{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:3LCXTFICH3424PVEQX6MVIOIFT","short_pith_number":"pith:3LCXTFIC","canonical_record":{"source":{"id":"2109.13383","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-09-27T23:01:39Z","cross_cats_sorted":[],"title_canon_sha256":"cdb693d02039687cbe29a0519a8c54c7d6832deaacaeeb5cfb73604e8b781853","abstract_canon_sha256":"e1468e0515bcf538988031c50527bdc2935c9167106149937b5bdc9c5ce02711"},"schema_version":"1.0"},"canonical_sha256":"dac57995023ef9ae3ea485fccaa1c82ce7c9ec90e4ed53524df7837baaab89de","source":{"kind":"arxiv","id":"2109.13383","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.13383","created_at":"2026-07-05T04:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"2109.13383v3","created_at":"2026-07-05T04:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.13383","created_at":"2026-07-05T04:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"3LCXTFICH342","created_at":"2026-07-05T04:27:07Z"},{"alias_kind":"pith_short_16","alias_value":"3LCXTFICH3424PVE","created_at":"2026-07-05T04:27:07Z"},{"alias_kind":"pith_short_8","alias_value":"3LCXTFIC","created_at":"2026-07-05T04:27:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:3LCXTFICH3424PVEQX6MVIOIFT","target":"record","payload":{"canonical_record":{"source":{"id":"2109.13383","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-09-27T23:01:39Z","cross_cats_sorted":[],"title_canon_sha256":"cdb693d02039687cbe29a0519a8c54c7d6832deaacaeeb5cfb73604e8b781853","abstract_canon_sha256":"e1468e0515bcf538988031c50527bdc2935c9167106149937b5bdc9c5ce02711"},"schema_version":"1.0"},"canonical_sha256":"dac57995023ef9ae3ea485fccaa1c82ce7c9ec90e4ed53524df7837baaab89de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:27:07.926156Z","signature_b64":"0tntI4VEAAkdrP81WZbYfUA4xoW4aNCf8NJDJjK+DHq90B1AH+iiHCP7qNnGO1fsTpkfPsrQwbvbE0RhOKDjCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dac57995023ef9ae3ea485fccaa1c82ce7c9ec90e4ed53524df7837baaab89de","last_reissued_at":"2026-07-05T04:27:07.925744Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:27:07.925744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.13383","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:27:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"peUAz7wOticlnZUvwCAnIK+gafyPmtCyfErVUOSHYaX+2Lphq/2+nj0ROsMobYmLLHe9swOOGwWFeFC5hhS/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:14:50.386505Z"},"content_sha256":"57ae86aa48e336b29b5394b58fa53382e5dca7da3ef2c2106104833640ccd5b4","schema_version":"1.0","event_id":"sha256:57ae86aa48e336b29b5394b58fa53382e5dca7da3ef2c2106104833640ccd5b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:3LCXTFICH3424PVEQX6MVIOIFT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Varieties of general type with doubly exponential asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Burt Totaro, Chengxi Wang, Louis Esser","submitted_at":"2021-09-27T23:01:39Z","abstract_excerpt":"We construct smooth projective varieties of general type with the smallest known volume and others with the most known vanishing plurigenera in high dimensions. The optimal volume bound is expected to decay doubly exponentially with dimension, and our examples achieve this decay rate. We also consider the analogous questions for other types of varieties. For example, in every dimension we conjecture the terminal Fano variety of minimal volume, and the canonical Calabi-Yau variety of minimal volume. In each case, our examples exhibit doubly exponential behavior."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.13383","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.13383/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:27:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b+QrW0NGPAEoA4rwSjIYoaru35EOveNzE5WeOqO/6Zw/t9MOLvB1p4Z4jZaoPFUZUZpO9W1apURyg530iFh4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:14:50.386981Z"},"content_sha256":"4f46854592e38d9fe288f97e123ba2c271c7e81469b4c86dbfc3005c85208e00","schema_version":"1.0","event_id":"sha256:4f46854592e38d9fe288f97e123ba2c271c7e81469b4c86dbfc3005c85208e00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LCXTFICH3424PVEQX6MVIOIFT/bundle.json","state_url":"https://pith.science/pith/3LCXTFICH3424PVEQX6MVIOIFT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LCXTFICH3424PVEQX6MVIOIFT/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":"2026-08-11T20:14:50Z","links":{"resolver":"https://pith.science/pith/3LCXTFICH3424PVEQX6MVIOIFT","bundle":"https://pith.science/pith/3LCXTFICH3424PVEQX6MVIOIFT/bundle.json","state":"https://pith.science/pith/3LCXTFICH3424PVEQX6MVIOIFT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LCXTFICH3424PVEQX6MVIOIFT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:3LCXTFICH3424PVEQX6MVIOIFT","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":"e1468e0515bcf538988031c50527bdc2935c9167106149937b5bdc9c5ce02711","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-09-27T23:01:39Z","title_canon_sha256":"cdb693d02039687cbe29a0519a8c54c7d6832deaacaeeb5cfb73604e8b781853"},"schema_version":"1.0","source":{"id":"2109.13383","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.13383","created_at":"2026-07-05T04:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"2109.13383v3","created_at":"2026-07-05T04:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.13383","created_at":"2026-07-05T04:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"3LCXTFICH342","created_at":"2026-07-05T04:27:07Z"},{"alias_kind":"pith_short_16","alias_value":"3LCXTFICH3424PVE","created_at":"2026-07-05T04:27:07Z"},{"alias_kind":"pith_short_8","alias_value":"3LCXTFIC","created_at":"2026-07-05T04:27:07Z"}],"graph_snapshots":[{"event_id":"sha256:4f46854592e38d9fe288f97e123ba2c271c7e81469b4c86dbfc3005c85208e00","target":"graph","created_at":"2026-07-05T04:27:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.13383/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct smooth projective varieties of general type with the smallest known volume and others with the most known vanishing plurigenera in high dimensions. The optimal volume bound is expected to decay doubly exponentially with dimension, and our examples achieve this decay rate. We also consider the analogous questions for other types of varieties. For example, in every dimension we conjecture the terminal Fano variety of minimal volume, and the canonical Calabi-Yau variety of minimal volume. In each case, our examples exhibit doubly exponential behavior.","authors_text":"Burt Totaro, Chengxi Wang, Louis Esser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-09-27T23:01:39Z","title":"Varieties of general type with doubly exponential asymptotics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.13383","kind":"arxiv","version":3},"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":"sha256:57ae86aa48e336b29b5394b58fa53382e5dca7da3ef2c2106104833640ccd5b4","target":"record","created_at":"2026-07-05T04:27:07Z","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":"e1468e0515bcf538988031c50527bdc2935c9167106149937b5bdc9c5ce02711","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-09-27T23:01:39Z","title_canon_sha256":"cdb693d02039687cbe29a0519a8c54c7d6832deaacaeeb5cfb73604e8b781853"},"schema_version":"1.0","source":{"id":"2109.13383","kind":"arxiv","version":3}},"canonical_sha256":"dac57995023ef9ae3ea485fccaa1c82ce7c9ec90e4ed53524df7837baaab89de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dac57995023ef9ae3ea485fccaa1c82ce7c9ec90e4ed53524df7837baaab89de","first_computed_at":"2026-07-05T04:27:07.925744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:27:07.925744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tntI4VEAAkdrP81WZbYfUA4xoW4aNCf8NJDJjK+DHq90B1AH+iiHCP7qNnGO1fsTpkfPsrQwbvbE0RhOKDjCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:27:07.926156Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.13383","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57ae86aa48e336b29b5394b58fa53382e5dca7da3ef2c2106104833640ccd5b4","sha256:4f46854592e38d9fe288f97e123ba2c271c7e81469b4c86dbfc3005c85208e00"],"state_sha256":"ce4b61cec414ed1de30fd88706b288ae25e7a0198ad29a2669c2d18c8e6c2e9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bQeWFjNmj/2+sjaCnbiil2oWJJJMe7yh2veKroD02N8rd2A3284njf33i8iHAmTlzijPmNNIO44mC5jXDsc5Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T20:14:50.389976Z","bundle_sha256":"5cd698a70b40fac87c9cd6b621d97653ac499022e0d16c8a2ab399fb2dd47ae2"}}