{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LSAROQ4MQH5I5BJXS3VP5SSMDV","short_pith_number":"pith:LSAROQ4M","canonical_record":{"source":{"id":"1309.6302","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-24T19:54:00Z","cross_cats_sorted":[],"title_canon_sha256":"08527ceb83f47220a87d9b29edb143beca803747ffba7f8b33cc48fd55a8ebe2","abstract_canon_sha256":"720aa0edced34651908293ffe793fb55930173fbf3ac58d465cb32003ad55040"},"schema_version":"1.0"},"canonical_sha256":"5c8117438c81fa8e853796eafeca4c1d403b3be2e2cf16d5337f64a95469bc01","source":{"kind":"arxiv","id":"1309.6302","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6302","created_at":"2026-05-18T03:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6302v2","created_at":"2026-05-18T03:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6302","created_at":"2026-05-18T03:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"LSAROQ4MQH5I","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LSAROQ4MQH5I5BJX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LSAROQ4M","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LSAROQ4MQH5I5BJXS3VP5SSMDV","target":"record","payload":{"canonical_record":{"source":{"id":"1309.6302","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-24T19:54:00Z","cross_cats_sorted":[],"title_canon_sha256":"08527ceb83f47220a87d9b29edb143beca803747ffba7f8b33cc48fd55a8ebe2","abstract_canon_sha256":"720aa0edced34651908293ffe793fb55930173fbf3ac58d465cb32003ad55040"},"schema_version":"1.0"},"canonical_sha256":"5c8117438c81fa8e853796eafeca4c1d403b3be2e2cf16d5337f64a95469bc01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:21.642276Z","signature_b64":"YoF+Hn2C65wPvMvoEcGHZlk6jNEt9edaSq1KyqvqV84qUf9Aj0ldfi9gmYSXlU4ES5+5H6zl4/jITFVPSkb8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c8117438c81fa8e853796eafeca4c1d403b3be2e2cf16d5337f64a95469bc01","last_reissued_at":"2026-05-18T03:06:21.641833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:21.641833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.6302","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":"2026-05-18T03:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fTt7sOkWRY9U/OUo2HtWRfB0bx91njEXQICricUIk3We5b3VCQv02M1e9qQPNqUD+KuCDmuCvA5CT4upIrw3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:59:07.040259Z"},"content_sha256":"bc60627462aa02b86657c1c9902068d240bb1b6de376e03daa12270f04dcbad2","schema_version":"1.0","event_id":"sha256:bc60627462aa02b86657c1c9902068d240bb1b6de376e03daa12270f04dcbad2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LSAROQ4MQH5I5BJXS3VP5SSMDV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geography of irregular Gorenstein 3-folds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Tong Zhang","submitted_at":"2013-09-24T19:54:00Z","abstract_excerpt":"In this paper, we study the explicit geography problem of irregular Gorenstein minimal 3-folds of general type. We generalize the classical Noether-Castelnuovo inequalities for irregular surfaces to irregular 3-folds according to the Albanese dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6302","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":"2026-05-18T03:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HncqmYsvNUlbWCVnCHmcG1WaK7LSzqtKtpUBho3eokTYpwD8+wRqoFQm5a8G9IUuVjGdCqpNHBkZtJlwGinKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:59:07.041014Z"},"content_sha256":"114bc1d5d28dbc152d738fcbd92d261e04444fb8d1d74d0a0195ea78c44a3d7a","schema_version":"1.0","event_id":"sha256:114bc1d5d28dbc152d738fcbd92d261e04444fb8d1d74d0a0195ea78c44a3d7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LSAROQ4MQH5I5BJXS3VP5SSMDV/bundle.json","state_url":"https://pith.science/pith/LSAROQ4MQH5I5BJXS3VP5SSMDV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LSAROQ4MQH5I5BJXS3VP5SSMDV/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":"2026-06-12T00:59:07Z","links":{"resolver":"https://pith.science/pith/LSAROQ4MQH5I5BJXS3VP5SSMDV","bundle":"https://pith.science/pith/LSAROQ4MQH5I5BJXS3VP5SSMDV/bundle.json","state":"https://pith.science/pith/LSAROQ4MQH5I5BJXS3VP5SSMDV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LSAROQ4MQH5I5BJXS3VP5SSMDV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LSAROQ4MQH5I5BJXS3VP5SSMDV","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":"720aa0edced34651908293ffe793fb55930173fbf3ac58d465cb32003ad55040","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-24T19:54:00Z","title_canon_sha256":"08527ceb83f47220a87d9b29edb143beca803747ffba7f8b33cc48fd55a8ebe2"},"schema_version":"1.0","source":{"id":"1309.6302","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6302","created_at":"2026-05-18T03:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6302v2","created_at":"2026-05-18T03:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6302","created_at":"2026-05-18T03:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"LSAROQ4MQH5I","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LSAROQ4MQH5I5BJX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LSAROQ4M","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:114bc1d5d28dbc152d738fcbd92d261e04444fb8d1d74d0a0195ea78c44a3d7a","target":"graph","created_at":"2026-05-18T03:06:21Z","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 study the explicit geography problem of irregular Gorenstein minimal 3-folds of general type. We generalize the classical Noether-Castelnuovo inequalities for irregular surfaces to irregular 3-folds according to the Albanese dimension.","authors_text":"Tong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-24T19:54:00Z","title":"Geography of irregular Gorenstein 3-folds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6302","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:bc60627462aa02b86657c1c9902068d240bb1b6de376e03daa12270f04dcbad2","target":"record","created_at":"2026-05-18T03:06:21Z","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":"720aa0edced34651908293ffe793fb55930173fbf3ac58d465cb32003ad55040","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-24T19:54:00Z","title_canon_sha256":"08527ceb83f47220a87d9b29edb143beca803747ffba7f8b33cc48fd55a8ebe2"},"schema_version":"1.0","source":{"id":"1309.6302","kind":"arxiv","version":2}},"canonical_sha256":"5c8117438c81fa8e853796eafeca4c1d403b3be2e2cf16d5337f64a95469bc01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c8117438c81fa8e853796eafeca4c1d403b3be2e2cf16d5337f64a95469bc01","first_computed_at":"2026-05-18T03:06:21.641833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:21.641833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YoF+Hn2C65wPvMvoEcGHZlk6jNEt9edaSq1KyqvqV84qUf9Aj0ldfi9gmYSXlU4ES5+5H6zl4/jITFVPSkb8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:21.642276Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6302","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc60627462aa02b86657c1c9902068d240bb1b6de376e03daa12270f04dcbad2","sha256:114bc1d5d28dbc152d738fcbd92d261e04444fb8d1d74d0a0195ea78c44a3d7a"],"state_sha256":"411bbc22b7487ca5e8d5c0f55a4231fa2eef5417c468afc1f9b18c24a8bd17c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rv9clXStXgsPjowXc4zSHmVdMZWzUSjAMYpfFsESOfckkT6UN/LBE6x5wCylWmMYtdW5eowmuFGq/ohdbIxSDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:59:07.045437Z","bundle_sha256":"21232e4a0790a6d79ed9674690e9d8df74bf254ced78a45f909ab51de4f1b1ed"}}