Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T00:33:41.527785Z
Paper Citation Record · LEDGER
As of 16 August 2026, this Paper Citation Record lists 52 of 52 outbound references and 0 inbound Pith citation observations for arXiv:2608.12423.
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 2026-08-16T00:33:41.527785Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
52 of 52 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 01dce4cf-3193-4f76-b0ee-d50eeb162dec · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Einstein, The foundation of the general theory of relativity., Annalen Phys.49, 769 (1916)
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 78cda0c3-78bf-41d2-9095-663cc51084ed · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 172cfc4c-fd20-4ab5-99eb-6fd8ee8dc7db · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes −dy dq q=ϵsin 3 Θ −1 # dΘ.(4.28) The symmetry sin(π−Θ) = sin Θ(4.29) implies that the integrand is symmetric about closest approach. We may therefore write α= 2 Z π/2 0
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ce7e1d86-cd19-4818-9317-92f5abd3dc8f · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes (4.12) givesq c = 1/(3 √ 3)
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9b334dca-172b-4685-b77e-a9ae83f35ad0 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d5500fcf-e2bd-4a60-8ea7-c7ea8e348b8a · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Einstein, Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field, Science84, 506 (1936)
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fb32bbf4-dec0-4406-9bc0-9bd5a92fbdac · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation bb12405c-58d4-45ae-a2be-334c37a0642c · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a4f702a8-a087-4173-ae89-e3ffc2d060a9 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1efe6196-75db-4dc9-addc-6b5a572f6b97 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes An Exact Universal Gravitational Lensing Equation
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4b85b87c-454f-454b-90fc-feb773084725 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Spacetime perspective of Schwarzschild lensing
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c3811332-b356-4713-9a81-5cb7f79ebdc8 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9689cf4c-5549-4d7f-80c5-15185a95dbe9 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes On the exact gravitational lens equation in spherically symmetric and static spacetimes
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a66b4c0e-3866-48c2-81ee-2a484196b5f5 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Perlick, Gravitational lensing from a spacetime perspective, Living Rev
Reference 14
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 38c07550-6e3c-4232-a003-fca8232a3b76 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Epstein and I
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9d583117-13c5-4d2e-94cb-6a6a067a024e · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Fischbach and B
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3d590f94-321b-4256-b4d5-648fbf311c15 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e1c49e49-e371-46a2-a1f0-432110963dd1 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 888714d9-7daa-4aad-bd22-9d8fb0593abe · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Bodenner and C
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ea0b4c8e-67b0-40b1-8ba6-db10b6a92f1f · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational lensing in metric theories of gravity
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d3fcc88f-0b02-4870-898d-127f4f3bdf6d · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. I: Static, Spherically Symmetric Case
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3ecf8a6e-945b-4144-8539-9af9e794092f · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Formalism for testing theories of gravity using lensing by compact objects. II: Probing Post-Post-Newtonian metrics
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2bd8df5b-0f36-4000-be14-51105ff85aba · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1c576e21-d1ee-403a-8c1d-f20c3fd957ed · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes A comparison of approximate gravitational lens equations and a proposal for an improved new one
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9dbe35ec-a86c-4525-8e86-e7f15474c183 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes A generalized lens equation for light deflection in weak gravitational fields
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5c29058d-a9c5-4109-b9f6-946496d9af99 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Analytical formulas for gravitational lensing
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7b384564-09c0-4fe9-95c5-65daabda44ff · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Analytical formulas for gravitational lensing: higher order calculation
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 92b64dc5-f43d-4713-a3e3-e2d97adda015 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Computation of the general relativistic perihelion precession and of light deflection via the Laplace-Adomian Decomposition Method
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1b6e902d-23e1-440b-a814-e147dc4d9e11 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Higher-order corrections for the deflection of light around a massive object
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1a8fc997-4eb1-4644-a304-cc94e00194c5 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes The perturbative approach for the weak deflection angle
Reference 30
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5042834d-fb90-457d-94e9-05245612eb60 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Bending of Light and Inhomogeneous Picard-Fuchs Equation
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 36b49131-da05-4471-8e66-a4f2191a5509 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Applications of the Gauss-Bonnet theorem to gravitational lensing
Reference 32
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b69013ae-c4b0-4950-a76e-69be5b6f05db · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Universal properties of the near-horizon optical geometry
Reference 33
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d97da2d2-81d2-423e-9cf5-e925506dde5e · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit
Reference 34
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9256a10c-9f4d-4b5f-a574-78f4ee5659cd · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem
Reference 35
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bd3bfe79-8281-4622-8d35-6f919cb49190 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment
Reference 36
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0dabbaf5-239b-45fa-9abb-4b5b16bc62bf · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational lensing in dispersive media and deflection angle of charged massive particles in terms of curvature scalars and energy-momentum tensor
Reference 37
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c1a0bb27-d733-4d29-8337-87b3416a3b01 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes The effects of finite distance on the gravitational deflection angle of light
Reference 38
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 190633fe-c6ec-4ff8-8fa2-287e8c5f99a8 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Equivalence of Gibbons-Werner method to geodesics method in the study of gravitational lensing
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7a3a1739-e089-4100-8f2b-c35768cf9f75 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e2558c1a-27ce-4cb2-946c-d0ed3f4f5de0 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes The geometry of photon surfaces
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation feac103d-261d-4713-b092-726ba8b664ac · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Strong field limit of black hole gravitational lensing
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 17c2878c-23a0-42c2-bd32-de42a5b0b5c0 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational lensing in the strong field limit
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d060df74-6fa7-4514-92c7-c086771e3ac8 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Reissner-Nordstrom black hole lensing
Reference 44
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 854974c6-3dd7-44f4-9e61-3465d97a42b9 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Strong deflection limit of black hole gravitational lensing with arbitrary source distances
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 320922dc-dfba-4b90-a595-3be7022b62f1 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational Lensing by Black Holes
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 66111674-d9b8-472e-86cd-52cfbe887a98 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime
Reference 47
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8d4a0d64-a956-4aec-a04e-45f422a213ee · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6565b845-8336-4799-8f1f-d7aa8f203ec9 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational lensing inside and outside of a marginally unstable photon sphere in a general, static, spherically symmetric, and asymptotically-flat spacetime in strong deflection limits
Reference 49
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 453db8fe-b87b-456a-9f97-66d515219ec5 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Universal time delay in static spherically symmetric spacetimes for null and timelike signals
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 501f5aad-1e58-4598-b3aa-01f3098e6e46 · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Mayol, R
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b1b5cce0-fb62-480b-b3ce-b1059c06b10d · outbound
Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
No inbound Pith citation observations are available.