Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T21:31:41.300550Z
Paper Citation Record · LEDGER
Density of algebraic points on products of curves
As of 17 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 1 inbound Pith citation observation for arXiv:2507.00860.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-05T10:52:13.896803Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-05T10:52:14.783680Z
Reference resolution
26 of 26 outbound references displayed
- verified exact6
- verified fuzzy13
- unresolved3
- parse uncertain0
- malformed identifier3
- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation d8fcf4ab-15b8-4195-adc9-30bfbb28a816 · outbound
This paper cites Then it follows by Theorem 4.3 and Lemma 4.5 that 2 ∈ δ(E′ 1 ×E2), and in fact there exists a quadratic extension L/k over which both rk E′ 1(L) > 0 and rk E2(L) > 0.
Density of algebraic points on products of curves Then it follows by Theorem 4.3 and Lemma 4.5 that 2 ∈ δ(E′ 1 ×E2), and in fact there exists a quadratic extension L/k over which both rk E′ 1(L) > 0 and rk E2(L) > 0
Reference 1
- Resolution
- malformed identifier
- raw_fallback, observed 2026-08-06T21:31:41.924690Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 76879a23-69ac-454a-bda4-c1679a28f4d7 · outbound
This paper cites On (2,2)-decomposable genus 4 Jacobians.
Density of algebraic points on products of curves On (2,2)-decomposable genus 4 Jacobians
Reference 2
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- raw_fallback, observed 2026-08-06T21:31:41.694352Z
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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9dc5578c-922b-494d-b2cc-2c06e1a3e66d · outbound
This paper cites M. de Franchis and the theory of hyperelliptic surfaces.
Density of algebraic points on products of curves M. de Franchis and the theory of hyperelliptic surfaces
Reference 3
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- raw_fallback, observed 2026-08-06T21:31:41.800656Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ec60f1e7-11ec-43ef-865c-fcf57ff0563a · outbound
This paper cites When E1, E2 are isogenous over k, it follows immediately by Proposition 2.15 that δ(E1 × E2/k) = δ(E1/k) = δ(E2/k).
Density of algebraic points on products of curves When E1, E2 are isogenous over k, it follows immediately by Proposition 2.15 that δ(E1 × E2/k) = δ(E1/k) = δ(E2/k)
Reference 4
- Resolution
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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 88367ee4-abc1-4987-a086-d946abaf9b51 · outbound
This paper cites an unresolved cited work.
Density of algebraic points on products of curves Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T21:31:41.894996Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4b6dde13-95c2-46b3-8847-f936d7519797 · outbound
This paper cites If E has positive rank, the lower bound of Proposition 2.13 coincides with the upper bound, hence δ(C × E/k) = δ(C/k).
Density of algebraic points on products of curves If E has positive rank, the lower bound of Proposition 2.13 coincides with the upper bound, hence δ(C × E/k) = δ(C/k)
Reference 6
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- raw_fallback, observed 2026-08-06T21:31:41.880210Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b5fa0961-3892-4bc1-ae2f-f039f1d85802 · outbound
This paper cites We start by summarizing the upper and lower bounds for δ(C × D/k) which follow from the results of Sections 2 and 3.
Density of algebraic points on products of curves We start by summarizing the upper and lower bounds for δ(C × D/k) which follow from the results of Sections 2 and 3
Reference 7
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- raw_fallback, observed 2026-08-06T21:31:41.865199Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a2dabfeb-e480-4745-9888-7d2c642abbfb · outbound
This paper cites Pushing forward Z under the natural maps Sym2 C → Pic2 C → Pic0 C gives a curve in Pic0 C.
Density of algebraic points on products of curves Pushing forward Z under the natural maps Sym2 C → Pic2 C → Pic0 C gives a curve in Pic0 C
Reference 8
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8cc9e44c-e92c-41fd-b798-aa70fadf7c84 · outbound
This paper cites Proposition 7.1.
Density of algebraic points on products of curves Proposition 7.1
Reference 9
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c710c28d-828d-492c-9a7d-f86894066e0d · outbound
This paper cites Arbarello et al.
Density of algebraic points on products of curves Arbarello et al
Reference 10
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3ee87a9a-6289-4b45-bb6d-e97703e759d7 · outbound
This paper cites Subspace configurations and low degree points on curves.
Density of algebraic points on products of curves Subspace configurations and low degree points on curves
Reference 11
- Resolution
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- raw_fallback, observed 2026-08-06T21:31:41.755277Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4165b0a4-f9b4-4ea2-b48f-4deb768d9e56 · outbound
This paper cites Root numbers and ranks in positive characteristic.
Density of algebraic points on products of curves Root numbers and ranks in positive characteristic
Reference 12
- Resolution
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- raw_fallback, observed 2026-08-06T21:31:41.786129Z
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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a2eaee39-00a5-4072-ab33-c673e26c7a48 · outbound
This paper cites Let E2 be the elliptic curve 14.a.5 with Weierstrass equation y2 + xy + y = x3 − x, which has rank 0 over Q.
Density of algebraic points on products of curves Let E2 be the elliptic curve 14.a.5 with Weierstrass equation y2 + xy + y = x3 − x, which has rank 0 over Q
Reference 13
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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 34e7f0ac-68ed-4306-b70c-dd98e7f57dcb · outbound
This paper cites On the density of rational points on rational elliptic surfaces.
Density of algebraic points on products of curves On the density of rational points on rational elliptic surfaces
Reference 14
- Resolution
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- local_arxiv, observed 2026-08-06T21:31:41.550974Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e0a01848-410a-49a6-b17e-b76ddf961b50 · outbound
This paper cites Torsion phenomena for zero-cycles on a product of curves over a number field.
Density of algebraic points on products of curves Torsion phenomena for zero-cycles on a product of curves over a number field
Reference 15
- Resolution
- verified exact
- doi, observed 2026-08-06T21:31:41.415085Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5deb29af-100e-48d4-bde0-8824caa66e78 · outbound
This paper cites Potential Density of Rational Points on Algebraic Varieties.
Density of algebraic points on products of curves Potential Density of Rational Points on Algebraic Varieties
Reference 16
- Resolution
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- no resolver link, observed 2026-08-06T21:31:41.250838Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5c4e1194-0cdb-4a21-8f9c-6b4d3094a656 · outbound
This paper cites infinite families of pairs of curves over q with isomorphic jacobians.
Density of algebraic points on products of curves infinite families of pairs of curves over q with isomorphic jacobians
Reference 17
- Resolution
- malformed identifier
- raw_fallback, observed 2026-08-06T21:31:41.771553Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 92c7c5e2-8c32-4571-8eee-7a880286a903 · outbound
This paper cites Principally polarizable isogeny classes of abelian surfaces over finite fields.
Density of algebraic points on products of curves Principally polarizable isogeny classes of abelian surfaces over finite fields
Reference 18
- Resolution
- verified exact
- doi, observed 2026-08-06T21:31:41.384905Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d644cdd5-581d-44c2-96f2-f4f566ec6c95 · outbound
This paper cites On the torsion of elliptic curves over cubic number fields.
Density of algebraic points on products of curves On the torsion of elliptic curves over cubic number fields
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T21:31:41.264440Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7b8a0ceb-36db-43fa-939e-480e3463ed1a · outbound
This paper cites Root numbers and parity phenom- ena.
Density of algebraic points on products of curves Root numbers and parity phenom- ena
Reference 21
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- doi, observed 2026-08-06T21:31:41.355685Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 15d9b462-6f19-4fb3-b9c5-3e06e6bbfc0b · outbound
This paper cites Topology of rational points on isotrivial elliptic surfaces.
Density of algebraic points on products of curves Topology of rational points on isotrivial elliptic surfaces
Reference 22
- Resolution
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- doi, observed 2026-08-06T21:31:41.340215Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9c83052e-851c-4d60-9dd8-7f9299e3c730 · outbound
This paper cites Abelian Varieties and the Mordell–Lang Conjecture.
Density of algebraic points on products of curves Abelian Varieties and the Mordell–Lang Conjecture
Reference 23
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b1c99757-0e7d-4eed-9134-070ad09f6a5d · outbound
This paper cites Topology of rational points.
Density of algebraic points on products of curves Topology of rational points
Reference 24
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- raw_fallback, observed 2026-08-06T21:31:41.723916Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2b4dd4a2-db3e-4489-9b3e-968c78c2b5b6 · outbound
This paper cites Genus 2 curves with given split Jacobian.
Density of algebraic points on products of curves Genus 2 curves with given split Jacobian
Reference 25
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- raw_fallback, observed 2026-08-06T21:31:41.709204Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c78b186f-06e5-4096-afba-30ebbe025077 · outbound
This paper cites Isolated and Parameterized Points on Curves.
Density of algebraic points on products of curves Isolated and Parameterized Points on Curves
Reference 26
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T21:31:41.300550Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0717dd03-c0a3-4484-9338-7a4964fd18f0 · outbound
This paper cites Subspace configurations and low degree points on curves.
Density of algebraic points on products of curves Subspace configurations and low degree points on curves
Reference 2024
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-06T21:31:41.528301Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
Observation 2a494f32-a534-4bbc-9dd3-162dea576b40 · inbound
A primer on measures of irrationality cites this paper.
A primer on measures of irrationality Density of algebraic points on products of curves
Reference 2017
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T10:52:14.795918Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.