{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UKO26J34LXG24HO4VYLLOUQVQU","short_pith_number":"pith:UKO26J34","canonical_record":{"source":{"id":"2404.01559","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-04-02T01:46:26Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3edad9592c02a5888d57907f89eec0769295dd085da5c7b755372db0d7bc9bbb","abstract_canon_sha256":"4076ed41f57fb5e73b07b573d2374515e610dc77fb628d8cb2766894e77f3d08"},"schema_version":"1.0"},"canonical_sha256":"a29daf277c5dcdae1ddcae16b752158507d6aa6aeae5d63a6fa7998e09039d9b","source":{"kind":"arxiv","id":"2404.01559","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.01559","created_at":"2026-06-10T14:10:41Z"},{"alias_kind":"arxiv_version","alias_value":"2404.01559v3","created_at":"2026-06-10T14:10:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.01559","created_at":"2026-06-10T14:10:41Z"},{"alias_kind":"pith_short_12","alias_value":"UKO26J34LXG2","created_at":"2026-06-10T14:10:41Z"},{"alias_kind":"pith_short_16","alias_value":"UKO26J34LXG24HO4","created_at":"2026-06-10T14:10:41Z"},{"alias_kind":"pith_short_8","alias_value":"UKO26J34","created_at":"2026-06-10T14:10:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UKO26J34LXG24HO4VYLLOUQVQU","target":"record","payload":{"canonical_record":{"source":{"id":"2404.01559","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-04-02T01:46:26Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3edad9592c02a5888d57907f89eec0769295dd085da5c7b755372db0d7bc9bbb","abstract_canon_sha256":"4076ed41f57fb5e73b07b573d2374515e610dc77fb628d8cb2766894e77f3d08"},"schema_version":"1.0"},"canonical_sha256":"a29daf277c5dcdae1ddcae16b752158507d6aa6aeae5d63a6fa7998e09039d9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T14:10:41.794965Z","signature_b64":"zu99hLbqcwk09GCRe3j4OWs+itbzoN261qhzNTDM0pmeDFIIvO4uP1yUgKI1euzIssfO9LrGUONt0bzlMweCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a29daf277c5dcdae1ddcae16b752158507d6aa6aeae5d63a6fa7998e09039d9b","last_reissued_at":"2026-06-10T14:10:41.793861Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T14:10:41.793861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.01559","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":"2026-06-10T14:10:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RHNl3TWybXkzMhx3R/O8rH69D/3LNsjZocFVAtlJseaV6qiC6T2jUSimgQLb/UAGy8wmiwMYFm/dqfR8pc19AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:50:15.671373Z"},"content_sha256":"7fa0c8cebc65fcf89ca82f4279ddbc1e5a9e496f38639bfcd07cf6187befd943","schema_version":"1.0","event_id":"sha256:7fa0c8cebc65fcf89ca82f4279ddbc1e5a9e496f38639bfcd07cf6187befd943"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UKO26J34LXG24HO4VYLLOUQVQU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal model program for algebraically integrable foliations on klt varieties","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Fanjun Meng, Jihao Liu, Lingyao Xie","submitted_at":"2024-04-02T01:46:26Z","abstract_excerpt":"For lc algebraically integrable foliations on klt varieties, we prove the base-point-freeness theorem, the contraction theorem, and the existence of flips. The first result resolves a conjecture of Cascini and Spicer, while the latter two results strengthen a result of Cascini and Spicer by removing their assumption on the termination of flips.\n  Moreover, we prove the existence of the minimal model program for lc algebraically integrable foliations on klt varieties and the existence of good minimal models or Mori fiber spaces for lc algebraically integrable foliations polarized by ample divis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.01559","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/2404.01559/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":"2026-06-10T14:10:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u3XrjdkY1p9eXmB7D2ICRLkDPr3Ib3RKRakQyrwA5Rnc/+E1RKoNvh6o3rl/1FHMzxYe+bFuR4H+4xhH1P2bCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:50:15.671881Z"},"content_sha256":"6df4732d75c98314bfe95c76841575a98fe258a785e1c1a7478c095cd46e514f","schema_version":"1.0","event_id":"sha256:6df4732d75c98314bfe95c76841575a98fe258a785e1c1a7478c095cd46e514f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UKO26J34LXG24HO4VYLLOUQVQU/bundle.json","state_url":"https://pith.science/pith/UKO26J34LXG24HO4VYLLOUQVQU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UKO26J34LXG24HO4VYLLOUQVQU/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":"2026-08-03T16:50:15Z","links":{"resolver":"https://pith.science/pith/UKO26J34LXG24HO4VYLLOUQVQU","bundle":"https://pith.science/pith/UKO26J34LXG24HO4VYLLOUQVQU/bundle.json","state":"https://pith.science/pith/UKO26J34LXG24HO4VYLLOUQVQU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UKO26J34LXG24HO4VYLLOUQVQU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UKO26J34LXG24HO4VYLLOUQVQU","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":"4076ed41f57fb5e73b07b573d2374515e610dc77fb628d8cb2766894e77f3d08","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-04-02T01:46:26Z","title_canon_sha256":"3edad9592c02a5888d57907f89eec0769295dd085da5c7b755372db0d7bc9bbb"},"schema_version":"1.0","source":{"id":"2404.01559","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.01559","created_at":"2026-06-10T14:10:41Z"},{"alias_kind":"arxiv_version","alias_value":"2404.01559v3","created_at":"2026-06-10T14:10:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.01559","created_at":"2026-06-10T14:10:41Z"},{"alias_kind":"pith_short_12","alias_value":"UKO26J34LXG2","created_at":"2026-06-10T14:10:41Z"},{"alias_kind":"pith_short_16","alias_value":"UKO26J34LXG24HO4","created_at":"2026-06-10T14:10:41Z"},{"alias_kind":"pith_short_8","alias_value":"UKO26J34","created_at":"2026-06-10T14:10:41Z"}],"graph_snapshots":[{"event_id":"sha256:6df4732d75c98314bfe95c76841575a98fe258a785e1c1a7478c095cd46e514f","target":"graph","created_at":"2026-06-10T14:10:41Z","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/2404.01559/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For lc algebraically integrable foliations on klt varieties, we prove the base-point-freeness theorem, the contraction theorem, and the existence of flips. The first result resolves a conjecture of Cascini and Spicer, while the latter two results strengthen a result of Cascini and Spicer by removing their assumption on the termination of flips.\n  Moreover, we prove the existence of the minimal model program for lc algebraically integrable foliations on klt varieties and the existence of good minimal models or Mori fiber spaces for lc algebraically integrable foliations polarized by ample divis","authors_text":"Fanjun Meng, Jihao Liu, Lingyao Xie","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-04-02T01:46:26Z","title":"Minimal model program for algebraically integrable foliations on klt varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.01559","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":"sha256:7fa0c8cebc65fcf89ca82f4279ddbc1e5a9e496f38639bfcd07cf6187befd943","target":"record","created_at":"2026-06-10T14:10:41Z","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":"4076ed41f57fb5e73b07b573d2374515e610dc77fb628d8cb2766894e77f3d08","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2024-04-02T01:46:26Z","title_canon_sha256":"3edad9592c02a5888d57907f89eec0769295dd085da5c7b755372db0d7bc9bbb"},"schema_version":"1.0","source":{"id":"2404.01559","kind":"arxiv","version":3}},"canonical_sha256":"a29daf277c5dcdae1ddcae16b752158507d6aa6aeae5d63a6fa7998e09039d9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a29daf277c5dcdae1ddcae16b752158507d6aa6aeae5d63a6fa7998e09039d9b","first_computed_at":"2026-06-10T14:10:41.793861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T14:10:41.793861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zu99hLbqcwk09GCRe3j4OWs+itbzoN261qhzNTDM0pmeDFIIvO4uP1yUgKI1euzIssfO9LrGUONt0bzlMweCAw==","signature_status":"signed_v1","signed_at":"2026-06-10T14:10:41.794965Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.01559","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fa0c8cebc65fcf89ca82f4279ddbc1e5a9e496f38639bfcd07cf6187befd943","sha256:6df4732d75c98314bfe95c76841575a98fe258a785e1c1a7478c095cd46e514f"],"state_sha256":"5c4c287e6c3752fafc0ad981150f551cb6695ab42c9367d6d5967af8027d5ffb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EVlA3saIqw2tG73V7gY8rYF7sni9K2raJ6Y8jqs2mCLpfLFpdv6bX5o7RIv9SS0AQbL0MQHEKY607x+Lx0eaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:50:15.675531Z","bundle_sha256":"7f73f3b468b1148d4b689da9c5d6816a9e463c870eeab13eaf6556767056feb4"}}