{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GCK45IID37SYOKWNPZLI4SOY7E","short_pith_number":"pith:GCK45IID","canonical_record":{"source":{"id":"1103.6169","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-31T13:15:37Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"3a8e6b6f8762bf50e305343d8d5001e46acf53ade9499df0959bb1051a18f5fd","abstract_canon_sha256":"a767e5bd121d2683af1eab1537880934e6d678b6c4f9e3d0e443c1043f3b11e9"},"schema_version":"1.0"},"canonical_sha256":"3095cea103dfe5872acd7e568e49d8f9106eaedf981cbb6a114783661d2af21c","source":{"kind":"arxiv","id":"1103.6169","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.6169","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"arxiv_version","alias_value":"1103.6169v2","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.6169","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"pith_short_12","alias_value":"GCK45IID37SY","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GCK45IID37SYOKWN","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GCK45IID","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GCK45IID37SYOKWNPZLI4SOY7E","target":"record","payload":{"canonical_record":{"source":{"id":"1103.6169","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-31T13:15:37Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"3a8e6b6f8762bf50e305343d8d5001e46acf53ade9499df0959bb1051a18f5fd","abstract_canon_sha256":"a767e5bd121d2683af1eab1537880934e6d678b6c4f9e3d0e443c1043f3b11e9"},"schema_version":"1.0"},"canonical_sha256":"3095cea103dfe5872acd7e568e49d8f9106eaedf981cbb6a114783661d2af21c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:14.479309Z","signature_b64":"FgCshJESHYioQKQJeJDLYPTEpNQDkcaj/KNNcq8L5M1GsAcB+tN2EUWRA+wQuFvZbyRrpeTXu6RxRd59OK2nCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3095cea103dfe5872acd7e568e49d8f9106eaedf981cbb6a114783661d2af21c","last_reissued_at":"2026-05-18T03:51:14.478872Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:14.478872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.6169","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":"2026-05-18T03:51:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YHCkCWJGgqqGpfk0xSlImhctgeMKgCykFcmzdnqkM3Aoqp5nV9MDl/fkmzWl5w9+5saNWDsrBGtrFlo1JZjHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:04:02.929552Z"},"content_sha256":"e632b24876e201a7c7e64e8989320d5dbdf52280ee2b307e2a9bc060547c7879","schema_version":"1.0","event_id":"sha256:e632b24876e201a7c7e64e8989320d5dbdf52280ee2b307e2a9bc060547c7879"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GCK45IID37SYOKWNPZLI4SOY7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomology of the second Voronoi compactification of A_4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Klaus Hulek, Orsola Tommasi","submitted_at":"2011-03-31T13:15:37Z","abstract_excerpt":"In this paper we compute the cohomology groups of the second Voronoi compactification of the moduli space of abelian fourfolds in all degrees with the exception of the middle degree 10. We also compute the cohomology groups of the perfect cone compactification in degree < 10. The main tool is the investigation of the strata of the compactification corresponding to semi-abelic varieties with constant torus rank."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6169","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":"2026-05-18T03:51:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TMbETnjJm2ka19B4v1T9nqg/5VH7/Mmy/Qu6t/yH1eGKOX9JzCkw+o/fO9MkgABuykYhPTyrePDISbjVG10ZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:04:02.929885Z"},"content_sha256":"8562bfa18af8b5216993d7faa1dbd4e28d47c6e0892a31c940efe5fc58a5c72d","schema_version":"1.0","event_id":"sha256:8562bfa18af8b5216993d7faa1dbd4e28d47c6e0892a31c940efe5fc58a5c72d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCK45IID37SYOKWNPZLI4SOY7E/bundle.json","state_url":"https://pith.science/pith/GCK45IID37SYOKWNPZLI4SOY7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCK45IID37SYOKWNPZLI4SOY7E/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":"2026-06-01T17:04:02Z","links":{"resolver":"https://pith.science/pith/GCK45IID37SYOKWNPZLI4SOY7E","bundle":"https://pith.science/pith/GCK45IID37SYOKWNPZLI4SOY7E/bundle.json","state":"https://pith.science/pith/GCK45IID37SYOKWNPZLI4SOY7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCK45IID37SYOKWNPZLI4SOY7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GCK45IID37SYOKWNPZLI4SOY7E","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":"a767e5bd121d2683af1eab1537880934e6d678b6c4f9e3d0e443c1043f3b11e9","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-31T13:15:37Z","title_canon_sha256":"3a8e6b6f8762bf50e305343d8d5001e46acf53ade9499df0959bb1051a18f5fd"},"schema_version":"1.0","source":{"id":"1103.6169","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.6169","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"arxiv_version","alias_value":"1103.6169v2","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.6169","created_at":"2026-05-18T03:51:14Z"},{"alias_kind":"pith_short_12","alias_value":"GCK45IID37SY","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GCK45IID37SYOKWN","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GCK45IID","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:8562bfa18af8b5216993d7faa1dbd4e28d47c6e0892a31c940efe5fc58a5c72d","target":"graph","created_at":"2026-05-18T03:51:14Z","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":"In this paper we compute the cohomology groups of the second Voronoi compactification of the moduli space of abelian fourfolds in all degrees with the exception of the middle degree 10. We also compute the cohomology groups of the perfect cone compactification in degree < 10. The main tool is the investigation of the strata of the compactification corresponding to semi-abelic varieties with constant torus rank.","authors_text":"Klaus Hulek, Orsola Tommasi","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-31T13:15:37Z","title":"Cohomology of the second Voronoi compactification of A_4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6169","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:e632b24876e201a7c7e64e8989320d5dbdf52280ee2b307e2a9bc060547c7879","target":"record","created_at":"2026-05-18T03:51:14Z","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":"a767e5bd121d2683af1eab1537880934e6d678b6c4f9e3d0e443c1043f3b11e9","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-31T13:15:37Z","title_canon_sha256":"3a8e6b6f8762bf50e305343d8d5001e46acf53ade9499df0959bb1051a18f5fd"},"schema_version":"1.0","source":{"id":"1103.6169","kind":"arxiv","version":2}},"canonical_sha256":"3095cea103dfe5872acd7e568e49d8f9106eaedf981cbb6a114783661d2af21c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3095cea103dfe5872acd7e568e49d8f9106eaedf981cbb6a114783661d2af21c","first_computed_at":"2026-05-18T03:51:14.478872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:14.478872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FgCshJESHYioQKQJeJDLYPTEpNQDkcaj/KNNcq8L5M1GsAcB+tN2EUWRA+wQuFvZbyRrpeTXu6RxRd59OK2nCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:14.479309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.6169","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e632b24876e201a7c7e64e8989320d5dbdf52280ee2b307e2a9bc060547c7879","sha256:8562bfa18af8b5216993d7faa1dbd4e28d47c6e0892a31c940efe5fc58a5c72d"],"state_sha256":"ffb9e4c0a3c90f00cc08de486b28281008b07a3b235562b67982bd7843554668"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I+dsGRZgw13gn3WNVwVNciKh9fjaP3yHpdIOj+/1D8gVd+0MoR0Mn+iSKFeUkhLp3jDQgVnP1OcINHGX1aWPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:04:02.931771Z","bundle_sha256":"4aeb84aa4fec08b298e3063e89165706b00de9c56ee4238559ca6f11cc7476ca"}}