Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-07-01T03:55:48.921447Z
Paper Citation Record · LEDGER
As of 20 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 0 inbound Pith citation observations for arXiv:2606.31649.
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 2026-07-01T03:55:48.921447Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+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
63 of 63 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation fbb595a3-5c7a-42d4-aec7-930d56251f5c · outbound
Tamagawa ratios and unbounded Selmer moments Integers expressible as the sum of two rational cubes
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 195d3bb9-f846-4c6b-9db2-63bed2682b45 · outbound
Tamagawa ratios and unbounded Selmer moments Bhargava, N
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c4a1831a-7441-4840-9b68-a74a693eb00f · outbound
Tamagawa ratios and unbounded Selmer moments On average sizes of Selmer groups and ranks in families of elliptic curves having marked points
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d77e1727-4827-42b8-a98d-b5781d2be629 · outbound
Tamagawa ratios and unbounded Selmer moments Bhargava, D.M
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 56cb0e18-78ea-4d74-9605-0f5d8dee4e07 · outbound
Tamagawa ratios and unbounded Selmer moments Bhargava, Z
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f2328128-43dc-430e-a63b-7bc716a11712 · outbound
Tamagawa ratios and unbounded Selmer moments Bhargava and A
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 3c8b8674-6bc6-42b5-81bd-f6b22ae450c0 · outbound
Tamagawa ratios and unbounded Selmer moments Bhargava and A
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e867ea79-4152-4983-927d-5b166b82eb8a · outbound
Tamagawa ratios and unbounded Selmer moments The average number of elements in the 4-Selmer groups of elliptic curves is 7
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d781e157-148a-4711-a4ed-67d20b474b60 · outbound
Tamagawa ratios and unbounded Selmer moments The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b26d25ee-03fe-460c-a8f6-0b706206b5c6 · outbound
Tamagawa ratios and unbounded Selmer moments Geometry-of-numbers methods over global fields II: Coregular representations
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a8a27944-e38f-40af-8859-4da99c2bd625 · outbound
Tamagawa ratios and unbounded Selmer moments Bhargava, T
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d16e307c-b527-43d9-ab62-3fbcce9f3c54 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 307f4842-2ecc-44ba-82b5-533f092ca492 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8489c733-9f8d-45d6-9075-1ad8022972a9 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d5f99905-bdd7-46b3-863d-9ae53ca2514c · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation bae83e1b-b3d8-4bdf-9fb2-929c05fc4bb8 · outbound
Tamagawa ratios and unbounded Selmer moments Selmer groups of families of elliptic curves with an $\ell$-isogeny
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1dd9e510-d14f-4604-ba1c-6d1f15750cb6 · outbound
Tamagawa ratios and unbounded Selmer moments Chatzidakis, L
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a718f5c5-55a7-47aa-a01d-2e52d1efce83 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6815f8d6-47a1-4026-ae5f-993bfaa7236f · outbound
Tamagawa ratios and unbounded Selmer moments Denef.p-adic semi-algebraic sets and cell decomposition.J
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b72c948e-b237-462f-ba43-6c1576e899a8 · outbound
Tamagawa ratios and unbounded Selmer moments Denef and F
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 42820a70-317c-4ec0-97e3-eae2121e9bda · outbound
Tamagawa ratios and unbounded Selmer moments Dokchitser and V
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9c0d6471-0b0d-4bc7-96d3-00957d902d39 · outbound
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8547e388-4f7d-48f8-ae61-167708565905 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f1ff62dc-af2f-4548-915f-f4ef8a0fcd8a · outbound
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8e7f188f-941a-41c6-99b1-6b8cd86da93b · outbound
Tamagawa ratios and unbounded Selmer moments Feng and M
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 03c35126-aaad-4f01-b5dc-886cee0943d4 · outbound
Tamagawa ratios and unbounded Selmer moments Friedlander and H
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation cdcf943a-53d2-4083-9f83-21a6c4ee7e8a · outbound
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 09833047-bcdc-421f-b9e1-a6643b789761 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 124ac87c-6b2f-426b-92b5-78a2e18dd33d · outbound
Tamagawa ratios and unbounded Selmer moments Heath-Brown
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b1ca5873-5dc9-498f-8186-bddb2355acd2 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a637027c-132c-4deb-aa42-9e815f0391d8 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 196f0942-abe2-4587-a505-7bcf05d6bef2 · outbound
Tamagawa ratios and unbounded Selmer moments Katz and B
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 5d74eff0-0889-436c-a47c-e38eb8a7c31c · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 998aa05d-4f12-4a55-801d-a919af8961e1 · outbound
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 79fe6e6b-6805-4543-9c96-85ccb9fd36ef · outbound
Tamagawa ratios and unbounded Selmer moments Klagsbrun and R.J
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 44798913-6879-4903-a867-c7be73fdd694 · outbound
Tamagawa ratios and unbounded Selmer moments Klagsbrun and R.J
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 45c03cc9-4c65-47cd-b360-ee0356c9b473 · outbound
Tamagawa ratios and unbounded Selmer moments Elliptic fibrations and $3 \cdot 2^k$
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 434e5482-42fd-4d0d-a358-ff0d690334fe · outbound
Tamagawa ratios and unbounded Selmer moments The second moment of the size of the $2$-Selmer group of elliptic curves
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 41d72ccb-aa41-4046-9b5d-9ac7ff0cab24 · outbound
Tamagawa ratios and unbounded Selmer moments Lagarias and A.M
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0ce23156-2e7e-43f1-b729-86266f26f59a · outbound
Tamagawa ratios and unbounded Selmer moments Lang and A
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 3904bc67-7264-4e3f-8aeb-e0607c2e23a6 · outbound
Tamagawa ratios and unbounded Selmer moments arXiv preprint arXiv:2103.08530 , year=
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a6e13fb2-7d91-4b75-8154-a6911605f640 · outbound
Tamagawa ratios and unbounded Selmer moments Morgan and A
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b0e125ce-2053-4a29-88b3-2023b5070940 · outbound
Tamagawa ratios and unbounded Selmer moments Nair and G
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 7cfd392d-a098-4987-8e14-7b4a654ac68b · outbound
Tamagawa ratios and unbounded Selmer moments Nair and G
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 50cc4bcd-a006-47c5-94e4-d054d17ed284 · outbound
Tamagawa ratios and unbounded Selmer moments Neukirch, A
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation adcee2f8-95fc-4efe-a2d6-b5ac7a15d8be · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 964cd3a6-c9a1-49c6-82c4-0e47ec335f92 · outbound
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 2eb9d037-4d63-477c-9723-168a0c5b5411 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 064a40b9-0f8b-4558-8b8b-fa3333f74ad0 · outbound
Tamagawa ratios and unbounded Selmer moments Poonen and E
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6389e1eb-36b6-44f8-9730-dbe2a433d2ed · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8b1097b4-b08b-4a54-9378-ebdcf5890335 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation fccb0b31-c649-43a4-8e85-861615069537 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9fd94e39-a4f7-45da-b6a9-cb34193e75c3 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e5dfae57-920c-430c-9262-792af3c7f9fe · outbound
Tamagawa ratios and unbounded Selmer moments The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0f2f53d2-2515-4acc-86b2-e12aa96c76e7 · outbound
Tamagawa ratios and unbounded Selmer moments Swinnerton-Dyer
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation af167193-c6f5-4b8c-9a6c-fd392736780a · outbound
Tamagawa ratios and unbounded Selmer moments Thorner and A
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 7e752cc4-a72a-47be-ba20-aff454be34f2 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation afad3563-b9cb-4161-93de-969057464e12 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 22cbe65c-a9f8-445b-999f-df66d8320d73 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d222953d-329b-4530-a086-c3801961a597 · outbound
Tamagawa ratios and unbounded Selmer moments Xiong and A
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 2fb53638-b65d-4a82-b688-08d4315f3a50 · outbound
Tamagawa ratios and unbounded Selmer moments Xiong and A
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b523595f-54db-4ab1-93a3-97d00f3a0f49 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 783be6ae-d927-4a38-bc0e-e6f504b7e851 · outbound
Tamagawa ratios and unbounded Selmer moments Unresolved cited work
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
No inbound Pith citation observations are available.