Paper Citation Record · LEDGER

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height

As of 21 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2506.18874.

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

pith.paper-citation-record.v1
2506.18874 v2

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:53:36.107511Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T21:51:54.232329Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

24 of 24 outbound references displayed

verified exact6
verified fuzzy3
unresolved14
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c98e5cde-fe4f-4efd-9695-5755374d14e8 · outbound

This paper cites Introduction to Analytic Number Theory.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Introduction to Analytic Number Theory

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.486664Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8f1c2df7-d197-44cb-bb50-4d6244a0d169 · outbound

This paper cites Balakrishnan, Wei Ho, Nathan Kaplan, Simon Spicer, William Stein, and James Weigandt.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Balakrishnan, Wei Ho, Nathan Kaplan, Simon Spicer, William Stein, and James Weigandt

Reference 2

Resolution: verified exact; doi, observed 2026-08-15T18:53:36.735739Z

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 b71a63c0-a94d-487c-ad19-cd1f7a165ffa · outbound

This paper cites an unresolved cited work.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.623455Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7d05ce62-ed39-4cfb-b023-daf86009162b · outbound

This paper cites The average rank of elliptic curves.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height The average rank of elliptic curves

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.628946Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5000b798-e122-4327-9228-5c4cd8842d8d · outbound

This paper cites Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.636644Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0668d99f-1d52-4274-9981-ea0850aa9fbe · outbound

This paper cites Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0

Reference 6

Resolution: verified exact; doi, observed 2026-08-15T18:53:36.584363Z

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 ef79f2cf-74e7-48d3-b9aa-c19829224f5b · outbound

This paper cites Counting elliptic curves with a rational N -isogeny for small N.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Counting elliptic curves with a rational N -isogeny for small N

Reference 7

Resolution: verified exact; doi, observed 2026-08-15T18:53:36.570112Z

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 5016d8d9-4321-4662-ba8c-322b139b58ff · outbound

This paper cites The density and distribution of CM elliptic curves over Q.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height The density and distribution of CM elliptic curves over Q

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.750585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 914f7b1b-9e24-47cb-b95f-bdb2ec7eb790 · outbound

This paper cites SageMath code for the paper Counting elliptic curves over with bounded naive height, 2025.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height SageMath code for the paper Counting elliptic curves over with bounded naive height, 2025

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:53:37.187685Z

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 042a3cca-9530-4131-89e4-2606ceb67fcd · outbound

This paper cites On a probabilistic local-global principle for torsion on elliptic curves.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height On a probabilistic local-global principle for torsion on elliptic curves

Reference 10

Resolution: verified exact; doi, observed 2026-08-15T18:53:36.433212Z

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 6dc768a9-d720-43fe-95e2-75d21799cd72 · outbound

This paper cites Counting elliptic curves with prescribed torsion.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Counting elliptic curves with prescribed torsion

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:53:37.074215Z

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 06c87a68-d579-4f17-b6f8-e734fb1e4690 · outbound

This paper cites an unresolved cited work.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.770150Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11c5edb4-e65a-4491-a9b3-6fd47caa9297 · outbound

This paper cites an unresolved cited work.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.774921Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 040e28a5-60b6-49b9-8e49-eef767157dea · outbound

This paper cites an unresolved cited work.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.779292Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e57bf27a-bed1-4018-a294-ad58da774b6b · outbound

This paper cites The L -functions and modular forms database.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height The L -functions and modular forms database

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:53:37.003229Z

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 776a4161-8bf2-4936-89ed-f0444071ef69 · outbound

This paper cites Mossinghoff, Tom\' a s Oliveira e Silva, and Timothy S.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Mossinghoff, Tom\' a s Oliveira e Silva, and Timothy S

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.940095Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f818f1a-e3f6-4454-b67d-693b4953e6cd · outbound

This paper cites Montgomery and Robert C.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Montgomery and Robert C

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.975145Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b60594b4-491e-41d9-a57b-711e77fce76e · outbound

This paper cites Counting elliptic curves over the rationals with a 7-isogeny.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Counting elliptic curves over the rationals with a 7-isogeny

Reference 18

Resolution: verified exact; doi, observed 2026-08-15T18:53:36.288078Z

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 fd04c64e-f3f4-4511-b65e-d29c08b8d72b · outbound

This paper cites Heuristics for the arithmetic of elliptic curves.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Heuristics for the arithmetic of elliptic curves

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.983659Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0015c8f-a5fe-4495-9a96-88fa215ea480 · outbound

This paper cites Counting elliptic curves with an isogeny of degree three.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Counting elliptic curves with an isogeny of degree three

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.987742Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9d033183-7e46-4d98-b383-421dfc10478f · outbound

This paper cites From explicit estimates for primes to explicit estimates for the M \"obius function.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height From explicit estimates for primes to explicit estimates for the M \"obius function

Reference 21

Resolution: verified exact; doi, observed 2026-08-15T18:53:36.260877Z

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 35bebf66-1a85-4132-b4cc-2b66e79996c9 · outbound

This paper cites Silverman.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Silverman

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:35.997462Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b96ecc3b-4bff-4d94-a5e2-8e8eddb3b73e · outbound

This paper cites SageMath, the Sage Mathematics Software System (Version 10.6) , 2025.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height SageMath, the Sage Mathematics Software System (Version 10.6) , 2025

Reference 23

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T18:53:36.933979Z

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 10d8bcde-5dbe-41b2-8ff0-93535faff5e8 · outbound

This paper cites Washington.

Counting elliptic curves over $\mathbb{Q}$ with bounded naive height Washington

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T18:53:36.107511Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 7b9320ea-8428-4e25-95e1-8bc916f8ce1e · inbound

Upper bounds for moments of analytic ranks of elliptic curves over number fields cites this paper.

Upper bounds for moments of analytic ranks of elliptic curves over number fields Counting elliptic curves over $\mathbb{Q}$ with bounded naive height

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T21:51:54.232329Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.