Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-08T06:26:38.945329Z
Paper Citation Record · LEDGER
As of 4 August 2026, this Paper Citation Record lists 81 of 81 outbound references and 0 inbound Pith citation observations for arXiv:2604.23659.
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 2026-05-08T06:26:38.945329Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+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
81 of 81 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation a9c7abe7-b9d0-4ae7-a1f5-eaf416259e3b · outbound
Peak-valley mechanism for Hilbert space fragmentation Abanin, Ehud Altman, Immanuel Bloch, and Maksym Serbyn.Colloquium: Many-body localization, thermalization, and entanglement.Rev
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation f62408c8-9d92-4002-9ad0-9cb43185f15d · outbound
Peak-valley mechanism for Hilbert space fragmentation Polkovnikov, K
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 5a6d2510-d257-4472-9533-7b810600511b · outbound
Peak-valley mechanism for Hilbert space fragmentation Many-Body Localization and Thermalization in Quantum Statistical Mechanics
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 1b5e91db-4553-416c-8847-69b09f3b8731 · outbound
Peak-valley mechanism for Hilbert space fragmentation Quantum statistical me- chanics in a closed system
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 27e5603d-0416-4a42-b864-f10f6c679b9b · outbound
Peak-valley mechanism for Hilbert space fragmentation Chaos and quantum thermalization.Phys
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 346db16b-9408-4be4-a3ba-791b737facf8 · outbound
Peak-valley mechanism for Hilbert space fragmentation Srednicki, The approach to thermal equilibrium in quantized chaotic systems, Journal of Physics A: Mathematical and General 32(7), 1163 (1999), doi:10.1088/0305-4470/32/7/007
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation dc07b50b-4e92-4bcc-a552-41de323082e3 · outbound
Peak-valley mechanism for Hilbert space fragmentation Kim , author T
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 5669842c-ddd3-4b68-81fe-efb767423536 · outbound
Peak-valley mechanism for Hilbert space fragmentation Hild , author T
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation e481eb10-0340-404e-be16-17e71206a4cb · outbound
Peak-valley mechanism for Hilbert space fragmentation Serbyn, D
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 48249d03-12fe-4581-a147-7ccbc7110a38 · outbound
Peak-valley mechanism for Hilbert space fragmentation Schreiber, S
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation ad1f0417-5a6c-4cdf-bec0-5c947045a579 · outbound
Peak-valley mechanism for Hilbert space fragmentation \ Desaules , author A
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation e2caed8c-abce-4b34-ae50-e1ca155ec2e3 · outbound
Peak-valley mechanism for Hilbert space fragmentation Unresolved cited work
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 68738dbe-89c8-4f3c-9559-7dc1950353b6 · outbound
Peak-valley mechanism for Hilbert space fragmentation Moudgalya, N
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation c36cbb7b-05d3-4057-a876-dd1551b62861 · outbound
Peak-valley mechanism for Hilbert space fragmentation Chandran, T
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation d7405028-681f-435c-b764-6cbe5349dac9 · outbound
Peak-valley mechanism for Hilbert space fragmentation Khemani , author M
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 0fad50df-818c-4cda-90cd-d4c70f89bcdd · outbound
Peak-valley mechanism for Hilbert space fragmentation Rakovszky , author P
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 9b0e01d1-4be4-4a83-a237-814580c91256 · outbound
Peak-valley mechanism for Hilbert space fragmentation Moudgalya, B
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 1f641216-a87c-4faa-802a-5253a43317b2 · outbound
Peak-valley mechanism for Hilbert space fragmentation Sala , author T
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 4c9ae3d8-cce6-4513-8dd1-e1e37e7d78b6 · outbound
Peak-valley mechanism for Hilbert space fragmentation Unresolved cited work
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 48a416e9-dd4c-4b38-a58c-c6a8758387f9 · outbound
Peak-valley mechanism for Hilbert space fragmentation \ Yang , author F
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 8173d8f4-cb6d-446a-87a5-84c3fb0fa337 · outbound
Peak-valley mechanism for Hilbert space fragmentation Brighi , author M
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation a7e26c3b-c65f-4512-a8ac-270f5d3f9a5a · outbound
Peak-valley mechanism for Hilbert space fragmentation Wang \ and\ author Z.-C
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation cb767941-5cef-4703-8782-bac2b61238d1 · outbound
Peak-valley mechanism for Hilbert space fragmentation Aditya , author D
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 06f5f473-d357-4ded-8500-0d2ddbeafcbc · outbound
Peak-valley mechanism for Hilbert space fragmentation Aditya ,\ 10.1103/7j6x-74f1 journal journal Phys
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 44fdeca0-944f-4000-8e97-f28a85232282 · outbound
Peak-valley mechanism for Hilbert space fragmentation Khudorozhkov , author A
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 6e8225b2-b481-4893-80f9-4d1c8af5c188 · outbound
Peak-valley mechanism for Hilbert space fragmentation Chattopadhyay , author B
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation a562f8eb-799a-4f04-9e2b-6a8e4b88858c · outbound
Peak-valley mechanism for Hilbert space fragmentation Will , author R
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation ea5058df-9b6c-4c35-8699-2ca29d48e079 · outbound
Peak-valley mechanism for Hilbert space fragmentation Yoshinaga, H
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 25190d22-d7b1-480a-8f6c-143d115be664 · outbound
Peak-valley mechanism for Hilbert space fragmentation Nicolau , author A
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 22c379ba-0fcd-49f6-aca3-07ba55532383 · outbound
Peak-valley mechanism for Hilbert space fragmentation Unresolved cited work
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 585e6335-46d2-4d42-a231-b670a0ee30fc · outbound
Peak-valley mechanism for Hilbert space fragmentation Kohlert , author S
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 2301fa68-baa2-4526-b63c-c23d879568c5 · outbound
Peak-valley mechanism for Hilbert space fragmentation Zhao , author P
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 4152981f-97ce-4fcc-bce5-e3008e8fce0a · outbound
Peak-valley mechanism for Hilbert space fragmentation \ Wang , author Y.-H
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation cc0d8b6a-19f3-40ba-9107-f2a4b27beac6 · outbound
Peak-valley mechanism for Hilbert space fragmentation Adler , author D
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation cf266c3e-c9a4-4bc0-97c3-c2ff01f97cd7 · outbound
Peak-valley mechanism for Hilbert space fragmentation Motrunich
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 5caa17e4-100e-4eff-9f62-e53f14e6d310 · outbound
Peak-valley mechanism for Hilbert space fragmentation Moudgalya \ and\ author O
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 1aad6861-fbe2-4306-8672-34aea0d11e8c · outbound
Peak-valley mechanism for Hilbert space fragmentation Motrunich
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 01426ec4-0c5e-4617-bd0c-932c630a3d05 · outbound
Peak-valley mechanism for Hilbert space fragmentation Dyn amics in systems with modulated symmetries
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 40c90948-31b2-4aed-94a1-9efe863408ed · outbound
Peak-valley mechanism for Hilbert space fragmentation Feldmeier, P
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 3c76fe5c-0fcf-450c-a8b0-c993da45b969 · outbound
Peak-valley mechanism for Hilbert space fragmentation Hart , author A
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation aa7fd92c-1971-4211-a7d7-59c9344165ee · outbound
Peak-valley mechanism for Hilbert space fragmentation Iaconis , author A
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 8b6143c2-bd59-412d-8414-3cf23262b0ef · outbound
Peak-valley mechanism for Hilbert space fragmentation Chamon, Quantum glassiness in strongly correlated clean systems: An example of topological overprotection, Physical Review Letters94, 10.1103/physrevlett.94.040402 (2005)
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 139ca743-ce34-417d-b0b9-e8775cfafc6d · outbound
Peak-valley mechanism for Hilbert space fragmentation Nandkishore and M
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 3e862648-25c2-442f-bb35-bb59357a90cb · outbound
Peak-valley mechanism for Hilbert space fragmentation Prem , author J
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation b4a5dc27-dc57-4310-9a43-f5724eba4065 · outbound
Peak-valley mechanism for Hilbert space fragmentation Vijay, J
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 78d75648-6c76-4fa3-bbd0-b5faaa1e59e8 · outbound
Peak-valley mechanism for Hilbert space fragmentation Vijay, J
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation b2e8f77f-f6d1-4a4c-a539-aa8bc914c1c8 · outbound
Peak-valley mechanism for Hilbert space fragmentation Pretko, Phys
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 373bd465-0cb8-43b2-82ab-2a1310f454f2 · outbound
Peak-valley mechanism for Hilbert space fragmentation Pretko, Phys
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation ff3d50a7-58d4-4651-b3ec-76ca6af80c16 · outbound
Peak-valley mechanism for Hilbert space fragmentation Pretko and L
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 8fc63ad5-227a-401e-a684-eedf4115088b · outbound
Peak-valley mechanism for Hilbert space fragmentation Morningstar, V
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 0837be7f-24c3-4077-bf70-7e902b480be5 · outbound
Peak-valley mechanism for Hilbert space fragmentation Unresolved cited work
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 679b4629-2fea-4c4b-8f37-9d020b58415d · outbound
Peak-valley mechanism for Hilbert space fragmentation Unresolved cited work
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation f1803bb6-6e0c-4cfa-9f02-a4714d8567d9 · outbound
Peak-valley mechanism for Hilbert space fragmentation and Toffoli, T
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation accf53e8-7449-4fb6-b41b-204d19b200fa · outbound
Peak-valley mechanism for Hilbert space fragmentation Unresolved cited work
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation bc702b40-beea-4bc3-bd6c-9152769c436a · outbound
Peak-valley mechanism for Hilbert space fragmentation Salberger \ and\ author V
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation c906ccd3-cb35-4cf6-9a46-ec044c828afb · outbound
Peak-valley mechanism for Hilbert space fragmentation Bravyi , author L
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 24243523-13ec-49cb-a588-f11e1fad09b0 · outbound
Peak-valley mechanism for Hilbert space fragmentation Zhang , author A
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 874c4046-c5ae-45dc-8d94-fb6fd5808696 · outbound
Peak-valley mechanism for Hilbert space fragmentation Barbiero , author L
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation c98133fd-afdf-48b5-ba8a-a6206f19589c · outbound
Peak-valley mechanism for Hilbert space fragmentation Richter \ and\ author A
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 52cbdf36-452d-44a6-a4d6-47812c18ff74 · outbound
Peak-valley mechanism for Hilbert space fragmentation Jeyaretnam, T
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation f216016e-550d-4232-b124-1cf673fa5256 · outbound
Peak-valley mechanism for Hilbert space fragmentation Li , author P
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 0c324aa7-7493-4cd9-8949-8c82300b03a7 · outbound
Peak-valley mechanism for Hilbert space fragmentation Hahn , author P
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 8deed17c-a8f3-4593-a15d-2e159ac02f1f · outbound
Peak-valley mechanism for Hilbert space fragmentation Patil , author A
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 0aa24c7e-2585-42fa-bcf6-b0b4e2bac455 · outbound
Peak-valley mechanism for Hilbert space fragmentation Anyons in an exactly solved model and beyond
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 544205ce-f84c-42c2-8133-6757c11eefb1 · outbound
Peak-valley mechanism for Hilbert space fragmentation Yao \ and\ author S
Reference 65
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 5c76c57d-a0d8-4430-9f9f-e935e41b8445 · outbound
Peak-valley mechanism for Hilbert space fragmentation Fu ,\ 10.1103/PhysRevB.106.L161412 journal journal Phys
Reference 66
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 2323c905-fb1c-4d40-bb98-e01c413e7460 · outbound
Peak-valley mechanism for Hilbert space fragmentation Affleck , author T
Reference 67
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 842a76ce-e083-4623-aad2-3b6beae98648 · outbound
Peak-valley mechanism for Hilbert space fragmentation Part I , author =
Reference 68
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation a58979d1-a8c3-44d2-b344-6a5bb89dc6e2 · outbound
Peak-valley mechanism for Hilbert space fragmentation An introduction to lattice gauge theory and spin systems
Reference 69
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation bfb18787-4875-42dc-b6e2-5d4db706cfdd · outbound
Peak-valley mechanism for Hilbert space fragmentation & Wigner, E
Reference 70
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 0b114bd9-7148-4041-a587-ecc132e953ca · outbound
Peak-valley mechanism for Hilbert space fragmentation Lieb , author T
Reference 71
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 8622f967-fcc8-4611-9c60-42f69bc730b9 · outbound
Peak-valley mechanism for Hilbert space fragmentation Pozderac , author S
Reference 72
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 1132c3cc-36d5-469b-8a18-448078796022 · outbound
Peak-valley mechanism for Hilbert space fragmentation Amico, R
Reference 73
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation ac290749-3ee5-4cc6-b961-5a4328efbb21 · outbound
Peak-valley mechanism for Hilbert space fragmentation Bauer \ and\ author C
Reference 74
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 32fe8fd6-7992-4e51-b97e-c467a58d1a74 · outbound
Peak-valley mechanism for Hilbert space fragmentation Unresolved cited work
Reference 75
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation d905171b-641e-4b9f-b26b-d212d42db783 · outbound
Peak-valley mechanism for Hilbert space fragmentation Yu , author D
Reference 76
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 25454e63-52a2-4cde-85a1-25048f5d09f9 · outbound
Peak-valley mechanism for Hilbert space fragmentation Herviou , author J
Reference 77
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 40f746cf-6378-479d-bd98-a3e10b220966 · outbound
Peak-valley mechanism for Hilbert space fragmentation Francica \ and\ author L
Reference 78
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation fe4bcd54-817e-4cd2-933f-c7f7b09a257a · outbound
Peak-valley mechanism for Hilbert space fragmentation Physical Review A83(4) (2011) https://doi.org/10.1103/physreva.83.042330
Reference 79
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 9c2ae275-f2ca-43af-92e8-d2a0a7689dbd · outbound
Peak-valley mechanism for Hilbert space fragmentation Lehmann , author P
Reference 80
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
Observation 4e463969-cf0e-44b9-ac3c-3397cdd7e56e · outbound
Peak-valley mechanism for Hilbert space fragmentation Unresolved cited work
Reference 81
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.
No inbound Pith citation observations are available.