{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NHSLXWGQLM3MNWW3HW4XZIPCFL","short_pith_number":"pith:NHSLXWGQ","canonical_record":{"source":{"id":"1908.00171","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2019-08-01T01:45:42Z","cross_cats_sorted":[],"title_canon_sha256":"7c48f84bf33cdc2d4c438570ff5e5c02e21f36057884283f47e4578307cc7548","abstract_canon_sha256":"158f60fbadbf14a0b4f4022b882484c7b0b6807776731502d0cd6ddbda7dabf9"},"schema_version":"1.0"},"canonical_sha256":"69e4bbd8d05b36c6dadb3db97ca1e22ad7baac1f789944dedba4ddc6b809d0c7","source":{"kind":"arxiv","id":"1908.00171","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00171","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00171v3","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00171","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_12","alias_value":"NHSLXWGQLM3M","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_16","alias_value":"NHSLXWGQLM3MNWW3","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_8","alias_value":"NHSLXWGQ","created_at":"2026-07-05T06:48:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NHSLXWGQLM3MNWW3HW4XZIPCFL","target":"record","payload":{"canonical_record":{"source":{"id":"1908.00171","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2019-08-01T01:45:42Z","cross_cats_sorted":[],"title_canon_sha256":"7c48f84bf33cdc2d4c438570ff5e5c02e21f36057884283f47e4578307cc7548","abstract_canon_sha256":"158f60fbadbf14a0b4f4022b882484c7b0b6807776731502d0cd6ddbda7dabf9"},"schema_version":"1.0"},"canonical_sha256":"69e4bbd8d05b36c6dadb3db97ca1e22ad7baac1f789944dedba4ddc6b809d0c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:48:43.810105Z","signature_b64":"VAbRB1pANRvoy10H9zcAHoVV/v1k8xU5YDePGbJlBgtO/hhP27Yrrjr4XKo6jIwrFa4Dv5kDiWhdDC9TxmHOCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69e4bbd8d05b36c6dadb3db97ca1e22ad7baac1f789944dedba4ddc6b809d0c7","last_reissued_at":"2026-07-05T06:48:43.809728Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:48:43.809728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.00171","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":"2026-07-05T06:48:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4BxQZz+w6duao/gIECO3pXfltWmIg0+8+6fOuJcOLOCiQ6e4vsz4f7tHuSh6PsT58f3vxO7q+urqCVddR2okAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:45:41.930493Z"},"content_sha256":"0629c338efb8abf96cfd1310df19cd9d0f2fb2a552b8fa698a4cba2f324f8069","schema_version":"1.0","event_id":"sha256:0629c338efb8abf96cfd1310df19cd9d0f2fb2a552b8fa698a4cba2f324f8069"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NHSLXWGQLM3MNWW3HW4XZIPCFL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On mixed-$\\omega$-sheaves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Osamu Fujino","submitted_at":"2019-08-01T01:45:42Z","abstract_excerpt":"We introduce the notion of mixed-$\\omega$-sheaves and use it for the study of a relative version of Fujita's freeness conjecture. It is related to the Iitaka conjecture. We note that the notion of mixed-$\\omega$-sheaves is a generalization of that of Nakayama's $\\omega$-sheaves in some sense. One of the main motivations of this paper is to make Nakayama's theory of $\\omega$-sheaves more accessible and make it applicable to the study of log canonical pairs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00171","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/1908.00171/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":"2026-07-05T06:48:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"duQZtlWFavBQ4JbBgfL0DTk104J6W33zpgWlJXbbXc9DQ2ZXSCePgGmHzpQYMJ8p2LZHcmnRqz5vtcmWON53Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:45:41.931044Z"},"content_sha256":"668f209951c6b0a04b8a3aa86a4f1eb49f5d32c11fd27194b1ad21d0078d037d","schema_version":"1.0","event_id":"sha256:668f209951c6b0a04b8a3aa86a4f1eb49f5d32c11fd27194b1ad21d0078d037d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NHSLXWGQLM3MNWW3HW4XZIPCFL/bundle.json","state_url":"https://pith.science/pith/NHSLXWGQLM3MNWW3HW4XZIPCFL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NHSLXWGQLM3MNWW3HW4XZIPCFL/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":"2026-08-14T08:45:41Z","links":{"resolver":"https://pith.science/pith/NHSLXWGQLM3MNWW3HW4XZIPCFL","bundle":"https://pith.science/pith/NHSLXWGQLM3MNWW3HW4XZIPCFL/bundle.json","state":"https://pith.science/pith/NHSLXWGQLM3MNWW3HW4XZIPCFL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NHSLXWGQLM3MNWW3HW4XZIPCFL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NHSLXWGQLM3MNWW3HW4XZIPCFL","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":"158f60fbadbf14a0b4f4022b882484c7b0b6807776731502d0cd6ddbda7dabf9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2019-08-01T01:45:42Z","title_canon_sha256":"7c48f84bf33cdc2d4c438570ff5e5c02e21f36057884283f47e4578307cc7548"},"schema_version":"1.0","source":{"id":"1908.00171","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00171","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00171v3","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00171","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_12","alias_value":"NHSLXWGQLM3M","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_16","alias_value":"NHSLXWGQLM3MNWW3","created_at":"2026-07-05T06:48:43Z"},{"alias_kind":"pith_short_8","alias_value":"NHSLXWGQ","created_at":"2026-07-05T06:48:43Z"}],"graph_snapshots":[{"event_id":"sha256:668f209951c6b0a04b8a3aa86a4f1eb49f5d32c11fd27194b1ad21d0078d037d","target":"graph","created_at":"2026-07-05T06:48:43Z","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/1908.00171/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the notion of mixed-$\\omega$-sheaves and use it for the study of a relative version of Fujita's freeness conjecture. It is related to the Iitaka conjecture. We note that the notion of mixed-$\\omega$-sheaves is a generalization of that of Nakayama's $\\omega$-sheaves in some sense. One of the main motivations of this paper is to make Nakayama's theory of $\\omega$-sheaves more accessible and make it applicable to the study of log canonical pairs.","authors_text":"Osamu Fujino","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2019-08-01T01:45:42Z","title":"On mixed-$\\omega$-sheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00171","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":"sha256:0629c338efb8abf96cfd1310df19cd9d0f2fb2a552b8fa698a4cba2f324f8069","target":"record","created_at":"2026-07-05T06:48:43Z","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":"158f60fbadbf14a0b4f4022b882484c7b0b6807776731502d0cd6ddbda7dabf9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2019-08-01T01:45:42Z","title_canon_sha256":"7c48f84bf33cdc2d4c438570ff5e5c02e21f36057884283f47e4578307cc7548"},"schema_version":"1.0","source":{"id":"1908.00171","kind":"arxiv","version":3}},"canonical_sha256":"69e4bbd8d05b36c6dadb3db97ca1e22ad7baac1f789944dedba4ddc6b809d0c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69e4bbd8d05b36c6dadb3db97ca1e22ad7baac1f789944dedba4ddc6b809d0c7","first_computed_at":"2026-07-05T06:48:43.809728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:48:43.809728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VAbRB1pANRvoy10H9zcAHoVV/v1k8xU5YDePGbJlBgtO/hhP27Yrrjr4XKo6jIwrFa4Dv5kDiWhdDC9TxmHOCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:48:43.810105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00171","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0629c338efb8abf96cfd1310df19cd9d0f2fb2a552b8fa698a4cba2f324f8069","sha256:668f209951c6b0a04b8a3aa86a4f1eb49f5d32c11fd27194b1ad21d0078d037d"],"state_sha256":"2d4288419323871428191995263a1de69fbccb98c691cdff189589f4791b1549"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g2jOQ9KrEx9A2ngd4U1fQD4Z46zZje7cYihMCmMbDtExgbpAS1ZrCDem/ubUtTbukc55mwalQovlfJa/4HNOCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T08:45:41.934985Z","bundle_sha256":"70bdad96ecd97a56e6ff769c7955df3fc3a865d752fb15faacefdcf73179a99b"}}