{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:6GOVPKKYU32A5MPCEMRYVPHHIV","short_pith_number":"pith:6GOVPKKY","schema_version":"1.0","canonical_sha256":"f19d57a958a6f40eb1e223238abce7457d27d7ab45d4f9174812ea73b0a3695f","source":{"kind":"arxiv","id":"2409.00891","version":2},"attestation_state":"computed","paper":{"title":"Shadow line distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Barry Mazur, Jennifer S. Balakrishnan, Karl Rubin, Mirela \\c{C}iperiani","submitted_at":"2024-09-02T02:00:12Z","abstract_excerpt":"Let $E$ be an elliptic curve over $\\mathbb{Q}$ with Mordell--Weil rank $2$ and $p$ be an odd prime of good ordinary reduction. For every imaginary quadratic field $K$ satisfying the Heegner hypothesis, there is (subject to the Shafarevich--Tate conjecture) a line, i.e., a free $\\mathbb{Z}_p$-submodule of rank $1$, in $ E(K)\\otimes \\mathbb{Z}_p$ given by universal norms coming from the Mordell--Weil groups of subfields of the anticyclotomic $\\mathbb{Z}_p$-extension of $K$; we call it the {\\it shadow line}. When the twist of $E$ by $K$ has analytic rank $1$, the shadow line is conjectured to lie"},"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":"2409.00891","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-09-02T02:00:12Z","cross_cats_sorted":[],"title_canon_sha256":"0a044c633b2fc6ebf51f360b2637a5ba3c831e4ed9370c4bc3b04ab6d05e78cb","abstract_canon_sha256":"d3afe9271060936e954245b2c099b7ac1a3b3e799b8ae21ec68a7b4ff0e4b710"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:01:55.502812Z","signature_b64":"AMl/2fANC0/FM+xLQZmT84ggyQC6Z4tYjMtzQpc3lteiOdb6BshLIluiNWduqhpupQI1YKC5CalpdgCgvlsdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f19d57a958a6f40eb1e223238abce7457d27d7ab45d4f9174812ea73b0a3695f","last_reissued_at":"2026-07-05T11:01:55.502336Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:01:55.502336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shadow line distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Barry Mazur, Jennifer S. Balakrishnan, Karl Rubin, Mirela \\c{C}iperiani","submitted_at":"2024-09-02T02:00:12Z","abstract_excerpt":"Let $E$ be an elliptic curve over $\\mathbb{Q}$ with Mordell--Weil rank $2$ and $p$ be an odd prime of good ordinary reduction. For every imaginary quadratic field $K$ satisfying the Heegner hypothesis, there is (subject to the Shafarevich--Tate conjecture) a line, i.e., a free $\\mathbb{Z}_p$-submodule of rank $1$, in $ E(K)\\otimes \\mathbb{Z}_p$ given by universal norms coming from the Mordell--Weil groups of subfields of the anticyclotomic $\\mathbb{Z}_p$-extension of $K$; we call it the {\\it shadow line}. When the twist of $E$ by $K$ has analytic rank $1$, the shadow line is conjectured to lie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.00891","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.00891/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2409.00891","created_at":"2026-07-05T11:01:55.502393+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.00891v2","created_at":"2026-07-05T11:01:55.502393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.00891","created_at":"2026-07-05T11:01:55.502393+00:00"},{"alias_kind":"pith_short_12","alias_value":"6GOVPKKYU32A","created_at":"2026-07-05T11:01:55.502393+00:00"},{"alias_kind":"pith_short_16","alias_value":"6GOVPKKYU32A5MPC","created_at":"2026-07-05T11:01:55.502393+00:00"},{"alias_kind":"pith_short_8","alias_value":"6GOVPKKY","created_at":"2026-07-05T11:01:55.502393+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.08583","citing_title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6GOVPKKYU32A5MPCEMRYVPHHIV","json":"https://pith.science/pith/6GOVPKKYU32A5MPCEMRYVPHHIV.json","graph_json":"https://pith.science/api/pith-number/6GOVPKKYU32A5MPCEMRYVPHHIV/graph.json","events_json":"https://pith.science/api/pith-number/6GOVPKKYU32A5MPCEMRYVPHHIV/events.json","paper":"https://pith.science/paper/6GOVPKKY"},"agent_actions":{"view_html":"https://pith.science/pith/6GOVPKKYU32A5MPCEMRYVPHHIV","download_json":"https://pith.science/pith/6GOVPKKYU32A5MPCEMRYVPHHIV.json","view_paper":"https://pith.science/paper/6GOVPKKY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.00891&json=true","fetch_graph":"https://pith.science/api/pith-number/6GOVPKKYU32A5MPCEMRYVPHHIV/graph.json","fetch_events":"https://pith.science/api/pith-number/6GOVPKKYU32A5MPCEMRYVPHHIV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6GOVPKKYU32A5MPCEMRYVPHHIV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6GOVPKKYU32A5MPCEMRYVPHHIV/action/storage_attestation","attest_author":"https://pith.science/pith/6GOVPKKYU32A5MPCEMRYVPHHIV/action/author_attestation","sign_citation":"https://pith.science/pith/6GOVPKKYU32A5MPCEMRYVPHHIV/action/citation_signature","submit_replication":"https://pith.science/pith/6GOVPKKYU32A5MPCEMRYVPHHIV/action/replication_record"}},"created_at":"2026-07-05T11:01:55.502393+00:00","updated_at":"2026-07-05T11:01:55.502393+00:00"}