{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LMLRYXPXX4UZEHAYZGJOIRUA45","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":"4e46d3550c7a3d6c0b051e6d20c9e9edc8231af7ea5370c34dbe84fda0e87535","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-08-07T07:05:53Z","title_canon_sha256":"7d27b9e01c24415a36b9a162ad2ec2bb648f7965db70bbfeb068a6e1e87ec85a"},"schema_version":"1.0","source":{"id":"2508.05082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.05082","created_at":"2026-07-05T11:50:06Z"},{"alias_kind":"arxiv_version","alias_value":"2508.05082v1","created_at":"2026-07-05T11:50:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.05082","created_at":"2026-07-05T11:50:06Z"},{"alias_kind":"pith_short_12","alias_value":"LMLRYXPXX4UZ","created_at":"2026-07-05T11:50:06Z"},{"alias_kind":"pith_short_16","alias_value":"LMLRYXPXX4UZEHAY","created_at":"2026-07-05T11:50:06Z"},{"alias_kind":"pith_short_8","alias_value":"LMLRYXPX","created_at":"2026-07-05T11:50:06Z"}],"graph_snapshots":[{"event_id":"sha256:31675855f55fc3a8111fd5add3a894b483da9c1ab89ffba7c0fe9cab16ad543b","target":"graph","created_at":"2026-07-05T11:50:06Z","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/2508.05082/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the volumes of divisors in Calabi--Yau type varieties. We show that given a klt Calabi--Yau pair $(X,B)$ and an integral divisor $A$ on $X$, the volume of $A$ is in a fixed discrete set depending only on the dimension and singularities of $(X,B)$. As an application, we prove a boundedness result of polarized log Calabi--Yau pairs which was conjectured by Birkar.","authors_text":"Junpeng Jiao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-08-07T07:05:53Z","title":"Discreteness of volumes of divisors on Calabi-Yau type varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.05082","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":"sha256:37ca2a382bfbdaf355e0ab1ae24a6ff0660276ce5661484e5608a903d16360c9","target":"record","created_at":"2026-07-05T11:50:06Z","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":"4e46d3550c7a3d6c0b051e6d20c9e9edc8231af7ea5370c34dbe84fda0e87535","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-08-07T07:05:53Z","title_canon_sha256":"7d27b9e01c24415a36b9a162ad2ec2bb648f7965db70bbfeb068a6e1e87ec85a"},"schema_version":"1.0","source":{"id":"2508.05082","kind":"arxiv","version":1}},"canonical_sha256":"5b171c5df7bf29921c18c992e44680e7659ac03004325d8ac931a65483294631","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b171c5df7bf29921c18c992e44680e7659ac03004325d8ac931a65483294631","first_computed_at":"2026-07-05T11:50:06.683939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:50:06.683939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8vK8Bw13nRLUID2MpKPoHM0Z4nzXL0kSP+8nD602LIAfdIYPXbeQTq7lW3mQzLsYtVZ/+bsUu+Ua4JOY/FEvAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:50:06.684399Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.05082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37ca2a382bfbdaf355e0ab1ae24a6ff0660276ce5661484e5608a903d16360c9","sha256:31675855f55fc3a8111fd5add3a894b483da9c1ab89ffba7c0fe9cab16ad543b"],"state_sha256":"334c62a240e03f1096f05fadf9e9af436cf9d05d2c58f2616319186113b7f921"}