{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JQHJ3MHGSVHYJ6L5QZ7FBTC2NZ","short_pith_number":"pith:JQHJ3MHG","canonical_record":{"source":{"id":"1708.05820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-19T07:49:35Z","cross_cats_sorted":[],"title_canon_sha256":"5ac8ea921750ad907b022b61453f7eecea1aaffa9e23ea57121dd2ed12178e34","abstract_canon_sha256":"b1b0913822a1c2721fe02ca0e2f011a03fc822122667f681e638677b54b8b1af"},"schema_version":"1.0"},"canonical_sha256":"4c0e9db0e6954f84f97d867e50cc5a6e70247fab5cb6c47023e772887446946f","source":{"kind":"arxiv","id":"1708.05820","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05820","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05820v2","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05820","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"pith_short_12","alias_value":"JQHJ3MHGSVHY","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JQHJ3MHGSVHYJ6L5","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JQHJ3MHG","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JQHJ3MHGSVHYJ6L5QZ7FBTC2NZ","target":"record","payload":{"canonical_record":{"source":{"id":"1708.05820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-19T07:49:35Z","cross_cats_sorted":[],"title_canon_sha256":"5ac8ea921750ad907b022b61453f7eecea1aaffa9e23ea57121dd2ed12178e34","abstract_canon_sha256":"b1b0913822a1c2721fe02ca0e2f011a03fc822122667f681e638677b54b8b1af"},"schema_version":"1.0"},"canonical_sha256":"4c0e9db0e6954f84f97d867e50cc5a6e70247fab5cb6c47023e772887446946f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:03.787577Z","signature_b64":"C91a8SGnCmrWg4ZHaHJqCxmnsePfr5ULehqldgTGOHQD3utoPBoGZlzXCzSrT7Dl6hyKdnekdaUIyZPI/6a0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c0e9db0e6954f84f97d867e50cc5a6e70247fab5cb6c47023e772887446946f","last_reissued_at":"2026-05-17T23:47:03.787041Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:03.787041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.05820","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6houq74Ffg8AWVJECagRLEdKqDEMoOol+LhbGy/OU2UvupLhfGwG3L8rWiu/SzkWtUeaSYRj0e0QhB1SKVIQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:23:11.437508Z"},"content_sha256":"ea5f52da81ec5090bef26551039ccdc45555e10fc5211019174abf822e173d7d","schema_version":"1.0","event_id":"sha256:ea5f52da81ec5090bef26551039ccdc45555e10fc5211019174abf822e173d7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JQHJ3MHGSVHYJ6L5QZ7FBTC2NZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heights of CM cycles and derivatives of L-series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tian An Wong, Yara Elias","submitted_at":"2017-08-19T07:49:35Z","abstract_excerpt":"We extend the work of S. Zhang and Yuan-Zhang-Zhang to obtain a Gross-Zagier formula for modular forms of even weight in terms of an arithmetic intersection pairing of CM-cycles on Kuga-Sato varieties over Shimura curves. Combined with a result of the first author and de Vera-Piquero adapting Kolyvagin's method of Euler systems to this setting, we bound the associated Selmer and Tate-Shafarevich groups, assuming the non-vanishing of the derivative of the L-function at the central point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05820","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hEG8cZcdc/yKLZP65qCYXRXELU8xpx58sTzKU3gIUECGaNwO+3AWPSqusu8A2BBXpjCa/hAg2ebs0Gleeyg6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:23:11.437855Z"},"content_sha256":"49f890f5d86dd26a9fc7ae5fbc5909f0952b987761060ce0f6f7be5d86e60d3a","schema_version":"1.0","event_id":"sha256:49f890f5d86dd26a9fc7ae5fbc5909f0952b987761060ce0f6f7be5d86e60d3a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JQHJ3MHGSVHYJ6L5QZ7FBTC2NZ/bundle.json","state_url":"https://pith.science/pith/JQHJ3MHGSVHYJ6L5QZ7FBTC2NZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JQHJ3MHGSVHYJ6L5QZ7FBTC2NZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T09:23:11Z","links":{"resolver":"https://pith.science/pith/JQHJ3MHGSVHYJ6L5QZ7FBTC2NZ","bundle":"https://pith.science/pith/JQHJ3MHGSVHYJ6L5QZ7FBTC2NZ/bundle.json","state":"https://pith.science/pith/JQHJ3MHGSVHYJ6L5QZ7FBTC2NZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JQHJ3MHGSVHYJ6L5QZ7FBTC2NZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JQHJ3MHGSVHYJ6L5QZ7FBTC2NZ","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":"b1b0913822a1c2721fe02ca0e2f011a03fc822122667f681e638677b54b8b1af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-19T07:49:35Z","title_canon_sha256":"5ac8ea921750ad907b022b61453f7eecea1aaffa9e23ea57121dd2ed12178e34"},"schema_version":"1.0","source":{"id":"1708.05820","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05820","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05820v2","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05820","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"pith_short_12","alias_value":"JQHJ3MHGSVHY","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JQHJ3MHGSVHYJ6L5","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JQHJ3MHG","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:49f890f5d86dd26a9fc7ae5fbc5909f0952b987761060ce0f6f7be5d86e60d3a","target":"graph","created_at":"2026-05-17T23:47:03Z","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 extend the work of S. Zhang and Yuan-Zhang-Zhang to obtain a Gross-Zagier formula for modular forms of even weight in terms of an arithmetic intersection pairing of CM-cycles on Kuga-Sato varieties over Shimura curves. Combined with a result of the first author and de Vera-Piquero adapting Kolyvagin's method of Euler systems to this setting, we bound the associated Selmer and Tate-Shafarevich groups, assuming the non-vanishing of the derivative of the L-function at the central point.","authors_text":"Tian An Wong, Yara Elias","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-19T07:49:35Z","title":"Heights of CM cycles and derivatives of L-series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05820","kind":"arxiv","version":2},"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:ea5f52da81ec5090bef26551039ccdc45555e10fc5211019174abf822e173d7d","target":"record","created_at":"2026-05-17T23:47:03Z","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":"b1b0913822a1c2721fe02ca0e2f011a03fc822122667f681e638677b54b8b1af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-19T07:49:35Z","title_canon_sha256":"5ac8ea921750ad907b022b61453f7eecea1aaffa9e23ea57121dd2ed12178e34"},"schema_version":"1.0","source":{"id":"1708.05820","kind":"arxiv","version":2}},"canonical_sha256":"4c0e9db0e6954f84f97d867e50cc5a6e70247fab5cb6c47023e772887446946f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c0e9db0e6954f84f97d867e50cc5a6e70247fab5cb6c47023e772887446946f","first_computed_at":"2026-05-17T23:47:03.787041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:03.787041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C91a8SGnCmrWg4ZHaHJqCxmnsePfr5ULehqldgTGOHQD3utoPBoGZlzXCzSrT7Dl6hyKdnekdaUIyZPI/6a0Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:03.787577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05820","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea5f52da81ec5090bef26551039ccdc45555e10fc5211019174abf822e173d7d","sha256:49f890f5d86dd26a9fc7ae5fbc5909f0952b987761060ce0f6f7be5d86e60d3a"],"state_sha256":"5a60f368fa93112928f8f45f3a23247820269f553d6d4ce5a6ce72598581d040"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/NihwHj5mE4sXgsf1gsDt5fRSMuDvxXOo5s/c62klK1Ir5PEm0gEh7kJ3z98yOClM041C4NxXPFeVxRqis2VBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:23:11.439774Z","bundle_sha256":"f6b260c71af0d7fc1e7276fef938a620506dfa6bd9a409a21ec95fb3b4b6dfd4"}}