Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T04:26:48.649152Z
Paper Citation Record · LEDGER
As of 8 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 0 inbound Pith citation observations for arXiv:2506.10809.
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 2026-08-07T04:26:48.649152Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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
53 of 53 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation dabcd6bc-48a8-4a81-bcb1-36c9b31f9b4f · outbound
Warped products over one-dimensional base spaces and the RCD condition Alexander and Richard L
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation fe127d9d-1ac8-4893-8df5-7ae998edf769 · outbound
Warped products over one-dimensional base spaces and the RCD condition Alexander and Richard L
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 16f1e600-e383-4899-a582-de31bdc5c699 · outbound
Warped products over one-dimensional base spaces and the RCD condition Alexander and Richard L
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 23de0c3e-0517-4ea9-a42d-2c7d9e81219d · outbound
Warped products over one-dimensional base spaces and the RCD condition Alexander and Richard L
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 33c9d99c-db0a-49af-9c97-05e48feb1e5a · outbound
Warped products over one-dimensional base spaces and the RCD condition Gradient flows in metric spaces and in the space of probability measures
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ffe08a24-e8b5-4dab-b8fc-d674e091136e · outbound
Warped products over one-dimensional base spaces and the RCD condition Metric measure spaces with Rie- mannian Ricci curvature bounded from below
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a68b03b3-3772-471f-91c6-21352dbb49f7 · outbound
Warped products over one-dimensional base spaces and the RCD condition Bakry- ´Emery curvature- dimension condition and Riemannian Ricci curvature bounds
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 733f28be-49d9-4c74-be90-0d7a4829dad5 · outbound
Warped products over one-dimensional base spaces and the RCD condition Nonlinear Diffusion Equa- tions and Curvature Conditions in Metric Measure Spaces
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 344fa5fa-8434-43b6-a19b-2ff8dbed53f5 · outbound
Warped products over one-dimensional base spaces and the RCD condition Anderson
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation f69f4e01-d947-4f38-b3e5-73b794abc684 · outbound
Warped products over one-dimensional base spaces and the RCD condition Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d959be70-ccd4-4961-9a2a-665f5ee2a725 · outbound
Warped products over one-dimensional base spaces and the RCD condition A course in metric geometry , vol- ume 33 of Graduate Studies in Mathematics
Reference 11
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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 964d553c-33a5-4b41-aaf3-45ce83b7cfa7 · outbound
Warped products over one-dimensional base spaces and the RCD condition Generalized cones admit- ting a curvature-dimension condition, 2025
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6f0bb31f-2fd1-4ab4-a9cb-ed4ee895e9c5 · outbound
Warped products over one-dimensional base spaces and the RCD condition The globalization theorem for the curvature- dimension condition
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 92c6e80d-d4ca-4cb1-91e2-1af702590357 · outbound
Warped products over one-dimensional base spaces and the RCD condition Scalar and mean curvature comparison via the Dirac operator
Reference 14
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cdbb297c-575b-462a-b5ff-e52ae07b37d2 · outbound
Warped products over one-dimensional base spaces and the RCD condition Differentiability of Lipschitz functions on metric measure spaces
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d32c1c74-2b6c-4b33-b8df-c5eb03ec9351 · outbound
Warped products over one-dimensional base spaces and the RCD condition Unresolved cited work
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bc7a3d01-c18e-41ba-8919-5f678c75f969 · outbound
Warped products over one-dimensional base spaces and the RCD condition Unresolved cited work
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4c42c6a0-8e93-40fb-bad5-c7ed2cbb438d · outbound
Warped products over one-dimensional base spaces and the RCD condition Almost volume cone implies almost metric cone for annuluses centered at a compact set in $RCD(K, N)$-spaces
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 449b1836-8c0f-44e8-a3b0-736510029a33 · outbound
Warped products over one-dimensional base spaces and the RCD condition Characterization of tangent cones of non- collapsed limits with lower Ricci bounds and applications
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3742a366-afb6-428e-b569-bb8721b3cf30 · outbound
Warped products over one-dimensional base spaces and the RCD condition Maximal volume entropy rigidity for RCD∗(−(N − 1), N) spaces
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d092f540-4309-44d7-b50f-d8bb4983c859 · outbound
Warped products over one-dimensional base spaces and the RCD condition From volume cone to metric cone in the non- smooth setting
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7cb06e50-17a2-4bf2-a5c8-f59b8d462123 · outbound
Warped products over one-dimensional base spaces and the RCD condition H¨ older continuity of tangent cones in RCD(K, N) spaces and applications to nonbranching
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation aadcb108-3885-449e-b4f8-d4cc9db93fc2 · outbound
Warped products over one-dimensional base spaces and the RCD condition On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5ea40292-159e-41d4-a85a-01e23d8c6546 · outbound
Warped products over one-dimensional base spaces and the RCD condition The splitting theorem in non-smooth context
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 44910695-dabc-47ef-9d6e-0ae36da65044 · outbound
Warped products over one-dimensional base spaces and the RCD condition An overview of the proof of the splitting theorem in spaces with non- negative Ricci curvature
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a8fc2a66-4cc7-46e6-990a-a201ce78bce5 · outbound
Warped products over one-dimensional base spaces and the RCD condition On the differential structure of metric measure spaces and applications
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a0f119b3-2df3-49e9-b9ab-0822c1033ce3 · outbound
Warped products over one-dimensional base spaces and the RCD condition Nonsmooth differential geometry—an approach tailored for spaces with Ricci curvature bounded from below
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3af4633b-bba9-4547-b6ba-aba2e7adbc50 · outbound
Warped products over one-dimensional base spaces and the RCD condition De Giorgi and Gromov working together
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 38001d86-8993-4623-9087-7982ad32d7af · outbound
Warped products over one-dimensional base spaces and the RCD condition Sobolev spaces on warped products
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation db3c206d-19c2-4d95-ade5-6ebaa4cb2678 · outbound
Warped products over one-dimensional base spaces and the RCD condition Heat flow on Alexandrov spaces
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c90bc458-18e0-4c08-8510-17fdb7ef5648 · outbound
Warped products over one-dimensional base spaces and the RCD condition A general splitting principle on RCD spaces and applications to spaces with positive spectrum
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6a83b0e1-c017-4bdd-9a3b-2e4146e3bc1e · outbound
Warped products over one-dimensional base spaces and the RCD condition Convergence of pointed non- compact metric measure spaces and stability of Ricci curvature bounds and heat flows
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b825b1f5-7c03-4957-bb1d-e0fe31070266 · outbound
Warped products over one-dimensional base spaces and the RCD condition Sobolev met Poincar´ e
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 11f9f1d4-a609-4874-b2e4-a7235b35049b · outbound
Warped products over one-dimensional base spaces and the RCD condition Lower Ricci curvature and nonex- istence of manifold structure
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a543fb9a-f5bd-4705-b617-5c7b97ef58bc · outbound
Warped products over one-dimensional base spaces and the RCD condition CD meets CAT
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7db17550-822e-4cf0-b610-7ccc872105b4 · outbound
Warped products over one-dimensional base spaces and the RCD condition Ricci curvature bounds for warped products
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 265244c6-a38e-4903-877a-0ed9ccd7bcdd · outbound
Warped products over one-dimensional base spaces and the RCD condition Cones over metric measure spaces and the maximal diameter theorem
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation fb835f60-bf8c-484e-8053-89c6940bfb4a · outbound
Warped products over one-dimensional base spaces and the RCD condition Obata’s rigidity theorem for metric measure spaces
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation da7045cf-4b5d-4ac4-9692-d1e0de041c54 · outbound
Warped products over one-dimensional base spaces and the RCD condition Warped products and synthetic lower curvature bounds: an overview
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2210477a-e624-4235-a7cb-c3bb338fd11d · outbound
Warped products over one-dimensional base spaces and the RCD condition Geometry and analysis of Dirichlet forms.Adv
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a84ef434-fce6-43a1-9f1a-b5471f38e8b7 · outbound
Warped products over one-dimensional base spaces and the RCD condition Infinitesimal Bishop-Gromov condition for Alexandrov spaces
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 108ca575-1026-4230-a2f8-fa56832aa470 · outbound
Warped products over one-dimensional base spaces and the RCD condition Some geometric properties of the Bakry- ´Emery-Ricci tensor
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 04fc1076-ff1f-48ca-884c-6e3ac7149c34 · outbound
Warped products over one-dimensional base spaces and the RCD condition Ricci curvature for metric-measure spaces via optimal transport
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c3b7e504-81d9-441a-be6e-d1a400e5bfa0 · outbound
Warped products over one-dimensional base spaces and the RCD condition Ricci curvature in dimension 2
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2d906eb3-b650-42f2-89b1-18e790650013 · outbound
Warped products over one-dimensional base spaces and the RCD condition On the measure contraction property of metric measure spaces
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 22287281-3fba-44d8-8f1f-1c401ff6497a · outbound
Warped products over one-dimensional base spaces and the RCD condition Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation fb4911c4-f0cb-4414-8e94-16ccef3bbf43 · outbound
Warped products over one-dimensional base spaces and the RCD condition Methods of modern mathematical physics
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6143b481-92ac-4321-a40f-18af631d63af · outbound
Warped products over one-dimensional base spaces and the RCD condition Self-improvement of the Bakry-´Emery condition and Wasserstein contraction of the heat flow in RCD( K, ∞) metric measure spaces
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 84018b35-3d79-420c-983f-e88d3e89e6b0 · outbound
Warped products over one-dimensional base spaces and the RCD condition Analysis on local Dirichlet spaces
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 36685870-d58d-4d1f-9f1c-7c4a23feb5a7 · outbound
Warped products over one-dimensional base spaces and the RCD condition Analysis on local Dirichlet spaces
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7aa9bc29-6f1b-43ae-a2d6-7f1dfa7c18d5 · outbound
Warped products over one-dimensional base spaces and the RCD condition On the geometry of metric measure spaces
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8aebf0f2-1fe8-4f34-8fc7-86cccc923f6a · outbound
Warped products over one-dimensional base spaces and the RCD condition On the geometry of metric measure spaces
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5a56a064-2c29-4982-84d9-942824898194 · outbound
Warped products over one-dimensional base spaces and the RCD condition Bakry-´ emery, Hardy, and spectral gap estimates on manifolds with conical singularities
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
No inbound Pith citation observations are available.