Paper Citation Record · LEDGER

Divisibility Biases in the Orders of Elliptic Curve Reductions

As of 11 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2606.25067.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2606.25067 v2

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T10:31:47.749970Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

37 of 37 outbound references displayed

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verified fuzzy0
unresolved37
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External citation measurements

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Outbound references

Observation 916a3585-5927-490a-a35d-cbdfa51c2994 · outbound

This paper cites an unresolved cited work.

Divisibility Biases in the Orders of Elliptic Curve Reductions Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:43.112631Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7ea0adb-6596-45aa-a1bb-630c6a860085 · outbound

This paper cites Banks and Igor E.

Divisibility Biases in the Orders of Elliptic Curve Reductions Banks and Igor E

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:43.256259Z

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Observation 3fc32fb1-0cf9-45cc-8868-f0e8a8c2aa2b · outbound

This paper cites 1, 81–91.

Divisibility Biases in the Orders of Elliptic Curve Reductions 1, 81–91

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:43.420338Z

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Observation 495b92b9-54f9-4533-adb2-97934d87e8df · outbound

This paper cites Lecture Notes, vol.

Divisibility Biases in the Orders of Elliptic Curve Reductions Lecture Notes, vol

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:43.606740Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83a41d06-192c-423d-b9cc-1322388d129a · outbound

This paper cites Ram Murty,The square sieve and the Lang-Trotter conjecture, Canad.

Divisibility Biases in the Orders of Elliptic Curve Reductions Ram Murty,The square sieve and the Lang-Trotter conjecture, Canad

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:43.767811Z

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Observation 361e7d2a-ecb0-4044-aeb4-38840fbda4bb · outbound

This paper cites Daniels, ´Alvaro Lozano-Robledo, and Jackson S.

Divisibility Biases in the Orders of Elliptic Curve Reductions Daniels, ´Alvaro Lozano-Robledo, and Jackson S

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:43.835903Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c76a37fb-6593-4160-b4a3-b66b52ec3d8b · outbound

This paper cites an unresolved cited work.

Divisibility Biases in the Orders of Elliptic Curve Reductions Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:43.909856Z

Source-reported events for the cited work

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Observation d2add394-2b78-4daa-a7e3-c35e754eb961 · outbound

This paper cites Z.272 (2012), no.

Divisibility Biases in the Orders of Elliptic Curve Reductions Z.272 (2012), no

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:44.035407Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee39a896-cf17-49f1-b7c5-85e3a57942e0 · outbound

This paper cites Elkies,Elliptic curves with 3-adic galois representation surjective mod 3 but not mod 9, 2006.

Divisibility Biases in the Orders of Elliptic Curve Reductions Elkies,Elliptic curves with 3-adic galois representation surjective mod 3 but not mod 9, 2006

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:44.165508Z

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Unavailable: canonical work link unavailable.

Observation 57a89cbf-e6b7-4b92-9c1e-b6dec9ec6948 · outbound

This paper cites Hamakiotes, Sung Min Lee, Jacob Mayle, and Tian Wang,On the density of coprime reductions of elliptic curves, 2026.

Divisibility Biases in the Orders of Elliptic Curve Reductions Hamakiotes, Sung Min Lee, Jacob Mayle, and Tian Wang,On the density of coprime reductions of elliptic curves, 2026

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:44.270332Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f35e5cf-01ec-4394-96a0-2de90a29ff4e · outbound

This paper cites Howe,On the group orders of elliptic curves over finite fields, Compositio Math.85(1993), no.

Divisibility Biases in the Orders of Elliptic Curve Reductions Howe,On the group orders of elliptic curves over finite fields, Compositio Math.85(1993), no

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:44.398003Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 663ee5e3-9b24-4681-9949-604793e677a4 · outbound

This paper cites 4, 569–592.

Divisibility Biases in the Orders of Elliptic Curve Reductions 4, 569–592

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:44.572601Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d2e03f3-4f8f-45f1-ae84-9316e16518d5 · outbound

This paper cites Ann.345(2009), no.

Divisibility Biases in the Orders of Elliptic Curve Reductions Ann.345(2009), no

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:44.679891Z

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Unavailable: canonical work link unavailable.

Observation 86bfd899-3a12-4d30-9f76-3b8f459eb835 · outbound

This paper cites an unresolved cited work.

Divisibility Biases in the Orders of Elliptic Curve Reductions Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:44.792213Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 858494e5-b9b4-41e4-a0d9-bd160bc54b55 · outbound

This paper cites Number Theory11(2025), no.

Divisibility Biases in the Orders of Elliptic Curve Reductions Number Theory11(2025), no

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:44.957476Z

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Observation 3baed216-4997-480c-8e6b-002121a7f275 · outbound

This paper cites Math.131(1988), no.

Divisibility Biases in the Orders of Elliptic Curve Reductions Math.131(1988), no

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:45.047532Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9d2f9668-1867-4181-828b-38b5da15c5fd · outbound

This paper cites Lang and H.

Divisibility Biases in the Orders of Elliptic Curve Reductions Lang and H

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:45.126073Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acca3c0c-a9eb-4988-aac3-91d0ccc42bcd · outbound

This paper cites an unresolved cited work.

Divisibility Biases in the Orders of Elliptic Curve Reductions Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:45.348539Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a096ba9-a4af-4c21-94ee-0c76868a36cc · outbound

This paper cites an unresolved cited work.

Divisibility Biases in the Orders of Elliptic Curve Reductions Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:45.480244Z

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Observation 53c49d63-c1fd-4550-8bec-9b90cbb7624d · outbound

This paper cites an unresolved cited work.

Divisibility Biases in the Orders of Elliptic Curve Reductions Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:45.669069Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2719eea0-177d-44a4-a495-dadf499bf176 · outbound

This paper cites an unresolved cited work.

Divisibility Biases in the Orders of Elliptic Curve Reductions Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:45.752234Z

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Observation 9a35c4b0-5508-40c1-9977-622b093af997 · outbound

This paper cites Math.23 (2017), 897–925.

Divisibility Biases in the Orders of Elliptic Curve Reductions Math.23 (2017), 897–925

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:45.899804Z

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Observation f4bfa445-4984-4d88-bb1e-d6ae272c1c82 · outbound

This paper cites Math., vol.

Divisibility Biases in the Orders of Elliptic Curve Reductions Math., vol

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:45.971411Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 65aff2cd-14c6-425d-8ddc-7c17cabb3d3f · outbound

This paper cites Mazur,Rational isogenies of prime degree (with an appendix by D.

Divisibility Biases in the Orders of Elliptic Curve Reductions Mazur,Rational isogenies of prime degree (with an appendix by D

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:46.115131Z

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Unavailable: canonical work link unavailable.

Observation c5969635-7063-4af0-9a55-c089676f2568 · outbound

This paper cites Ram Murty, V.

Divisibility Biases in the Orders of Elliptic Curve Reductions Ram Murty, V

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:46.215400Z

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Unavailable: canonical work link unavailable.

Observation 5e3d75f1-7bd2-4162-b4b1-eef44f09088a · outbound

This paper cites Sutherland, and David Zureick-Brown, ℓ-adic images of Galois for elliptic curves over Q (and an appendix with John Voight), Forum Math.

Divisibility Biases in the Orders of Elliptic Curve Reductions Sutherland, and David Zureick-Brown, ℓ-adic images of Galois for elliptic curves over Q (and an appendix with John Voight), Forum Math

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:46.458443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01da8d8e-00bb-44d9-a72e-9bf23601dabc · outbound

This paper cites an unresolved cited work.

Divisibility Biases in the Orders of Elliptic Curve Reductions Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:46.604495Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2bfeafb0-18c8-4539-bc9f-44bbcaf46b8c · outbound

This paper cites Math.15(1972), no.

Divisibility Biases in the Orders of Elliptic Curve Reductions Math.15(1972), no

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:46.705604Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec62bca5-fa59-409b-840d-fbdec9b06506 · outbound

This paper cites Hautes´Etudes Sci.

Divisibility Biases in the Orders of Elliptic Curve Reductions Hautes´Etudes Sci

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:46.874748Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe34eef8-17ea-4f27-8974-1ee84a0fb527 · outbound

This paper cites 7, A K Peters, Ltd., Wellesley, MA, 1998, With the collaboration of Willem Kuyk and John Labute, Revised reprint of the 1968 original.

Divisibility Biases in the Orders of Elliptic Curve Reductions 7, A K Peters, Ltd., Wellesley, MA, 1998, With the collaboration of Willem Kuyk and John Labute, Revised reprint of the 1968 original

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:46.967358Z

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Observation 3de7998f-010e-4d86-affa-7da874a9b214 · outbound

This paper cites an unresolved cited work.

Divisibility Biases in the Orders of Elliptic Curve Reductions Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:47.148820Z

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Unavailable: canonical work link unavailable.

Observation 512ee00b-a5d7-4f8e-ad61-46291b0bdca6 · outbound

This paper cites Shparlinski,Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves, Acta Arith.170(2015), no.

Divisibility Biases in the Orders of Elliptic Curve Reductions Shparlinski,Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves, Acta Arith.170(2015), no

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:47.280859Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73378bf0-89af-4ae6-96f1-63dd0f982f7a · outbound

This paper cites Silverman,The arithmetic of elliptic curves, second ed., Graduate Texts in Mathematics, vol.

Divisibility Biases in the Orders of Elliptic Curve Reductions Silverman,The arithmetic of elliptic curves, second ed., Graduate Texts in Mathematics, vol

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:47.335148Z

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Unavailable: canonical work link unavailable.

Observation d05766c4-da4a-4265-8c75-722c014ed3cb · outbound

This paper cites Sutherland,Computing images of Galois representations attached to elliptic curves, Forum Math.

Divisibility Biases in the Orders of Elliptic Curve Reductions Sutherland,Computing images of Galois representations attached to elliptic curves, Forum Math

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:47.509955Z

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Unavailable: canonical work link unavailable.

Observation eb2a865a-65f5-402e-bbda-76a5df9c2019 · outbound

This paper cites an unresolved cited work.

Divisibility Biases in the Orders of Elliptic Curve Reductions Unresolved cited work

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:47.609775Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12eb87f2-32d0-4ef0-b082-7f2f7e207fb4 · outbound

This paper cites Math., vol.

Divisibility Biases in the Orders of Elliptic Curve Reductions Math., vol

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:47.678974Z

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Unavailable: canonical work link unavailable.

Observation 5231c502-e08a-40f0-a38e-156b4f8bdd19 · outbound

This paper cites an unresolved cited work.

Divisibility Biases in the Orders of Elliptic Curve Reductions Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-02T10:31:47.749970Z

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Pith citing papers

No inbound Pith citation observations are available.