, M

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 196e9794-4f47-413e-bddc-0c03c2a6c9fa · outbound

This paper cites Andersson, and J.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Andersson, and J

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 0a0b1246-2516-417e-af42-71ab52ab146a · outbound

This paper cites Andr´ easson,The Einstein-Vlasov system/kinetic theory, Living Rev.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Andr´ easson,The Einstein-Vlasov system/kinetic theory, Living Rev

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 3a661c32-a91b-40e2-a76c-fbbf93929355 · outbound

This paper cites Ashtekar, and B.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Ashtekar, and B

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 6efbbe7d-3f55-4dd8-b027-b6e119943b99 · outbound

This paper cites Bartnik,The mass of an asymptotically flat manifold, Comm.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Bartnik,The mass of an asymptotically flat manifold, Comm

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 9dfbd6f1-9ee6-4111-8a6e-327b276fa022 · outbound

This paper cites Bartnik,New definition of quasilocal mass, Phys.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Bartnik,New definition of quasilocal mass, Phys

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 9042d718-f2c3-489f-adb6-f607ecbbacc9 · outbound

This paper cites Bartnik,Energy in general relativity, Tsing Hua lectures on geometry and analysis, (Hsinchu 1990-91), 5–27, International Press, Cambridge, MA 1997.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Bartnik,Energy in general relativity, Tsing Hua lectures on geometry and analysis, (Hsinchu 1990-91), 5–27, International Press, Cambridge, MA 1997

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 7bf958c5-f779-4604-9ccb-f6292304341d · outbound

This paper cites Bartnik,Mass and 3-metrics of non-negative scalar curvature, Proceed- ings of the International Congress of Mathematicians, Beijing,II(2002), 231–240, Higher Ed.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Bartnik,Mass and 3-metrics of non-negative scalar curvature, Proceed- ings of the International Congress of Mathematicians, Beijing,II(2002), 231–240, Higher Ed

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 74c4cd4a-6321-4eef-8880-28670505893c · outbound

This paper cites Chru´ sciel,Boundary conditions at spatial infinity from a Hamiltonian point of view, Topological Properties and Global Structure of Space-Time (P.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Chru´ sciel,Boundary conditions at spatial infinity from a Hamiltonian point of view, Topological Properties and Global Structure of Space-Time (P

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation f5524d3a-7d8c-4847-a67e-5feaa72867bf · outbound

This paper cites an unresolved cited work.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 3dde5c31-27d3-4b7c-b5f8-36f756c5b30e · outbound

This paper cites Corvino, and L.-H.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Corvino, and L.-H

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 86322ac9-713f-4b46-a592-5a4bb8c2eb24 · outbound

This paper cites Dong, and A.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Dong, and A

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation b6fd7033-5b6e-44b3-8fbc-da0ae7a935d9 · outbound

This paper cites Eichmair,The Plateau problem for marginally trapped surfaces, J.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Eichmair,The Plateau problem for marginally trapped surfaces, J

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 046e4ad4-0653-4cbb-be41-c0d5457f2736 · outbound

This paper cites Gl¨ ockle,Initial data sets with dominant energy condition admitting no smooth DEC spacetime extension, Proc.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Gl¨ ockle,Initial data sets with dominant energy condition admitting no smooth DEC spacetime extension, Proc

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 008494a4-f6fd-49a7-970d-1223aa67f845 · outbound

This paper cites Hawking and G.F.R.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Hawking and G.F.R

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 87ff058d-e65e-4c75-bff3-c3c208a91872 · outbound

This paper cites Hayward,General laws of black-hole dynamics, Phys.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Hayward,General laws of black-hole dynamics, Phys

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 7b1cff98-c485-43b3-9c2a-9617b5989c81 · outbound

This paper cites Huang, and D.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Huang, and D

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation c54002c0-ae41-409a-8e43-fa4caf3b4314 · outbound

This paper cites Huisken, and T.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Huisken, and T

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 00d2c3ec-3a1f-4d36-8930-bcc543abe6e8 · outbound

This paper cites McCormick, and P.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes McCormick, and P

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 72c2cc8c-899c-4dbb-904b-a951678bd841 · outbound

This paper cites McCormick,An overview of Bartnik’s quasi-local mass, Beijing J.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes McCormick,An overview of Bartnik’s quasi-local mass, Beijing J

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 3c277ce7-1091-4e0a-b8a4-2c7ebbe3c1ac · outbound

This paper cites Mantoulidis, and R.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Mantoulidis, and R

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 65cf069d-d8a2-4817-9295-f2bdd43680db · outbound

This paper cites Penrose,Some unsolved problems in classical general relativity, Ann.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Penrose,Some unsolved problems in classical general relativity, Ann

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 7c0e57f7-b9f1-4a75-8fd2-ac360f521ae4 · outbound

This paper cites Schoen,Estimates for stable minimal surfaces in three-dimensional manifolds, Ann.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Schoen,Estimates for stable minimal surfaces in three-dimensional manifolds, Ann

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 97031d90-c9d0-4a42-bfa5-a9934d0a9e96 · outbound

This paper cites Schoen, and S.-T.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Schoen, and S.-T

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 71609354-f3e3-4064-afc3-b23d0e714804 · outbound

This paper cites Simon,Lectures on geometric measure theory, Proc.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Simon,Lectures on geometric measure theory, Proc

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 3b13b652-9020-400f-8bfa-7da47a277219 · outbound

This paper cites Szabados,Quasi-local energy-momentum and angular momentum in general relativity, Living Rev.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Szabados,Quasi-local energy-momentum and angular momentum in general relativity, Living Rev

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation f2ac1c32-faa9-4d31-be0a-72e56f2f9f52 · outbound

This paper cites White,On the bumpy metrics theorem for minimal submanifolds, Amer.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes White,On the bumpy metrics theorem for minimal submanifolds, Amer

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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Observation 6c818a9d-8f96-4051-b936-c3ca575f5d51 · outbound

This paper cites Witten,A simple proof of the positive energy theorem, Comm.

Spacetime Bartnik Mass Positivity and Temporal Monotonicity for Black Holes Witten,A simple proof of the positive energy theorem, Comm

Reference 33

Resolution: unresolved; no resolver link, observed 2026-06-27T20:56:59.185526Z

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