Paper Citation Record · LEDGER

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions

As of 17 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 7 inbound Pith citation observations for arXiv:2509.05103.

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

pith.paper-citation-record.v1
2509.05103 v3

Coverage vector

measured 58 of 58 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T05:46:11.438359Z

measured 65 of 65 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T14:21:24.515983Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T08:37:46.281544Z

Reference resolution

58 of 58 outbound references displayed

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External citation measurements

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Outbound references

Observation 219cd55b-facf-49bc-b203-50eeba9a7539 · outbound

This paper cites an unresolved cited work.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Unresolved cited work

Reference 1

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Observation d7bfc383-2b86-4f95-a0e9-68809418d733 · outbound

This paper cites an unresolved cited work.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Unresolved cited work

Reference 2

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Observation 3a595b48-0bc8-4dc4-808a-f44123e30d03 · outbound

This paper cites an unresolved cited work.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Unresolved cited work

Reference 3

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Observation d976ca22-49c0-43ed-9d09-ef6c40513e25 · outbound

This paper cites Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions

Reference 4

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Observation ecd70a08-7c44-4443-937f-cf63af0bbfc9 · outbound

This paper cites P-V criticality of charged AdS black holes.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions P-V criticality of charged AdS black holes

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:07.561190Z

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Observation f591e908-8ef4-402d-bfc0-d5c7e4b67e1a · outbound

This paper cites Reentrant Phase Transitions in Rotating AdS Black Holes.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Reentrant Phase Transitions in Rotating AdS Black Holes

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:07.622455Z

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Observation 0eb428fd-f793-4cbb-b17b-66c09737b710 · outbound

This paper cites The Large N Limit of Superconformal Field Theories and Supergravity.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions The Large N Limit of Superconformal Field Theories and Supergravity

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:07.698275Z

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Observation 552de9e6-1d3a-425f-be44-71ab921cdf6a · outbound

This paper cites Black holes and the butterfly effect.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Black holes and the butterfly effect

Reference 8

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Observation 791ee356-69d2-4346-ac26-55777bd5932d · outbound

This paper cites Multiple Shocks.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Multiple Shocks

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:07.815511Z

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Observation 54528edd-0288-454b-a152-f14a67d62eb5 · outbound

This paper cites A bound on chaos.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions A bound on chaos

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:07.884066Z

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Observation 187d4301-d81b-4028-b3e4-2da068a4c39c · outbound

This paper cites Hashimoto and N.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Hashimoto and N

Reference 11

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Observation 1d11fd38-137a-4d42-b9c2-ec2a6a4695e2 · outbound

This paper cites Zhao, Y.-Z.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Zhao, Y.-Z

Reference 12

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Observation 450151b3-c19d-492f-ac70-eec7efb84472 · outbound

This paper cites Presence of horizon makes particle motion chaotic.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Presence of horizon makes particle motion chaotic

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:08.073922Z

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Observation 62442d4e-91e0-4c1e-930b-cf165ca98785 · outbound

This paper cites Lei, X.-H.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Lei, X.-H

Reference 14

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Observation fd72f0e0-34ba-42bf-b23c-df6470a5c7ec · outbound

This paper cites Kan and B.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Kan and B

Reference 15

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Observation 0761384a-d970-465d-b728-584686a3ef91 · outbound

This paper cites Cardoso, A.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Cardoso, A

Reference 16

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Source-reported events for the cited work

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Observation 507d276c-d013-4681-892b-f399195b0c6f · outbound

This paper cites Quasinormal Modes of Black Holes with Multiple Photon Spheres.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Quasinormal Modes of Black Holes with Multiple Photon Spheres

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:08.307479Z

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Observation 0ab8043a-9c71-4b68-b37e-77cf3f7f0dcb · outbound

This paper cites Signature of the Van der Waals like small-large charged AdS black hole phase transition in quasinormal modes.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Signature of the Van der Waals like small-large charged AdS black hole phase transition in quasinormal modes

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:08.311201Z

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Observation d77b2128-1db6-455a-aff9-91a656270f2a · outbound

This paper cites Thermodynamics, Phase Transition and Quasinormal modes with Weyl corrections.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Thermodynamics, Phase Transition and Quasinormal modes with Weyl corrections

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:08.390267Z

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Observation 14c962ea-4999-4eb8-93cb-9178dbcaa873 · outbound

This paper cites Behavior of Quasinormal Modes and high dimension RN-AdS Black Hole phase transition.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Behavior of Quasinormal Modes and high dimension RN-AdS Black Hole phase transition

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:08.488033Z

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Observation 63e1e668-6cfe-489e-bf20-986f9f918e30 · outbound

This paper cites Behavior of quasinormal modes and Van der Waals-like phase transition of charged AdS black holes in massive gravity.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Behavior of quasinormal modes and Van der Waals-like phase transition of charged AdS black holes in massive gravity

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-05T05:46:12.503019Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 71e5040d-2758-49be-9cf3-574bff7dfdc7 · outbound

This paper cites Phase transition and Quasinormal modes for Charged black holes in 4D Einstein-Gauss-Bonnet gravity.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Phase transition and Quasinormal modes for Charged black holes in 4D Einstein-Gauss-Bonnet gravity

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-05T05:46:12.278411Z

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Observation 8779bfc1-7752-49d7-a8d7-bce3786d6dab · outbound

This paper cites Dynamical stability from quasi normal modes in 2nd, 1st and 0th order holographic superfluid phase transitions.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Dynamical stability from quasi normal modes in 2nd, 1st and 0th order holographic superfluid phase transitions

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:08.747042Z

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Observation 4fd9912d-e7be-4c97-95bc-f486b43af9bc · outbound

This paper cites Dynamical evolution of spinodal decomposition in holographic superfluids.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Dynamical evolution of spinodal decomposition in holographic superfluids

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:08.932545Z

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Observation 9def9c7a-581e-431c-9424-c05f72975376 · outbound

This paper cites Dynamical and thermodynamic crossovers in the supercritical region of a holographic superfluid model.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Dynamical and thermodynamic crossovers in the supercritical region of a holographic superfluid model

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:09.082394Z

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Observation 355783c8-b7e7-4d3f-a323-f95a0a8f934f · outbound

This paper cites Zhao, Z.-Y.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Zhao, Z.-Y

Reference 26

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Observation f122b53e-ea88-41e2-9fad-6110d926691d · outbound

This paper cites Hou, Y.-Q.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Hou, Y.-Q

Reference 27

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Observation eb5dc5d7-0177-4bb6-b639-1c8a0132f870 · outbound

This paper cites Probing Phase Structure of Black Holes with Lyapunov Exponents.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Probing Phase Structure of Black Holes with Lyapunov Exponents

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:09.507828Z

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Observation 0b57f3e0-aec7-478e-89a3-7d016f8844cc · outbound

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Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Unresolved cited work

Reference 29

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Observation 3c4d3406-8f95-4d28-859d-00ae4ecdddbd · outbound

This paper cites Probing the thermodynamics of charged Gauss Bonnet AdS black holes with the Lyapunov exponent.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Probing the thermodynamics of charged Gauss Bonnet AdS black holes with the Lyapunov exponent

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:09.690280Z

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Observation ee295214-3b11-42d8-a373-81509d954d1e · outbound

This paper cites Phase structure of the de Sitter Spacetime with KR field based on the Lyapunov exponent.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Phase structure of the de Sitter Spacetime with KR field based on the Lyapunov exponent

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:09.761063Z

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Observation 30182374-b7d8-429d-a74e-e46b9110e29b · outbound

This paper cites Shukla, P.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Shukla, P

Reference 32

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Observation 3979adbe-2188-4201-bf83-a6740f0e412a · outbound

This paper cites Lyapunov Exponents and Phase Transition of Hayward AdS Black Hole.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Lyapunov Exponents and Phase Transition of Hayward AdS Black Hole

Reference 33

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Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:46:13.483105Z

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Observation fb38aed8-db66-4809-940f-acb526df1539 · outbound

This paper cites an unresolved cited work.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Unresolved cited work

Reference 35

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Observation 02d132cd-9a16-4f9d-a80e-3bf1566dcbeb · outbound

This paper cites Probing Thermodynamic Phase Transitions of 4D R-Charged Black Holes via Lyapunov Exponent.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Probing Thermodynamic Phase Transitions of 4D R-Charged Black Holes via Lyapunov Exponent

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.155737Z

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Observation 5b746de1-3695-4f42-b4f3-b9b27f401066 · outbound

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Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Unresolved cited work

Reference 37

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This paper cites Wei and Y.-X.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Wei and Y.-X

Reference 38

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Observation bd958bd0-a0b3-4162-b678-118fc43ebab6 · outbound

This paper cites Probing the relationship between the null geodesics and thermodynamic phase transition for rotating Kerr-AdS black holes.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Probing the relationship between the null geodesics and thermodynamic phase transition for rotating Kerr-AdS black holes

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.331338Z

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Observation fba0d63e-523a-4643-bc2e-d6301b838bdd · outbound

This paper cites Circular orbit of a test particle and phase transition of a black hole.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Circular orbit of a test particle and phase transition of a black hole

Reference 40

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Observation 2ee29d4c-815d-43c1-b0fd-b73c728da293 · outbound

This paper cites Photon sphere and reentrant phase transition of charged Born-Infeld-AdS black holes.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Photon sphere and reentrant phase transition of charged Born-Infeld-AdS black holes

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.436470Z

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Observation 223a9b36-7c15-4d6e-93e0-4ef4bbc4ab33 · outbound

This paper cites Photon orbits and phase transitions in Born-Infeld-dilaton black holes.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Photon orbits and phase transitions in Born-Infeld-dilaton black holes

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.486916Z

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Observation 22394c43-c7b7-4dda-8ce2-4fb51e89a2f3 · outbound

This paper cites Photon Orbits and Thermodynamic Phase Transition of Regular AdS Black Holes.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Photon Orbits and Thermodynamic Phase Transition of Regular AdS Black Holes

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.525118Z

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Observation 0e95f413-b4f6-4518-8181-d0db9103934d · outbound

This paper cites Photon orbits and phase transition for Non-Linear charged Anti-de Sitter black holes.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Photon orbits and phase transition for Non-Linear charged Anti-de Sitter black holes

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.612234Z

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Observation d311b750-3679-4af9-878a-49c518a22b38 · outbound

This paper cites Kumar, S.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Kumar, S

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.678820Z

Source-reported events for the cited work

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Observation 42affbfc-f3b1-49b4-9877-b34ab6964504 · outbound

This paper cites Yang, S.-P.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Yang, S.-P

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.749971Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98bd8f88-aa45-4089-b201-4bd7b3126cf8 · outbound

This paper cites Geometric Approach to Circular Photon Orbits and Black Hole Shadows.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Geometric Approach to Circular Photon Orbits and Black Hole Shadows

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.786752Z

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Observation fb2b61f2-9115-472d-b9d0-cf4daed13d36 · outbound

This paper cites Chern,Differential Geometry(Peking University Press, 2006).

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Chern,Differential Geometry(Peking University Press, 2006)

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:46:13.372471Z

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Observation e1a9d83f-c4d2-422a-a09c-88a3775e1d4a · outbound

This paper cites The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.868927Z

Source-reported events for the cited work

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Observation 303ad024-ebe8-4dce-8566-68986f7a2ab4 · outbound

This paper cites Circular orbit of a particle and weak gravitational lensing.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Circular orbit of a particle and weak gravitational lensing

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.924322Z

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Unavailable: canonical work link unavailable.

Observation a14fab70-0ff2-4ca5-a8ba-7817b2ccf31c · outbound

This paper cites Gravitational Lensing of Schwarzschild and Charged Black Holes Immersed in Perfect Fluid Dark Matter Halo.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Gravitational Lensing of Schwarzschild and Charged Black Holes Immersed in Perfect Fluid Dark Matter Halo

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.965244Z

Source-reported events for the cited work

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Observation 55c7350b-b5cf-4bf5-8452-653bcf711e77 · outbound

This paper cites Bounds for Lyapunov exponent of circular light orbits in black holes.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Bounds for Lyapunov exponent of circular light orbits in black holes

Reference 52

Resolution: verified exact; local_arxiv, observed 2026-08-05T05:46:11.646411Z

Source-reported events for the cited work

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Observation aa97f9cd-5c7b-4595-915e-8fb50763fe87 · outbound

This paper cites The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:11.048623Z

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Unavailable: canonical work link unavailable.

Observation b5825786-4316-4de2-915b-cac27ab6cf6c · outbound

This paper cites J., inConference Proceedings of GR5(1968).

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions J., inConference Proceedings of GR5(1968)

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:46:13.284480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a39a743c-c6e8-41cb-b67f-ca3b293ea07f · outbound

This paper cites an unresolved cited work.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Unresolved cited work

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:11.162505Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea92d21c-79e9-46cb-8603-b9026c50881e · outbound

This paper cites Kumar, A.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Kumar, A

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:46:13.157002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 5fd25db8-df53-48b8-84af-b7af5026cae9 · outbound

This paper cites Banerjee and D.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Banerjee and D

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:46:12.952462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1b45b49d-a4e2-447f-9ff0-059afcec2650 · outbound

This paper cites Banerjee and D.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions Banerjee and D

Reference 58

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Observation d976ca22-49c0-43ed-9d09-ef6c40513e25 · inbound