Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T20:05:14.642082Z
Paper Citation Record · LEDGER
As of 12 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 2 inbound Pith citation observations for arXiv:2412.06122.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T20:05:14.642082Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-02T10:46:52.640436Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-04T06:59:37.333217Z
65 of 65 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation fc39cd93-eebf-425d-b492-862b48e8dcbc · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Blandford-Znajek jets in MOdified Gravity
Reference 1
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 873771ce-3396-415f-ae07-a9a2499cbee1 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Then, a fourth-order symplectic integrator is constructed as SH 4 (h) = SH 2 (γh) ◦ SH 2 (δh) ◦ SH 2 (γh)
Reference 2
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 2d37d956-d76e-465b-8ed7-24f2a3b5b3a6 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Black hole merger estimates in Einstein-Maxwell and Einstein-Maxwell-dilaton gravity
Reference 3
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 a08418c8-0420-4449-b794-6abca8d9e2bd · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Dark matter and dark energy,
Reference 4
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1dbe8444-538b-460e-92b2-154cdde1a245 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms The Cosmological Constant and Dark Energy
Reference 5
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 365402f4-c0b8-424b-839c-fb5e4639da07 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms A Modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis,
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1918e4a2-436d-4d06-a42c-9ada6a121eec · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Scalar-Tensor-Vector Gravity Theory
Reference 7
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 96aca068-34f5-4990-841e-6b65dbe6d6a8 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms The MOG weak field approximation and observational test of galaxy rotation curves
Reference 8
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 037e3081-cd5a-45a5-8a97-62f7b82d01e8 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms The MOG Weak Field approximation II. Observational test of Chandra X-ray Clusters
Reference 9
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f12f8571-add7-407e-983a-a91ea59ec027 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Galaxy cluster masses without non-baryonic dark mat- ter,
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f14ac154-02ae-4b48-b702-38cf6ac48216 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Rotational Velocity Curves in the Milky Way as a Test of Modified Gravity
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2469e213-f98b-464f-b1f9-6062f07f1bf5 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Structure Growth and the CMB in Modified Gravity (MOG)
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b680d17b-d110-4716-91b3-71f23601de13 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Scalar and Vector Field Constraints, Deflection of Light and Lensing in Modified Gravity (MOG)
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a3f1d3a7-5981-4bfb-9767-b8f78000df76 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Modified Gravity Black Holes and their Observable Shadows
Reference 14
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 52d062df-34b1-48ed-9641-d40f4ed0974b · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Inner-most stable circular orbit in Kerr-MOG black hole
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8c2f2138-d02a-4aab-9e53-066161a2545c · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Observational signature of near-extremal Kerr-like black holes in a modified gravity theory at the Event Horizon Telescope
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d3c89568-e258-4037-a348-03ba966d5143 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Image of Kerr-Melvin black hole with thin accretion disk
Reference 17
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9d53f3e5-da7f-4afc-90af-3358d8e002ba · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Geodesic motion in Euclidean Schwarzschild geometry
Reference 18
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7d1e0e51-74b6-4a4f-ae8f-c61c210220e6 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Chaos Bound and its violation in Black p-brane
Reference 19
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 204301b6-9bfc-4c35-8df6-2d062dc825a6 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Presence of horizon makes particle motion chaotic
Reference 20
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c719f8fc-0600-44c7-a3ba-1b4754d6cf40 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Induction of chaotic fluctuations in particle dynamics in a uniformly accelerated frame
Reference 21
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 f707a949-c4c0-4afe-b60a-213b9d5e0d76 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Black Holes in Modified Gravity (MOG)
Reference 22
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8a14d59d-6ead-4a10-817f-50c7fa45b4a3 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A$^*$
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6e0167bf-c4ba-4a06-9486-512cafac4d49 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Velocity scaling method to correct individual Kepler energies,
Reference 24
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 fac72b65-aeca-459f-b61b-0c35c3c4ee8c · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Symplectic integrators for Hamiltonian problems: an overview,
Reference 25
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 5a73d805-88d3-48b3-b539-9425ebbc0b81 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Discrete mechanics and variational integrators,
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 05b4c423-a729-4ea9-a4f5-09ec92a33954 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Numerical Hamiltonian Problems,
Reference 27
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 bef7e5df-90ef-4970-88e2-5c73e8cc8884 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms On difference schemes and symplectic geometry,
Reference 28
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 37dbe06e-caa0-4736-97d2-21231d6eb7a9 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms A Canonical Integration Technique,
Reference 29
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 39f6d18e-cf81-4d93-9246-70d8b2de4e05 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Symplectic integrator for general near-integrable Hamiltonian system,
Reference 30
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 e53372fd-0bb7-4c29-87a3-ba04169becb7 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Fractal decomposition of exponential operators with applications to many- body theories and Monte Carlo simulations,
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 082bcdc0-4aa2-439d-aa75-ba82b30a948b · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Symplectic structure of post-Newtonian Hamiltonian for spinning compact binaries,
Reference 32
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 176b6ec2-7426-4593-8ff6-e61e391de18d · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Manifold corrections on spinning compact binaries,
Reference 33
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 6ec17690-06ad-421d-ad23-7e91481530dd · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Global symplectic structure-preserving integrators for spinning compact binaries,
Reference 34
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 43ecdfa5-ea86-4d1c-8314-e708ccaa779a · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Regular dynamics of canonical post-Newtonian Hamiltonian for spinning compact binaries with next-to-leading order spin-orbit interactions,
Reference 35
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 2dbda50b-9fc8-4339-9fa8-6f806718f756 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Dynamics of spin effects of compact binaries,
Reference 36
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 08b55714-5756-4ba1-b8db-7044e1a60740 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms On preference of Yoshida construction over Forest– Ruth fourth-order symplectic algorithm,
Reference 37
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 f5163e89-3df7-4fc9-9e0e-2c300d61344e · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms On post-Newtonian orbits and the Galactic-center stars
Reference 38
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 8112b4ab-48c2-467c-b11f-933924a2f3ec · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Splitting methods,
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0ded5ae6-ae97-47ec-a80e-70af37ca0aeb · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Symplectic maps for the n-body problem,
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c0cb0170-4bfe-497f-9c4a-a3ac94e7602c · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Symplectic integrators from composite operator factorizations,
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b721f6a3-7503-4b2c-be2b-794bf5d208ce · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Forward Symplectic Integrators for Solving Gravitational Few-Body Problems
Reference 42
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 c24cc0bc-37a9-4210-88dc-c8a59bacfc92 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Symplectic integrators with potential derivatives to third order,
Reference 43
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 51753a08-f6f8-46d8-b991-bf221ee1762c · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Explicit symplectic integrators with adaptive time steps in curved spacetimes
Reference 44
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a5d8718a-1ace-416b-8e5b-bfeed2b41465 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Construction of Explicit Symplectic Integrators in General Relativity. I. Schwarzschild Black Holes
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a194a1ba-9808-485b-a069-310a17936cad · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Construction of explicit symplectic integrators in general relativity. II. Reissner-Nordstrom black holes
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5d39725f-906c-44b4-acfc-b7becf4f4867 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Construction of explicit symplectic integrators in general relativity. III. Reissner-Nordstrom-(anti)-de Sitter black holes
Reference 47
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 f4fb4f3e-62a0-4f73-a9df-8680b9c310c4 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Construction of explicit symplectic integrators in general relativity. IV. Kerr black holes
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation aaf67168-40b9-40eb-9f79-80692f2fe84d · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Practical Symplectic Methods with Time Transformation for the Few-Body Prob- lem,
Reference 49
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 99f4573a-c7af-4f0c-8c71-e6f3ba152f00 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Chaos in a Magnetized Brane-World Spacetime Using Explicit Symplectic Integrators,
Reference 50
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 ffeeb6f6-a0ca-4cca-bd2f-c25a4fc72d2e · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Chaotic Motion of Charged Test Particles in a Magnetized Schwarzschild Black Hole,
Reference 51
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 0b20579c-8df1-4d2f-b021-e90d9ac431bd · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Electromagnetic field and chaotic charged-particle motion around hairy black holes in Horndeski gravity
Reference 52
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 127af85c-e649-4054-93fa-a553d9317fe2 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Effects of Two Quantum Correction Parameters on Chaotic Dynamics of Particles Near Renormalized Group Improved Schwarzschild Black Holes
Reference 53
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 253d3001-92c3-4a50-9e58-4302990af878 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Chaos from the ring string in Gauss-Bonnet black hole in $AdS_5$ space
Reference 54
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 815f17f2-4444-439b-9798-4bc91522df71 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Black Hole Thermodynamics in MOdified Gravity (MOG)
Reference 55
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 351f17d5-636b-4b67-badf-48940d658d70 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Charged particle motion and acceleration around Kerr-MOG black hole
Reference 56
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 9ba6b80f-d04e-4c36-a452-99a32aad67dc · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Black hole in a uniform magnetic field,
Reference 57
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 34d76cfc-ed47-4781-8a0b-f0d040090f79 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms On correctors of symplectic integrators,
Reference 58
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 5a876fe3-092b-4f55-9f90-1a5a992e8545 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Symplectic Integration of Hamiltonian Systems,
Reference 59
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b361190e-5aa7-4158-81cb-6c3e477e0c98 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Construction of higher order symplectic integrators,
Reference 60
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 33da1d79-2294-4bfe-a149-5aa01b865648 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms A Note on the Construction of Explicit Symplectic Integrators for Schwarzschild Spacetimes,
Reference 61
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a0dd0505-67b8-4469-8e20-d2cb5f879ccf · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Chaotic dynamics of string around charged black brane with hyperscaling violation
Reference 62
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8723c93e-1e3f-4072-ac8f-8ad8c7820fa7 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms On the Structure of Symplectic Mappings. The Fast Lya- punov Indicator: a Very Sensitive Tool,
Reference 63
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 faac65a7-5629-45cd-8907-744645bfd090 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Lyapunov indices with two nearby trajectories in a curved spacetime
Reference 64
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ff7b37ba-4571-4aea-992b-139d9b97c990 · outbound
Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories
Reference 65
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 3743890d-914a-4981-85e7-1888de78503c · inbound
Rational Orbits and Gravitational Waves in Static Spherical Spacetimes: An Open-Source Numerical Framework Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms
Reference 13
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 1932112b-7615-4c18-be61-d4fb351cc271 · inbound
Rational Orbits and Gravitational Waves in Static Spherical Spacetimes: An Open-Source Numerical Framework Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.