{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:H6XOCTY6VOHIEHMRORXI43WCXF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6a86bf22f123b92740ed9fd1d1df0e0669900454f7f1a30aba4b211705b106f2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-06-14T10:41:45Z","title_canon_sha256":"cd4306d49d22a3383cdbc2df015daa562a8f41d089e77d3b729cbcded702cecf"},"schema_version":"1.0","source":{"id":"1106.2668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2668","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2668v1","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2668","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"pith_short_12","alias_value":"H6XOCTY6VOHI","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"H6XOCTY6VOHIEHMR","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"H6XOCTY6","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:80ab184fe95744d15a5eadc4cdd964792bf6cda67f9b1579a96eb8b3e73f9ffb","target":"graph","created_at":"2026-05-18T04:20:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove formulas for the p-adic logarithm of quaternionic Darmon points on p-adic tori and modular abelian varieties over Q having purely multiplicative reduction at p. These formulas are amenable to explicit computations and are the first to treat Stark-Heegner type points on higher-dimensional abelian varieties.","authors_text":"M. Longo, S. Vigni","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-06-14T10:41:45Z","title":"Quaternionic Darmon points on p-adic tori and abelian varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2668","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8d871f48c8c5c08317b1da7cdae74adca066148bd64713b5adf1412b068db607","target":"record","created_at":"2026-05-18T04:20:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6a86bf22f123b92740ed9fd1d1df0e0669900454f7f1a30aba4b211705b106f2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-06-14T10:41:45Z","title_canon_sha256":"cd4306d49d22a3383cdbc2df015daa562a8f41d089e77d3b729cbcded702cecf"},"schema_version":"1.0","source":{"id":"1106.2668","kind":"arxiv","version":1}},"canonical_sha256":"3faee14f1eab8e821d91746e8e6ec2b96535893335c41deae396273756e1c41c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3faee14f1eab8e821d91746e8e6ec2b96535893335c41deae396273756e1c41c","first_computed_at":"2026-05-18T04:20:04.347468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:04.347468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yOWXbOLH3QVVkPFJplqjWGkaTYPprDFOoPrN4pkXqpMbPKjBSRdgEwwYUk5OgNzJWr7WVdT1WD8pYkK7SCy1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:04.347867Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d871f48c8c5c08317b1da7cdae74adca066148bd64713b5adf1412b068db607","sha256:80ab184fe95744d15a5eadc4cdd964792bf6cda67f9b1579a96eb8b3e73f9ffb"],"state_sha256":"cc90d04f1643f62fafb500d9eec06ff1f87a214412078b00f115406220601a21"}