Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T01:07:42.501518Z
Paper Citation Record · LEDGER
As of 19 August 2026, this Paper Citation Record lists 71 of 71 outbound references and 2 inbound Pith citation observations for arXiv:2505.02315.
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 2026-08-16T01:07:42.501518Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-12T19:40:21.874309Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-07T12:09:18.707619Z
71 of 71 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 3b47f7dd-caef-4138-8a48-29465c297410 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Angenent, S
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a96b5708-dcb7-4f52-b101-252b6a591618 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Bamler, C
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 891fdcfd-0d01-4cd2-8a65-e6b7a93f0ee2 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 46c4c346-9aaa-41a6-b6fc-1fc3b0ae879b · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature B¨ ohm, B
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation fbc84a9f-38b2-412b-9e35-0f201f15634b · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Brendle, Ancient solutions to the Ricci flow in dimension 3, Acta M ath
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 821e6c93-7d71-4877-910a-f15c3b7e21e5 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Brendle, P
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c9321430-521e-4501-9f5a-426ccafe5d9f · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f1521eb6-d819-42b2-9329-1a1569eac636 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation adb962d0-0043-4b4e-a2c9-61f8319d1b12 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e2fe78a9-afff-40a9-a1d1-e37bb00a95b5 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b9c91702-916d-4fe2-9850-f56e5289be6f · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation cd4d1c37-e22c-458d-8257-a5c43d15f023 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 08fcf539-807a-452a-9422-a17807b86324 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Rigidity of four-dimensional K\"ahler-Ricci solitons
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4042e161-bf53-48d7-8127-4903f1c71501 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 507b7a7d-ff85-43ab-8dfc-008664a70c94 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Catino, Complete gradient shrinking Ricci solitons with pinched curvature, Math
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d71fdd5a-82da-4834-83dd-ad8e18b433c0 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Colding, W.P
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 002f3b57-b930-44c9-ad17-a15f56903409 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f8b79507-9464-4aa6-9269-db3360b4d86e · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Chen, Pointwise 1 / 4-pinched 4-manifolds
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3559c759-2e45-45cf-9677-d7e6709cc1dc · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7b758582-f4b5-46d0-bfe3-2e531304afd8 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b5182e59-397c-42a6-a4fa-a8429771f9e4 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Cheng, D
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 00bb470e-135d-41bb-9afd-abab32c85233 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation eba720ee-8c81-4753-a1f1-44f038e9a669 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ec67749d-9d66-4d4a-8f74-1942d7cbfb36 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 46f07867-13d4-4cb2-9fd8-355f4c3a92c4 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Cifarelli, R
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 2b6d62a4-ab03-4364-b33a-5c018c347b2c · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Conlon, A
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4e380fcb-1a8e-40b5-8d0c-412666039ace · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Eminenti, G
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e8daddff-2fd8-4ee4-a6d8-7bab64156b19 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Feldman, T
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d2c1f458-14fc-480c-9599-96e2e6430b5c · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Fern´ andez-L´ opez, E
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 54819ce2-74c5-4fae-9337-75ae3b4360ab · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Fern´ andez-L´ opez, E
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a7e65b0b-ba98-4042-894f-7d3f7c4f47fe · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7a7aafe8-081b-4dc5-88d6-667b72dc5055 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9f24d8db-5ddf-44c5-bd1c-f4edf5dbdf25 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Hamilton, Three-manifolds with positive Ricci curvature, J
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 928ecffb-7119-46f5-95af-e468702a4f80 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Hamilton, Four-manifolds with positive curvature operator, J
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 49ac8d42-0c95-4f24-80db-89113eccd51d · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Hamilton, The formation of singularities in the Ricci flow, Surve ys in Differential Geometry, Inter- national Press, Boston, vol
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 538648a1-7176-4f7d-9eee-c5ed136fb40c · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Haslhofer, R
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 8f81a1d2-0086-44bb-b190-f7b75924ab97 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Ishii, On the equivalence of two notions of weak solutions, visc osity solutions and distribution solu- tions, Funkcial
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e80d3e3b-690b-40df-b741-89fcb4041bba · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Ivey, Ricci solitons on compact three-manifolds, Diff
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7db17713-03a5-46c4-90ab-39cbfacbc5f5 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Kotschwar, A local version of Bando’s theorem on the real-a nalyticity of solutions to the Ricci flow, Bull
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 103bdeef-07a5-4cbb-93f3-d73296390658 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Kotschwar, L
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ff1715e1-4353-4b11-bef9-72e6a3f3a62d · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Kotschwar, L
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b92e31f0-02a7-4448-9dea-14b2a115ee59 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 676468fd-c134-4f39-bf24-1700c375c1c7 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation df44a348-2bb6-490f-b50b-f0591491ce9a · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 8dbb0389-d8e7-42e5-9925-1029edc001e7 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e28557bc-2022-4f8f-9b15-d766daaa3bc3 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 1b2b2936-f3b0-4ae6-be6e-ded961a7de8c · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation aebee0ba-3a1a-4475-8e63-33bd30bd85ca · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Munteanu, N
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f5e66210-36ad-431e-b21e-1b4077b4b595 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Munteanu, J
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c8d033b7-a276-4664-aaaf-0db2481a6d5d · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Munteanu, J
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation cfa17b7a-86e5-4043-a80d-71f81780997f · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Munteanu, J
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation fe0fbb08-71d0-4f74-bbf2-225efa6e881b · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Munteanu, J
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a54de6aa-e94f-49e9-8ec3-d8786ed639ad · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Munteanu, J
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3da5e719-e38b-43f0-8d0d-62ceeb083a0e · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Naber, Noncompact shrinking four solitons with nonnegative curvature, J
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3d84c414-c09e-42a9-bd97-1d333b7b215c · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 29b4bdf1-8326-4b9b-a01c-613856e98cde · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Ni, Ancient solutions to K¨ ahler-Ricci flow, Math
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ff5ccf7a-edaa-4d82-bccc-c630827eab2e · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Some rigidity results on shrinking gradient Ricci soliton
Reference 57
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 462208f5-f56a-4358-9c4f-c6d1a2053d4b · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Perelman, The entropy formula for the Ricci flow and its geom etric applications, (2002), arXiv:math.DG/0211159
Reference 58
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 50709849-627b-4eca-8694-117b9e6b183b · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Perelman, Ricci flow with surgery on three-manifolds, (2003 ), arXiv:math.DG/0303109
Reference 59
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b89f00f6-d4ca-490c-a5d2-0db80cd449d2 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Perelman, Finite extinction time for the solutions to the Ricci fl ow on certain three-manifolds, (2003), arXiv:math.DG/0307245
Reference 60
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d11966ba-e272-44de-9e39-477ea38a1088 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Petersen, W
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b67fd070-e578-47c6-ba05-b9fcb15a876e · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Petersen, W
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 5397c35f-a065-4561-8814-d46327f5a5da · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Pigola, M
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 34360e9e-8e95-4aee-8d18-e8cc08fb3d0f · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d95c6b0d-1749-4a3c-8e17-b2de819a1c9a · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 65
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 95461d1d-ab33-474f-9890-1ea79d1ea025 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 66
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 84990a56-039e-4785-b89e-25ba525e8e17 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 67
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a2b1aa8c-317e-4560-b392-f90970e2a4fb · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 68
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3ea42818-53cc-4c03-a5d1-9b9b5340134f · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Conformally invariant rigidity theorems on four-manifolds with boundary
Reference 69
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 75406da4-9ce3-432d-8781-ac272dc92932 · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Unresolved cited work
Reference 70
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 95404e17-9c63-47ee-942d-264e7a0a2a0f · outbound
Four-dimensional shrinkers with nonnegative Ricci curvature Zhu, Geometry of positive scalar curvature on complete man ifold, J
Reference 71
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 23b47a5f-7b67-47e4-b6dc-6f2ad6d80ff7 · inbound
Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature Four-dimensional shrinkers with nonnegative Ricci curvature
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 375151e6-de47-4283-b2a8-fc26abfc1238 · inbound
Rigidity of Five-Dimensional shrinking gradient Ricci solitons Four-dimensional shrinkers with nonnegative Ricci curvature
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.