{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:D4RMDUONPSENJQNVUPJ4MZ25PW","short_pith_number":"pith:D4RMDUON","canonical_record":{"source":{"id":"1407.0785","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-03T05:21:48Z","cross_cats_sorted":[],"title_canon_sha256":"66a26697f5347389c8993abae50ba97ec623a00aa34fe57f77c6887984b55813","abstract_canon_sha256":"b017208f0806959b6c1d2ba5ada01b1b7a36219edb3d18d2cd713673663183cb"},"schema_version":"1.0"},"canonical_sha256":"1f22c1d1cd7c88d4c1b5a3d3c6675d7dae2bfd24ca3416b6eab6a1d190bb1189","source":{"kind":"arxiv","id":"1407.0785","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0785","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0785v3","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0785","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"D4RMDUONPSEN","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D4RMDUONPSENJQNV","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D4RMDUON","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:D4RMDUONPSENJQNVUPJ4MZ25PW","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0785","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-03T05:21:48Z","cross_cats_sorted":[],"title_canon_sha256":"66a26697f5347389c8993abae50ba97ec623a00aa34fe57f77c6887984b55813","abstract_canon_sha256":"b017208f0806959b6c1d2ba5ada01b1b7a36219edb3d18d2cd713673663183cb"},"schema_version":"1.0"},"canonical_sha256":"1f22c1d1cd7c88d4c1b5a3d3c6675d7dae2bfd24ca3416b6eab6a1d190bb1189","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:53.312489Z","signature_b64":"unxk90hjKzTsCqQhnpT7JydvWQoiKRPToO4WdaZtuqd2Zp1dOL2NKgYFIWy3bQ2X5+bXrFYIq03Vgbo0gDDWCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f22c1d1cd7c88d4c1b5a3d3c6675d7dae2bfd24ca3416b6eab6a1d190bb1189","last_reissued_at":"2026-05-18T01:17:53.311762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:53.311762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0785","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ydkhNS61+QOS3aUV9NNJX1E5YtzLLWvIq1H1/TjD9kuLyB/PbQHYbH/TgR3QqJYaCEkduV5pCx4MXWTxgtbmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:17:41.789943Z"},"content_sha256":"c71d1a3c02d2c90217563c395f9bc4a35a8ceb1afc11027d086e0d9976d5b1d3","schema_version":"1.0","event_id":"sha256:c71d1a3c02d2c90217563c395f9bc4a35a8ceb1afc11027d086e0d9976d5b1d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:D4RMDUONPSENJQNVUPJ4MZ25PW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$p$-adic heights of generalized Heegner cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ariel Shnidman","submitted_at":"2014-07-03T05:21:48Z","abstract_excerpt":"We relate the $p$-adic heights of generalized Heegner cycles to the derivative of a $p$-adic $L$-function attached to a pair $(f, \\chi)$, where $f$ is an ordinary weight $2r$ newform and $\\chi$ is an unramified imaginary quadratic Hecke character of infinity type $(\\ell,0)$, with $0 < \\ell < 2r$. This generalizes the $p$-adic Gross-Zagier formula in the case $\\ell = 0$ due to Perrin-Riou (in weight two) and Nekov\\'a\\u{r} (in higher weight)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0785","kind":"arxiv","version":3},"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":"2026-05-18T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vHWFHxDgj47/DfE7AcXI/kiatP76ULFAXkPDHU6yr59Zi94qSfhe8XSs9Wi4j89WGj6wiVqiapj7v9+YNyZBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:17:41.790663Z"},"content_sha256":"7981949a755b4e1797b12674c857d71674d645f9bc382753df271e96a29113c9","schema_version":"1.0","event_id":"sha256:7981949a755b4e1797b12674c857d71674d645f9bc382753df271e96a29113c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4RMDUONPSENJQNVUPJ4MZ25PW/bundle.json","state_url":"https://pith.science/pith/D4RMDUONPSENJQNVUPJ4MZ25PW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4RMDUONPSENJQNVUPJ4MZ25PW/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":"2026-06-07T14:17:41Z","links":{"resolver":"https://pith.science/pith/D4RMDUONPSENJQNVUPJ4MZ25PW","bundle":"https://pith.science/pith/D4RMDUONPSENJQNVUPJ4MZ25PW/bundle.json","state":"https://pith.science/pith/D4RMDUONPSENJQNVUPJ4MZ25PW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4RMDUONPSENJQNVUPJ4MZ25PW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:D4RMDUONPSENJQNVUPJ4MZ25PW","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":"b017208f0806959b6c1d2ba5ada01b1b7a36219edb3d18d2cd713673663183cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-03T05:21:48Z","title_canon_sha256":"66a26697f5347389c8993abae50ba97ec623a00aa34fe57f77c6887984b55813"},"schema_version":"1.0","source":{"id":"1407.0785","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0785","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0785v3","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0785","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"D4RMDUONPSEN","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D4RMDUONPSENJQNV","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D4RMDUON","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:7981949a755b4e1797b12674c857d71674d645f9bc382753df271e96a29113c9","target":"graph","created_at":"2026-05-18T01:17:53Z","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 relate the $p$-adic heights of generalized Heegner cycles to the derivative of a $p$-adic $L$-function attached to a pair $(f, \\chi)$, where $f$ is an ordinary weight $2r$ newform and $\\chi$ is an unramified imaginary quadratic Hecke character of infinity type $(\\ell,0)$, with $0 < \\ell < 2r$. This generalizes the $p$-adic Gross-Zagier formula in the case $\\ell = 0$ due to Perrin-Riou (in weight two) and Nekov\\'a\\u{r} (in higher weight).","authors_text":"Ariel Shnidman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-03T05:21:48Z","title":"$p$-adic heights of generalized Heegner cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0785","kind":"arxiv","version":3},"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:c71d1a3c02d2c90217563c395f9bc4a35a8ceb1afc11027d086e0d9976d5b1d3","target":"record","created_at":"2026-05-18T01:17:53Z","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":"b017208f0806959b6c1d2ba5ada01b1b7a36219edb3d18d2cd713673663183cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-03T05:21:48Z","title_canon_sha256":"66a26697f5347389c8993abae50ba97ec623a00aa34fe57f77c6887984b55813"},"schema_version":"1.0","source":{"id":"1407.0785","kind":"arxiv","version":3}},"canonical_sha256":"1f22c1d1cd7c88d4c1b5a3d3c6675d7dae2bfd24ca3416b6eab6a1d190bb1189","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f22c1d1cd7c88d4c1b5a3d3c6675d7dae2bfd24ca3416b6eab6a1d190bb1189","first_computed_at":"2026-05-18T01:17:53.311762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:53.311762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"unxk90hjKzTsCqQhnpT7JydvWQoiKRPToO4WdaZtuqd2Zp1dOL2NKgYFIWy3bQ2X5+bXrFYIq03Vgbo0gDDWCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:53.312489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0785","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c71d1a3c02d2c90217563c395f9bc4a35a8ceb1afc11027d086e0d9976d5b1d3","sha256:7981949a755b4e1797b12674c857d71674d645f9bc382753df271e96a29113c9"],"state_sha256":"7a6d795de83a34a414119aff2e30091997f7fdf95dcaaea2aa2cb023252d4dc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QO4Bo5GvX+Ew8vGSXGkbfRStS4Esv8Kc8MzJ6yn8aRmRAuiJ3lxTxamj/62zP74LiyEyAjKWqNlv13BEbN+QDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:17:41.794066Z","bundle_sha256":"19b58efc23dae720d883b3ad2548acc143eb6e368173be9fa1815a641215d34a"}}