{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IHZH3G6NUFS4Y6C4BJGG4QFFI3","short_pith_number":"pith:IHZH3G6N","schema_version":"1.0","canonical_sha256":"41f27d9bcda165cc785c0a4c6e40a546d736349b7b75fb7a55134f6d53d67c5d","source":{"kind":"arxiv","id":"1710.04072","version":3},"attestation_state":"computed","paper":{"title":"CM Values of Green Functions Associated to Special Cycles on Shimura Varieties with Applications to Siegel 3-Fold $X_2(2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Peng Yu","submitted_at":"2017-10-10T05:16:52Z","abstract_excerpt":"We generalize the definition of CM cycles beyond the small and big CM ones studied by various authors and give a uniform formula for the CM values of Green functions associated to these special cycles in general using the idea of regularized theta lifts. Finally, as an application to Siegel 3-fold $X_2(2)$, we can compute special values of theta functions and Rosenhain $\\lambda$-invariants at a CM cycle, which is useful for genus two curve cryptography."},"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":"1710.04072","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-10T05:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"2d6354695b9ce2b0badc4aaee850174e97d0ff5b319d18e8a3bd20ff6f8c630d","abstract_canon_sha256":"1fd51e9328477e07e71face2e757cbc0be0cfd4acaa4922df331c3bf809378f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:00.072329Z","signature_b64":"Td2rhFGzRXxkHxLCo1wZxh9aK29zT/haTAWcmpR/ZChqI94bNGf3iQYIEryWZYu7tqwEne+kiqlSGD2BcYcfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41f27d9bcda165cc785c0a4c6e40a546d736349b7b75fb7a55134f6d53d67c5d","last_reissued_at":"2026-05-17T23:45:00.071857Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:00.071857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"CM Values of Green Functions Associated to Special Cycles on Shimura Varieties with Applications to Siegel 3-Fold $X_2(2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Peng Yu","submitted_at":"2017-10-10T05:16:52Z","abstract_excerpt":"We generalize the definition of CM cycles beyond the small and big CM ones studied by various authors and give a uniform formula for the CM values of Green functions associated to these special cycles in general using the idea of regularized theta lifts. Finally, as an application to Siegel 3-fold $X_2(2)$, we can compute special values of theta functions and Rosenhain $\\lambda$-invariants at a CM cycle, which is useful for genus two curve cryptography."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04072","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.04072","created_at":"2026-05-17T23:45:00.071924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.04072v3","created_at":"2026-05-17T23:45:00.071924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04072","created_at":"2026-05-17T23:45:00.071924+00:00"},{"alias_kind":"pith_short_12","alias_value":"IHZH3G6NUFS4","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IHZH3G6NUFS4Y6C4","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IHZH3G6N","created_at":"2026-05-18T12:31:21.493067+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/IHZH3G6NUFS4Y6C4BJGG4QFFI3","json":"https://pith.science/pith/IHZH3G6NUFS4Y6C4BJGG4QFFI3.json","graph_json":"https://pith.science/api/pith-number/IHZH3G6NUFS4Y6C4BJGG4QFFI3/graph.json","events_json":"https://pith.science/api/pith-number/IHZH3G6NUFS4Y6C4BJGG4QFFI3/events.json","paper":"https://pith.science/paper/IHZH3G6N"},"agent_actions":{"view_html":"https://pith.science/pith/IHZH3G6NUFS4Y6C4BJGG4QFFI3","download_json":"https://pith.science/pith/IHZH3G6NUFS4Y6C4BJGG4QFFI3.json","view_paper":"https://pith.science/paper/IHZH3G6N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.04072&json=true","fetch_graph":"https://pith.science/api/pith-number/IHZH3G6NUFS4Y6C4BJGG4QFFI3/graph.json","fetch_events":"https://pith.science/api/pith-number/IHZH3G6NUFS4Y6C4BJGG4QFFI3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IHZH3G6NUFS4Y6C4BJGG4QFFI3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IHZH3G6NUFS4Y6C4BJGG4QFFI3/action/storage_attestation","attest_author":"https://pith.science/pith/IHZH3G6NUFS4Y6C4BJGG4QFFI3/action/author_attestation","sign_citation":"https://pith.science/pith/IHZH3G6NUFS4Y6C4BJGG4QFFI3/action/citation_signature","submit_replication":"https://pith.science/pith/IHZH3G6NUFS4Y6C4BJGG4QFFI3/action/replication_record"}},"created_at":"2026-05-17T23:45:00.071924+00:00","updated_at":"2026-05-17T23:45:00.071924+00:00"}