{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SRTSPSTSJISLUKFLJHMO2U73C6","short_pith_number":"pith:SRTSPSTS","schema_version":"1.0","canonical_sha256":"946727ca724a24ba28ab49d8ed53fb1786aeea92aa66c1a38bb1d58bb807d260","source":{"kind":"arxiv","id":"1407.1099","version":1},"attestation_state":"computed","paper":{"title":"Indivisibility of Heegner points in the multiplicative case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christopher Skinner, Wei Zhang","submitted_at":"2014-07-04T00:47:12Z","abstract_excerpt":"For certain elliptic curves $E$ over $\\mathbb{Q}$ with multiplicative reduction at a prime $p\\geq 5$, we prove the $p$-indivisibility of the derived Heegner classes defined with respect to an imaginary quadratic field $K$, as conjectured by Kolyvagin. The conditions on $E$ include that $E[p]$ be irreducible and not finite at $p$ and that $p$ split in the imaginary quadratic field $K$, along with certain $p$-indivisibility conditions on various Tamagawa factors. The proof extends the arguments of the second author for the case where $E$ has good ordinary reduction at~$p$."},"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":"1407.1099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-04T00:47:12Z","cross_cats_sorted":[],"title_canon_sha256":"e88f20e106c51d79757f11418b2544c4df07639dbaae9718534ddceb2e3d3d5a","abstract_canon_sha256":"84943c75ca15c5e23bb38738c17228d89513737398b7fece88dbf5f6cf44d592"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:18.741713Z","signature_b64":"C7QFDQqEQmU0P/yWLZRRDwBe+AnTjcZ1zocP6Nw3j2uAGYlzqMXOFign32BfifUZbytZAQhtcrrb9MYln3bNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"946727ca724a24ba28ab49d8ed53fb1786aeea92aa66c1a38bb1d58bb807d260","last_reissued_at":"2026-05-18T02:48:18.740997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:18.740997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Indivisibility of Heegner points in the multiplicative case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christopher Skinner, Wei Zhang","submitted_at":"2014-07-04T00:47:12Z","abstract_excerpt":"For certain elliptic curves $E$ over $\\mathbb{Q}$ with multiplicative reduction at a prime $p\\geq 5$, we prove the $p$-indivisibility of the derived Heegner classes defined with respect to an imaginary quadratic field $K$, as conjectured by Kolyvagin. The conditions on $E$ include that $E[p]$ be irreducible and not finite at $p$ and that $p$ split in the imaginary quadratic field $K$, along with certain $p$-indivisibility conditions on various Tamagawa factors. The proof extends the arguments of the second author for the case where $E$ has good ordinary reduction at~$p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1099","kind":"arxiv","version":1},"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":"1407.1099","created_at":"2026-05-18T02:48:18.741131+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.1099v1","created_at":"2026-05-18T02:48:18.741131+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1099","created_at":"2026-05-18T02:48:18.741131+00:00"},{"alias_kind":"pith_short_12","alias_value":"SRTSPSTSJISL","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SRTSPSTSJISLUKFL","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SRTSPSTS","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SRTSPSTSJISLUKFLJHMO2U73C6","json":"https://pith.science/pith/SRTSPSTSJISLUKFLJHMO2U73C6.json","graph_json":"https://pith.science/api/pith-number/SRTSPSTSJISLUKFLJHMO2U73C6/graph.json","events_json":"https://pith.science/api/pith-number/SRTSPSTSJISLUKFLJHMO2U73C6/events.json","paper":"https://pith.science/paper/SRTSPSTS"},"agent_actions":{"view_html":"https://pith.science/pith/SRTSPSTSJISLUKFLJHMO2U73C6","download_json":"https://pith.science/pith/SRTSPSTSJISLUKFLJHMO2U73C6.json","view_paper":"https://pith.science/paper/SRTSPSTS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.1099&json=true","fetch_graph":"https://pith.science/api/pith-number/SRTSPSTSJISLUKFLJHMO2U73C6/graph.json","fetch_events":"https://pith.science/api/pith-number/SRTSPSTSJISLUKFLJHMO2U73C6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SRTSPSTSJISLUKFLJHMO2U73C6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SRTSPSTSJISLUKFLJHMO2U73C6/action/storage_attestation","attest_author":"https://pith.science/pith/SRTSPSTSJISLUKFLJHMO2U73C6/action/author_attestation","sign_citation":"https://pith.science/pith/SRTSPSTSJISLUKFLJHMO2U73C6/action/citation_signature","submit_replication":"https://pith.science/pith/SRTSPSTSJISLUKFLJHMO2U73C6/action/replication_record"}},"created_at":"2026-05-18T02:48:18.741131+00:00","updated_at":"2026-05-18T02:48:18.741131+00:00"}