Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-10T06:47:32.731947Z
Paper Citation Record · LEDGER
As of 6 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 1 inbound Pith citation observation for arXiv:2604.16978.
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 2026-05-10T06:47:32.731947Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-01T03:55:48.921447Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-01T11:45:47.026666Z
49 of 49 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 037f2d7b-1b6b-4bf6-b1c5-970f187e012e · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Most hyperelliptic curves over Q have no rational points
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation baab17ef-b952-4042-b20e-60126405b0f8 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava, The density of discriminants of quartic rings and fields,Ann
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 1f1a54f6-ff06-45d5-92e4-f5721140b8f7 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava, The density of discriminants of quintic rings and fields,Ann
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 19d13cb0-0d8a-418d-989b-d838214b0401 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations The geometric sieve and the density of squarefree values of invariant polynomials
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 318d6e7e-f866-4dcb-b430-af404ba579b0 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava and B
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 0efeaa6f-029d-46c0-bf52-6c2526e89da2 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava, B
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 1546d9b2-44af-47b5-9510-548d3d5015e8 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava and W
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 7902c80a-fd76-4f29-9f19-5a7b040cb125 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations On average sizes of Selmer groups and ranks in families of elliptic curves having marked points
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 2b66e0b5-9d94-4e00-b86e-496c833380fe · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava and A
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 1106f67d-2139-4ca1-b311-5844bcf209d6 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava and A
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 78f12e84-b41b-43d8-b801-30665e0447f3 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations The average number of elements in the 4-Selmer groups of elliptic curves is 7
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation ac342359-aebf-4960-8479-16765be6aa7f · outbound
Geometry-of-numbers methods over global fields II: Coregular representations The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation d02b3a87-e59a-4338-a947-71a62c56322f · outbound
Geometry-of-numbers methods over global fields II: Coregular representations org/abs/1512.03035
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 8f2ae9aa-d5cf-4bb1-ac86-8ead4deb57a9 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava, A
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 758acd22-2aa9-40f5-949d-88a3447ebdbf · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava, A
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 9ca33663-a44d-4ef7-8281-5c7995070e45 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava and C
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 04d6e9db-6ed6-46cf-aca2-c307adf51bce · outbound
Geometry-of-numbers methods over global fields II: Coregular representations A majority of elliptic curves over $\mathbb Q$ satisfy the Birch and Swinnerton-Dyer conjecture
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation c293058f-23af-48a4-82d5-00ca42b5e957 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava and I
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation b7819fcc-8938-4fe1-b857-c4ed9167e15a · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Bhargava and I
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation ab0dfd3f-ba05-47ca-8615-15fa95b30228 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Borel, Some finiteness properties of adele groups over number fields,Publ
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 24b5af46-bb34-48e3-bd2a-bc4aa2837f88 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups,Ann
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 19e470bd-d50c-4829-a439-7d72501c5812 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Borel, G
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation cf617b09-0944-4908-915f-94ed17d6b092 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Conrad, Finiteness theorems for algebraic groups over function fields,Compos
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation aff3bc89-1cda-4237-9cc4-93f5721e601a · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Unresolved cited work
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 1bdc25e9-6140-4ed8-8539-91d75c7f0d32 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Davenport and H
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation b25970d0-8966-4b6b-853c-9173b1cbca6f · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Unresolved cited work
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 0c8cfcfd-5e6b-4106-a3b4-da934bf13f57 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Unresolved cited work
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation d8db48c8-30bc-4d6d-b1e1-93ef4e1e6b21 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Fisher, Explicit 5-descent on elliptic curves,ANTS X–Proceedings of the Tenth Algorithmic Number Theorem Symposium, 395–411
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation fd1a4671-5f18-4447-8ea5-fe6460f53847 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Goldfeld, Conjectures on elliptic curves over quadratic fields,Number Theory, Carbondale 1979 (Proc
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 03a69577-2b69-4bad-9fe4-17a590aac260 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Laga, Graded Lie algebras, compactified Jacobians and arithmetic statistics,J
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 324b688c-c679-45e3-b929-b4a0ff742271 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Laga, The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3, Algebr
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 23756996-090a-4557-afab-5116edb7d07b · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Average size of 2-Selmer groups of elliptic curves over function fields
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 152bf311-6ae3-4524-b0c9-71c6bc838fb9 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Unresolved cited work
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation e9ed45c5-fdd2-4a65-89d5-4d5c017c6fdf · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Geometry-of-numbers over number fields and the density of ADE families of curves having squarefree discriminant
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 77eaa942-19c3-498c-933f-82547484394e · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Poonen, M
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 868ccc59-04f6-4196-a1d2-5bdc05e0f5b8 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Poonen and M
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation ccf78f11-fd75-4a0d-ab0d-677cb5f30557 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Romano, and J
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 0427667f-0c26-4623-8cd6-ee1108438283 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Unresolved cited work
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 3ccc1906-2091-4f7d-92e7-5cc605af4fff · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Unresolved cited work
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation c6fd0a30-b6d5-4d8d-ae18-d3db1477e89e · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Shankar, The average rank of elliptic curves over number fields, Ph.D thesis, Princeton 2012
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation e7038dc0-9f05-4898-950c-0ab73fe47d65 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Shankar and X
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 3f09c698-47a9-4bb6-b377-cc0ba8b7a129 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Monogenicity and 2-torsion in the class group of number fields of odd degree
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation d532aad0-d448-4e3d-bf28-1a2f2f575bd5 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Monogenic fields with odd class number Part II: even degree
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation ab94d4e9-d42c-44bf-b1e6-9bab590664f7 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Unresolved cited work
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation bf059a06-7976-436d-bb21-53c996d9177c · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Unresolved cited work
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 1aa49eaa-4221-46dc-90af-652770cbd04a · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Thorne,E 6 and the arithmetic of a family of non-hyperelliptic curves of genus 3,Forum Math
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation ca56dedd-0f68-4485-907b-ea07f5c6e140 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Thorne, On the average number of 2-Selmer elements of elliptic curves overF q(X) with two marked points.Doc
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation c4c42b71-cfb2-4e27-9dad-595a016f4b51 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Wang,Maximal linear spaces contained in the base loci of pencils of quadrics,Algebr
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation fce10c6f-f463-4978-9ab7-f4b6c984bda5 · outbound
Geometry-of-numbers methods over global fields II: Coregular representations Weil,Adeles and algebraic groups, Birkh¨ auser
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation b26d25ee-03fe-460c-a8f6-0b706206b5c6 · inbound
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 2026-08-06T06:34:29.942622+00:00.