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In this paper we work on solving the conjecture in case $\\mathscr{E}$ is rational by means of geometric and analytic methods. First, we show that for $\\mathscr{E}$ rational, the set $\\mathscr{E}(\\mathbb{Q})$ is Zariski-dense when $\\mathscr{E}$ is isotrivial with non-zero $j$-invariant and when $\\mathscr{E}$ is non-isotrivi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.01684","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-06T16:22:14Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"979a5c53a35c84862fb3a151b18d29d42d66fe6aea1c6583a7848f483b85f0d0","abstract_canon_sha256":"942928987ab3e253a1d22946578d98ba9f3828f188adc49dbd65301e3a328bc3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:30.830150Z","signature_b64":"eJKaGp2s1R5VO14XVOF7cPOTp0X/9cya3IfK5kSHFcSVpTjQ+BLWluRkIJXM+PSaZUqqs4QrJPgLstkjCo11Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bba56627d59dcfba7bd1b5becd36ed0e1516404e0eb9e3e39bfbe2bf7fbcf4dd","last_reissued_at":"2026-05-18T00:10:30.829382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:30.829382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the density of rational points on rational elliptic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Julie Desjardins","submitted_at":"2017-02-06T16:22:14Z","abstract_excerpt":"Let $\\mathscr{E}\\rightarrow\\mathbb{P}^1_\\mathbb{Q}$ be a non-trivial rational elliptic surface over $\\mathbb{Q}$ with base $\\mathbb{P}^1_\\mathbb{Q}$ (with a section). We conjecture that any non-trivial elliptic surface has a Zariski-dense set of $\\mathbb{Q}$-rational points. In this paper we work on solving the conjecture in case $\\mathscr{E}$ is rational by means of geometric and analytic methods. First, we show that for $\\mathscr{E}$ rational, the set $\\mathscr{E}(\\mathbb{Q})$ is Zariski-dense when $\\mathscr{E}$ is isotrivial with non-zero $j$-invariant and when $\\mathscr{E}$ is non-isotrivi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01684","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1702.01684","created_at":"2026-05-18T00:10:30.829520+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.01684v2","created_at":"2026-05-18T00:10:30.829520+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01684","created_at":"2026-05-18T00:10:30.829520+00:00"},{"alias_kind":"pith_short_12","alias_value":"XOSWMJ6VTXH3","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XOSWMJ6VTXH3U66R","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XOSWMJ6V","created_at":"2026-05-18T12:31:56.362134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.00860","citing_title":"Density of algebraic points on products of curves","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XOSWMJ6VTXH3U66RWW7M2NXNBY","json":"https://pith.science/pith/XOSWMJ6VTXH3U66RWW7M2NXNBY.json","graph_json":"https://pith.science/api/pith-number/XOSWMJ6VTXH3U66RWW7M2NXNBY/graph.json","events_json":"https://pith.science/api/pith-number/XOSWMJ6VTXH3U66RWW7M2NXNBY/events.json","paper":"https://pith.science/paper/XOSWMJ6V"},"agent_actions":{"view_html":"https://pith.science/pith/XOSWMJ6VTXH3U66RWW7M2NXNBY","download_json":"https://pith.science/pith/XOSWMJ6VTXH3U66RWW7M2NXNBY.json","view_paper":"https://pith.science/paper/XOSWMJ6V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.01684&json=true","fetch_graph":"https://pith.science/api/pith-number/XOSWMJ6VTXH3U66RWW7M2NXNBY/graph.json","fetch_events":"https://pith.science/api/pith-number/XOSWMJ6VTXH3U66RWW7M2NXNBY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XOSWMJ6VTXH3U66RWW7M2NXNBY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XOSWMJ6VTXH3U66RWW7M2NXNBY/action/storage_attestation","attest_author":"https://pith.science/pith/XOSWMJ6VTXH3U66RWW7M2NXNBY/action/author_attestation","sign_citation":"https://pith.science/pith/XOSWMJ6VTXH3U66RWW7M2NXNBY/action/citation_signature","submit_replication":"https://pith.science/pith/XOSWMJ6VTXH3U66RWW7M2NXNBY/action/replication_record"}},"created_at":"2026-05-18T00:10:30.829520+00:00","updated_at":"2026-05-18T00:10:30.829520+00:00"}