{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:UFHBQUIDULG5PU6DBJJIXBTCLW","short_pith_number":"pith:UFHBQUID","canonical_record":{"source":{"id":"0812.3962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-20T12:34:41Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"87169915e3e01bd8b6ff3d190995306a737f38b3cb062f5c6e95c071aac0b6ab","abstract_canon_sha256":"525d65eec712f0f11d7ebda3d16f1c4b5ce8d8e1ef05343a7464b719dc9353ef"},"schema_version":"1.0"},"canonical_sha256":"a14e185103a2cdd7d3c30a528b86625db5f77051303bb73a1472d5e4ee8ed091","source":{"kind":"arxiv","id":"0812.3962","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3962","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3962v1","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3962","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"UFHBQUIDULG5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"UFHBQUIDULG5PU6D","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"UFHBQUID","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:UFHBQUIDULG5PU6DBJJIXBTCLW","target":"record","payload":{"canonical_record":{"source":{"id":"0812.3962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-20T12:34:41Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"87169915e3e01bd8b6ff3d190995306a737f38b3cb062f5c6e95c071aac0b6ab","abstract_canon_sha256":"525d65eec712f0f11d7ebda3d16f1c4b5ce8d8e1ef05343a7464b719dc9353ef"},"schema_version":"1.0"},"canonical_sha256":"a14e185103a2cdd7d3c30a528b86625db5f77051303bb73a1472d5e4ee8ed091","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:10.869392Z","signature_b64":"UMH18AmBMhPHdQnh5ajVguny7LZEXWS8phYPCh333IMQgELXM5rWgIPT7jVxO9HFJFqaJk/P0pWLF7z6OU1gCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a14e185103a2cdd7d3c30a528b86625db5f77051303bb73a1472d5e4ee8ed091","last_reissued_at":"2026-05-18T02:58:10.868805Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:10.868805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.3962","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5rNlIC8ltWl7gaYuCpemSkZgAsv1fQ0NI0NbRMJcQ0Xj8X9iv4JBPHERsOP7n6cQN9TkoZVXoOC0GH35BgmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T02:47:37.129073Z"},"content_sha256":"150610fb054ea9a522c4a66060db94fe3e5647b4522137047ee5c0afeaf2d5c3","schema_version":"1.0","event_id":"sha256:150610fb054ea9a522c4a66060db94fe3e5647b4522137047ee5c0afeaf2d5c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:UFHBQUIDULG5PU6DBJJIXBTCLW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Siegel modular forms of genus 2 with the simplest divisor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Fabien Clery, Valery Gritsenko","submitted_at":"2008-12-20T12:34:41Z","abstract_excerpt":"We prove that there exist exactly eight Siegel modular forms with respect to the congruence subgroups of Hecke type of the paramodular groups of genus two vanishing precisely along the diagonal of the Siegel upper half-plane. This is a solution of a question formulated during the conference \"Black holes, Black Rings and Modular Forms\" (ENS, Paris, August 2007). These modular forms generalize the classical Igusa form and the forms constructed by Gritsenko and Nikulin in 1998."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3962","kind":"arxiv","version":1},"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":"2026-05-18T02:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"57rFa7MeIHIWWp76iGIA0q6ONmi5OOthEKxkQWwCNSKJS5gb8Tz5j51EruFChg+P/89ECS3fjrcHQOwgMbBOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T02:47:37.129500Z"},"content_sha256":"25a7f805eb275869368bd9f73ad039f2d5c871767522ea5f4c0feafc0a6dca2d","schema_version":"1.0","event_id":"sha256:25a7f805eb275869368bd9f73ad039f2d5c871767522ea5f4c0feafc0a6dca2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UFHBQUIDULG5PU6DBJJIXBTCLW/bundle.json","state_url":"https://pith.science/pith/UFHBQUIDULG5PU6DBJJIXBTCLW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UFHBQUIDULG5PU6DBJJIXBTCLW/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":"2026-07-02T02:47:37Z","links":{"resolver":"https://pith.science/pith/UFHBQUIDULG5PU6DBJJIXBTCLW","bundle":"https://pith.science/pith/UFHBQUIDULG5PU6DBJJIXBTCLW/bundle.json","state":"https://pith.science/pith/UFHBQUIDULG5PU6DBJJIXBTCLW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UFHBQUIDULG5PU6DBJJIXBTCLW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:UFHBQUIDULG5PU6DBJJIXBTCLW","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":"525d65eec712f0f11d7ebda3d16f1c4b5ce8d8e1ef05343a7464b719dc9353ef","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-20T12:34:41Z","title_canon_sha256":"87169915e3e01bd8b6ff3d190995306a737f38b3cb062f5c6e95c071aac0b6ab"},"schema_version":"1.0","source":{"id":"0812.3962","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3962","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3962v1","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3962","created_at":"2026-05-18T02:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"UFHBQUIDULG5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"UFHBQUIDULG5PU6D","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"UFHBQUID","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:25a7f805eb275869368bd9f73ad039f2d5c871767522ea5f4c0feafc0a6dca2d","target":"graph","created_at":"2026-05-18T02:58:10Z","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 that there exist exactly eight Siegel modular forms with respect to the congruence subgroups of Hecke type of the paramodular groups of genus two vanishing precisely along the diagonal of the Siegel upper half-plane. This is a solution of a question formulated during the conference \"Black holes, Black Rings and Modular Forms\" (ENS, Paris, August 2007). These modular forms generalize the classical Igusa form and the forms constructed by Gritsenko and Nikulin in 1998.","authors_text":"Fabien Clery, Valery Gritsenko","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-20T12:34:41Z","title":"The Siegel modular forms of genus 2 with the simplest divisor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3962","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":"sha256:150610fb054ea9a522c4a66060db94fe3e5647b4522137047ee5c0afeaf2d5c3","target":"record","created_at":"2026-05-18T02:58:10Z","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":"525d65eec712f0f11d7ebda3d16f1c4b5ce8d8e1ef05343a7464b719dc9353ef","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-20T12:34:41Z","title_canon_sha256":"87169915e3e01bd8b6ff3d190995306a737f38b3cb062f5c6e95c071aac0b6ab"},"schema_version":"1.0","source":{"id":"0812.3962","kind":"arxiv","version":1}},"canonical_sha256":"a14e185103a2cdd7d3c30a528b86625db5f77051303bb73a1472d5e4ee8ed091","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a14e185103a2cdd7d3c30a528b86625db5f77051303bb73a1472d5e4ee8ed091","first_computed_at":"2026-05-18T02:58:10.868805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:10.868805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UMH18AmBMhPHdQnh5ajVguny7LZEXWS8phYPCh333IMQgELXM5rWgIPT7jVxO9HFJFqaJk/P0pWLF7z6OU1gCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:10.869392Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3962","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:150610fb054ea9a522c4a66060db94fe3e5647b4522137047ee5c0afeaf2d5c3","sha256:25a7f805eb275869368bd9f73ad039f2d5c871767522ea5f4c0feafc0a6dca2d"],"state_sha256":"299b6d61d969cbb26d85b10f1b9bc4266088e1e483cbddaba86578c88bcbc572"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RHUOTX1YoFHRXSiXdVpVXe6aTqjq7ZkjW5gHCb1/XD+Vze6fmfVxtedZ4Kv90wbj7wzMqvkJWhddkogeKBZvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T02:47:37.131838Z","bundle_sha256":"8a3e4ad8b3e4c7cd63a624994ef49b03067a6dc2b85bcb75551a6100130a88f7"}}