Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:16:22.856051Z
Paper Citation Record · LEDGER
As of 10 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 4 inbound Pith citation observations for arXiv:2507.06836.
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 2026-08-06T19:16:22.856051Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-06-26T11:30:54.786651Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-04T08:29:42.396610Z
65 of 65 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 2a930f60-283c-475b-adda-431b3e7fdfba · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Ambrosio
Reference 1
Source-reported events for the cited work
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Observation f2230192-4002-4cc5-84b8-d5993bd89010 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Bakry and Michel ´Emery
Reference 2
Source-reported events for the cited work
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Observation cbe4cca2-fd4e-470a-bac2-debcfd4a7d81 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Beem, Paul E
Reference 3
Source-reported events for the cited work
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Observation 6fce1f4d-a810-429f-bbdb-53615dcdd824 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work
Reference 4
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Observation bfeca220-f6e2-4f28-b1c4-268b8a2c5d9b · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes
Reference 5
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Observation 51d57707-445b-4c99-b47a-43d7b7071edf · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Ordinary differential equations
Reference 6
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Observation c0cbf69f-322a-4475-8c67-ae669a5f875b · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work
Reference 7
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Observation 03599bad-2a28-4d03-b141-cc70e2bb74ae · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights R´ enyi’s entropy on Lorentzian spaces
Reference 8
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Observation b3fbc1e4-5916-431a-8e04-ef93f8d4d46e · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Exact d'Alembertian for Lorentz distance functions
Reference 9
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Observation bb0b733c-38c7-45d1-bd10-21fb86cb5f1b · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights New perspectives on the d’Alembertian from general relativity
Reference 10
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Observation 23ce7d29-66d4-4128-960e-fdfa9b1532a2 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Timelike Ricci bounds for low regularity spacetimes by optimal transport
Reference 11
Source-reported events for the cited work
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Observation 4189471b-c623-4eca-a183-45454848e80e · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights An elliptic proof of the splitting theorems from Lorentzian geometry
Reference 12
Source-reported events for the cited work
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Observation 2c7030d3-2bf5-465f-a348-fab6eeee6523 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Caffarelli, M
Reference 13
Source-reported events for the cited work
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Observation 157faa7e-42f1-4cc1-8636-ed10fe521e75 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights On the smoothness of isometries
Reference 14
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A Lorentzian splitting theorem for continuously differentiable metrics and weights Hawking’s singularity theorem for Lipschitz Lorentzian metrics
Reference 15
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Observation 2867f513-4130-4bf6-bf88-00cbedebcfc2 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Splitting theorems for weighted Finsler spacetimes via the $p$-d'Alembertian: beyond the Berwald case
Reference 16
Source-reported events for the cited work
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Observation 4b300966-25b1-4612-8680-ba74d4c4b222 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work
Reference 17
Source-reported events for the cited work
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Observation 8d90d85d-e157-4f55-a246-da01c89e8fcd · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights On the geometry of synthetic null hypersurfaces
Reference 18
Source-reported events for the cited work
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Observation 2215153b-2d36-4ee0-8746-4d4bed10d823 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds
Reference 19
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Observation 4d4b5bca-cd52-44d6-a72f-ff5f32bb8a7e · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Optimal transport in Lorentzian syn- thetic spaces, synthetic timelike Ricci curvature lower bounds and applications
Reference 20
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Observation f39d457f-7a96-481c-b9d8-a8ef5baa169e · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights The splitting theorem for manifolds of non- negative Ricci curvature
Reference 21
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Observation 6521d099-ff23-4ca2-8d39-1078cc260788 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Chru´ sciel and James D
Reference 22
Source-reported events for the cited work
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Observation 96ceb83b-f55e-4449-8271-d986c8973801 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Eschenburg
Reference 23
Source-reported events for the cited work
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Observation d112e8e4-3bdc-475c-b147-7a83a3ab592d · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work
Reference 24
Source-reported events for the cited work
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Observation 54cd3645-7f02-4d4f-8205-8018e9780fdf · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Evans and W
Reference 25
Source-reported events for the cited work
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Observation 9e12acd3-cabb-49c2-a939-674cbf32037a · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Feldman and R.J
Reference 26
Source-reported events for the cited work
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Observation b8e32f2c-5fae-497a-9d89-d2782dfa9787 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Galloway
Reference 27
Source-reported events for the cited work
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Observation 5bfe3460-9c88-4a87-aa93-633eb3e0ba1d · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights A note on the Lorentzian splitting theorem
Reference 28
Source-reported events for the cited work
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Observation 2651bda8-e1f1-4390-ae97-8d431e987d34 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Strings and other distributional sources in general relativity
Reference 29
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Observation bcb61d69-7258-4ec4-9575-67a94a45d529 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature
Reference 30
Source-reported events for the cited work
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Observation 4aa78ed5-4252-45f5-9e55-16f87aec736e · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights The splitting theorem in nonsmooth context
Reference 31
Source-reported events for the cited work
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Observation cede061b-1cf6-44a1-9ec3-ff343cf6f347 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Trudinger
Reference 32
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Observation e0a8a064-a275-4687-a3c2-7a7f622dc60b · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Singularity theorems for C 1-Lorentzian metrics
Reference 33
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Observation df16ad6c-aea2-4234-a7d6-08fae63f078b · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights On isometries and on a theorem of Liouville
Reference 34
Source-reported events for the cited work
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Observation bb6a6bd4-74ae-47a3-bc3f-132c744ed079 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work
Reference 35
Source-reported events for the cited work
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Observation 6fe0adc0-ec0e-4a83-9553-b978cb646aee · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Needle decompositions in Riemannian geometry
Reference 36
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A Lorentzian splitting theorem for continuously differentiable metrics and weights The Hawking-Penrose singularity theorem for C 1-Lorentzian metrics
Reference 37
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Observation 3233025d-0bde-4713-b450-27629b7859e6 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Lorentzian length spaces.Ann
Reference 38
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Observation 2f566f3e-23c2-4657-b63f-93856ad07be1 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work
Reference 39
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Observation 2070b612-5b15-4e2d-bb81-553852caf0b1 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Lorentz meets Lipschitz
Reference 40
Source-reported events for the cited work
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Observation f61afeb9-67df-4d3d-a033-b880c41b93df · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights LeFloch and Cristinel Mardare
Reference 41
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Observation 296c23f9-769e-4f16-9108-bbc7cb766d1f · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Geometry of weighted Lorentz- Finsler manifolds II: A splitting theorem
Reference 42
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Observation f6b5f082-759d-492f-bdd6-f8ab7f9b5b69 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work
Reference 43
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Observation dd9df1f7-543c-4334-a19d-59d2c47be09e · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work
Reference 44
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Observation f301d709-5e0d-4475-816d-d1f5b71f57ff · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Structure theory of metric measure spaces with lower Ricci curvature bounds.J
Reference 45
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Observation 0beec40d-9e41-4e24-9136-96c8125b2923 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights An optimal transport formulation of the Einstein equations of general relativity
Reference 46
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Observation 6164fafb-7342-4da6-b005-b2aea933192a · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work
Reference 47
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Observation 3b6f0ca5-7ce9-4d94-a72c-8725d03746f2 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights The existence of complete Riemannian metrics
Reference 48
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A Lorentzian splitting theorem for continuously differentiable metrics and weights On the curvature and heat flow on Hamiltonian systems
Reference 49
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Observation 4ad79790-c1a0-42a5-ad95-47a65cd0e1b0 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Semi-Riemannian geometry, volume 103 of Pure and Applied Mathematics
Reference 50
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Observation 89a40518-6b5e-46f9-bc9e-0a0af5b3666d · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Gravitational collapse and space-time singularities
Reference 51
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A Lorentzian splitting theorem for continuously differentiable metrics and weights Global hyperbolicity for spacetimes with continuous metrics
Reference 52
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A Lorentzian splitting theorem for continuously differentiable metrics and weights A note on the Gannon-Lee theorem
Reference 53
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Observation 2206d06e-7e3f-4bfc-8587-6e2c2311681e · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights On the Geroch–Traschen class of metrics
Reference 54
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Observation c57bacd8-ad5e-4220-8670-1a265c3a4b29 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work
Reference 55
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A Lorentzian splitting theorem for continuously differentiable metrics and weights Existence and regularity of isometries
Reference 56
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A Lorentzian splitting theorem for continuously differentiable metrics and weights Ricci curvature comparison in Riemannian and Lorentzian geometry
Reference 57
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A Lorentzian splitting theorem for continuously differentiable metrics and weights Unresolved cited work
Reference 58
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Observation d0f307c6-fc87-498f-b416-4b276a5c211d · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Trudinger and X.-J
Reference 59
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A Lorentzian splitting theorem for continuously differentiable metrics and weights Springer-Verlag, Berlin, 2009
Reference 60
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A Lorentzian splitting theorem for continuously differentiable metrics and weights Light rays, singularities, and all that
Reference 61
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Observation 2af0a67d-d1c2-4695-a768-10907e96ac0c · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Scalar-tensor gravitation and the Bakry- ´Emery-Ricci tensor
Reference 62
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Observation 12b4d137-2999-41ae-b7ef-895818080ff6 · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Cosmological singularity theorems and split- ting theorems for N -Bakry-´ emery spacetimes.J
Reference 63
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A Lorentzian splitting theorem for continuously differentiable metrics and weights Curvature-dimension bounds for Lorentzian splitting theorems
Reference 64
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Observation 51428bc6-8a11-44bd-a64f-81905e53522e · outbound
A Lorentzian splitting theorem for continuously differentiable metrics and weights Problem section
Reference 65
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Observation 09f32baa-73c4-4c60-b5e9-9093680bd544 · inbound
Stability of Synthetic Timelike Ricci Bounds under $C^0$-Limits and Applications to Impulsive Gravitational Waves A Lorentzian splitting theorem for continuously differentiable metrics and weights
Reference 6
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Observation f552f0cf-4e4b-43f6-87d2-ecf441483300 · inbound
Lorentzian coarea inequality A Lorentzian splitting theorem for continuously differentiable metrics and weights
Reference 9
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Observation e767dbb9-7e65-4151-83f3-beb0169299d3 · inbound
Lorentzian coarea inequality A Lorentzian splitting theorem for continuously differentiable metrics and weights
Reference 9
Source-reported events for the cited work
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Observation 56b2441c-7ffc-4add-8463-f94e1e970bc3 · inbound
Failure of local equi-Lipschitzness for families of Lorentz distances to Cauchy surface foliations A Lorentzian splitting theorem for continuously differentiable metrics and weights
Reference 5
Source-reported events for the cited work
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