{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HSHLI7LW6UTIBGBKOIYOKEUMM3","short_pith_number":"pith:HSHLI7LW","canonical_record":{"source":{"id":"1505.02711","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-11T17:43:37Z","cross_cats_sorted":[],"title_canon_sha256":"1b83e9027db0a745310caadd7029d492a96319fc4836fdde72548388904fe8e5","abstract_canon_sha256":"7089710f7f473acd0c1c9c5307cca8dc3a947cf55e263282963aeb617fedc7df"},"schema_version":"1.0"},"canonical_sha256":"3c8eb47d76f52680982a7230e5128c66f51d6da0ba8ae0a55f799f5fa31c63d4","source":{"kind":"arxiv","id":"1505.02711","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02711","created_at":"2026-05-18T01:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02711v2","created_at":"2026-05-18T01:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02711","created_at":"2026-05-18T01:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"HSHLI7LW6UTI","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HSHLI7LW6UTIBGBK","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HSHLI7LW","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HSHLI7LW6UTIBGBKOIYOKEUMM3","target":"record","payload":{"canonical_record":{"source":{"id":"1505.02711","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-11T17:43:37Z","cross_cats_sorted":[],"title_canon_sha256":"1b83e9027db0a745310caadd7029d492a96319fc4836fdde72548388904fe8e5","abstract_canon_sha256":"7089710f7f473acd0c1c9c5307cca8dc3a947cf55e263282963aeb617fedc7df"},"schema_version":"1.0"},"canonical_sha256":"3c8eb47d76f52680982a7230e5128c66f51d6da0ba8ae0a55f799f5fa31c63d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:53.602616Z","signature_b64":"SmkvSq/4wI8gty18Lo2avEOJuqcpowTpJrgbHNqOpM5DLC4np5DQkf2jc0Z5rds1L1TqKpmvWZ/QtwoClUCfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c8eb47d76f52680982a7230e5128c66f51d6da0ba8ae0a55f799f5fa31c63d4","last_reissued_at":"2026-05-18T01:38:53.601905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:53.601905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.02711","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":"2026-05-18T01:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kxioL51zDXsYTujxY5hAk6iVkI92qe4AygSOcwrKDKWsh6qR8FUgYljNF05AfxUt/7kKAqoxNUhfiaq+lPzJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:35:53.988883Z"},"content_sha256":"43891e0edcb9251266a06c1c1e68bcbeadc01cff07fee5efd03590573de02aea","schema_version":"1.0","event_id":"sha256:43891e0edcb9251266a06c1c1e68bcbeadc01cff07fee5efd03590573de02aea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HSHLI7LW6UTIBGBKOIYOKEUMM3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular moduli of higher level and special cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Stephan Ehlen","submitted_at":"2015-05-11T17:43:37Z","abstract_excerpt":"We describe the complex multiplication (CM) values of modular functions for $\\Gamma_0(N)$ whose divisor is given by a linear combination of Heegner divisors in terms of special cycles on the stack of CM elliptic curves. In particular, our results apply to Borcherds products of weight $0$ for $\\Gamma_0(N)$. By working out explicit formulas for the special cycles, we obtain the prime ideal factorizations of such CM values."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02711","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":"2026-05-18T01:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J1P4t8uWLUWn/Bk4mI/Exj3TK7zCBDxqtxtYmo/96oEAxL+/bkQIvXetlZtYCssta2Kxz5D0K3XEWu9CzrEtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:35:53.989226Z"},"content_sha256":"80dedf96c4ae30d502cfd7f61270adeb47f2d2e3506d6d5ee140fb12e3b9d26c","schema_version":"1.0","event_id":"sha256:80dedf96c4ae30d502cfd7f61270adeb47f2d2e3506d6d5ee140fb12e3b9d26c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HSHLI7LW6UTIBGBKOIYOKEUMM3/bundle.json","state_url":"https://pith.science/pith/HSHLI7LW6UTIBGBKOIYOKEUMM3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HSHLI7LW6UTIBGBKOIYOKEUMM3/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":"2026-06-24T21:35:53Z","links":{"resolver":"https://pith.science/pith/HSHLI7LW6UTIBGBKOIYOKEUMM3","bundle":"https://pith.science/pith/HSHLI7LW6UTIBGBKOIYOKEUMM3/bundle.json","state":"https://pith.science/pith/HSHLI7LW6UTIBGBKOIYOKEUMM3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HSHLI7LW6UTIBGBKOIYOKEUMM3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HSHLI7LW6UTIBGBKOIYOKEUMM3","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":"7089710f7f473acd0c1c9c5307cca8dc3a947cf55e263282963aeb617fedc7df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-11T17:43:37Z","title_canon_sha256":"1b83e9027db0a745310caadd7029d492a96319fc4836fdde72548388904fe8e5"},"schema_version":"1.0","source":{"id":"1505.02711","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02711","created_at":"2026-05-18T01:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02711v2","created_at":"2026-05-18T01:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02711","created_at":"2026-05-18T01:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"HSHLI7LW6UTI","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HSHLI7LW6UTIBGBK","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HSHLI7LW","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:80dedf96c4ae30d502cfd7f61270adeb47f2d2e3506d6d5ee140fb12e3b9d26c","target":"graph","created_at":"2026-05-18T01:38:53Z","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 describe the complex multiplication (CM) values of modular functions for $\\Gamma_0(N)$ whose divisor is given by a linear combination of Heegner divisors in terms of special cycles on the stack of CM elliptic curves. In particular, our results apply to Borcherds products of weight $0$ for $\\Gamma_0(N)$. By working out explicit formulas for the special cycles, we obtain the prime ideal factorizations of such CM values.","authors_text":"Stephan Ehlen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-11T17:43:37Z","title":"Singular moduli of higher level and special cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02711","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":"sha256:43891e0edcb9251266a06c1c1e68bcbeadc01cff07fee5efd03590573de02aea","target":"record","created_at":"2026-05-18T01:38:53Z","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":"7089710f7f473acd0c1c9c5307cca8dc3a947cf55e263282963aeb617fedc7df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-11T17:43:37Z","title_canon_sha256":"1b83e9027db0a745310caadd7029d492a96319fc4836fdde72548388904fe8e5"},"schema_version":"1.0","source":{"id":"1505.02711","kind":"arxiv","version":2}},"canonical_sha256":"3c8eb47d76f52680982a7230e5128c66f51d6da0ba8ae0a55f799f5fa31c63d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c8eb47d76f52680982a7230e5128c66f51d6da0ba8ae0a55f799f5fa31c63d4","first_computed_at":"2026-05-18T01:38:53.601905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:53.601905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SmkvSq/4wI8gty18Lo2avEOJuqcpowTpJrgbHNqOpM5DLC4np5DQkf2jc0Z5rds1L1TqKpmvWZ/QtwoClUCfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:53.602616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02711","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43891e0edcb9251266a06c1c1e68bcbeadc01cff07fee5efd03590573de02aea","sha256:80dedf96c4ae30d502cfd7f61270adeb47f2d2e3506d6d5ee140fb12e3b9d26c"],"state_sha256":"d043195e9c0eb542426d3989f2f68e3c763876de99e15b3f58c5666b8c9037b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y8Th6VfSDIgplUhCKTJDn1AnVShMECBQpy5l1thGIIdYkMrN2GfJppsuvjuChn306Q37/G+L29+KctctJGd6BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:35:53.991085Z","bundle_sha256":"3eb5f1278eff54142d2e86f4221259edfc10ecc68c787ca68d701a94ddb347a5"}}