Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T14:16:10.937561Z
Paper Citation Record · LEDGER
As of 12 August 2026, this Paper Citation Record lists 60 of 60 outbound references and 0 inbound Pith citation observations for arXiv:2505.19796.
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 2026-08-07T14:16:10.937561Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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
60 of 60 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 8b4d474d-71ff-4d3e-afa8-d6a0bfeff40f · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a34e717a-6117-49bf-bde4-85f4bd352e0e · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a93bc54c-580f-4d67-9ea5-723b640307d3 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 39533bfb-ae9f-49b4-9cb2-d252f06013ec · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b577b435-5162-4ce2-b9ba-e1d0aa87059c · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 834e2090-0b3d-4e08-be9f-1eadbce4263f · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 822b1e1a-9283-4724-b824-cbd70b0f3521 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 0d80fb3d-ea6f-48c2-a921-655023806022 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures 3.2 Topological Structures in Embedding Let 𝑃∈𝐸(𝐾) be a point of infinite order
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9a6b5800-a67c-48f8-bd7d-331761643344 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 61a72b2c-abd1-4e9c-946c-eb3e249a53e6 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures This loop 𝐿 is topologically nontrivial and represents a generator of the first homology group 𝐻ଵ(Φ(𝐸), ℤ)
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4ef7e6b3-3280-4a02-a7f1-593e2bbc0081 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 7b52db80-51bf-4f1f-9050-303756bc2696 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 91b37f76-9b1c-48a0-833f-97eb657f5c36 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 48bce7bc-701e-4447-9f89-b9779cf4293b · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9f399ad9-0f67-4f6f-a2ff-657411e01418 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 15401111-5061-41a3-a390-48f9f7b77030 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures topological zeta function
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c6ecc501-fa88-47c5-a89d-ca2ff6a429e7 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ed6a0e9e-d350-4bd7-97a3-37ff2b6e13e8 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 0a7ec983-6922-4338-9f71-4a0d79e6f35b · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 08e81eac-4da2-4675-9610-d73feff47f31 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation e53afab6-123f-4d2a-802c-8116026be62b · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 95dd038d-f01a-4950-b948-1a78044e96c1 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a9c93e21-5ff6-4a5c-aaba-17d4d360b3b7 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 96d3f754-81cf-4093-b686-5eb0ca54ff1d · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Our results show a consistent pattern across hundreds of elliptic curves: Observation 8.3
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4b32cc2f-7280-4a48-9450-850b7c4084c5 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 1ade8682-d369-4833-a4d0-decaa20558a4 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2d629699-5516-483d-990c-e3b586d7a775 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 45bc19b3-1cc6-4e81-90b8-911a52e1af51 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2d5655e4-7c48-48cc-b4b3-4fa6383216eb · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Similarly, the analytic aspects present additional challenges:
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 1405c3ba-6f8a-445d-8d62-a98087c700d1 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 157a72c0-cb57-4b8b-8703-2f3620aeb677 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f1c2055f-9439-4966-bce0-0c7e72c7fb59 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures 11.2 Proposed Approaches for Generalization 11.2.1 Higher-dimensional embedding construction Definition 11.2 (Generalized Embedding)
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 246cced8-35ff-477c-8e3a-ce0a70872a14 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation fad53d2c-570a-4b83-84ae-f1e7a73c4d6e · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures loop structures
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 199b360e-f457-4e52-a2d8-6dc4d85364d2 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 61e8cb95-936e-4d0f-ae00-93c5b6dbcccc · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures In our framework, this corresponds to the absence of infinite loops in the embedding
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation aa26e440-0bec-4e67-be76-0a6911379ab2 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures size" or
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 1201ad96-5807-4bb8-b13f-915dee15b3e3 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation e0ef77cf-6567-43d7-90d1-1ae328b8c25c · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 23f9345e-08f1-4cec-ab67-8a029f555785 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Our computational approach, which is based on the functions 𝐹new and 𝐹,௦, provides a practical tool for exploring these connections empirically
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2d8c3115-3384-4d26-8017-fa9d2b65c235 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 3b3fa38a-1cd1-4608-ab70-32f65fbd3410 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b40a616c-7d03-4a2e-8990-8a93105e7d6c · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a6c33647-dbb4-4d07-9ceb-d25b2b483cd8 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4070446a-cff0-497b-83d3-bea1d138ce86 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Bhargava and A
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation eef56122-d0d1-4997-99f4-dfd21b8a8f42 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c1c528c0-7f49-4386-9436-8be9899daf9e · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4e528b90-3c20-405f-a9bf-c4d06a1c8d31 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Breuil, B
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9b4658fa-f3b8-465a-bc2e-6aa6fb0af382 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Coates and A
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f0372bbd-be7f-4ce1-9fbf-d3c0d7a266e3 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c6f5a4d2-064e-4d57-95c5-e4cb55fc469b · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Dokchitser
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 97b4782d-706f-419a-b293-2dfe2881c781 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 89722e05-2181-4216-af59-fd1b9d933f36 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Three lectures on elliptic surfaces and curves of high rank
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 13e0f36f-906b-449b-8ecf-24d2068e6677 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ee1248b1-f396-43bb-80ef-615c7ac70139 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2c81e0df-642b-4f9e-a67a-c95b3c726fa7 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 77e76c68-1903-4f6c-b157-3742a66bc42f · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b4a08703-efa2-4478-9f95-af7d4a6f693e · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures main conjectures
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 7b258cfc-7c71-4e76-a025-710e45648320 · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Taylor and A
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c558dbe6-28e9-427e-b783-41a1b0163e7a · outbound
A Topological Perspective on the Birch and Swinnerton Dyer Conjectures Unresolved cited work
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
No inbound Pith citation observations are available.