{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:2QICGT3JEQLGEBG5QG6WFDYQRZ","short_pith_number":"pith:2QICGT3J","canonical_record":{"source":{"id":"2103.01417","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-03-02T02:04:51Z","cross_cats_sorted":[],"title_canon_sha256":"6ce4fc74dd7a034434369228c18859c38a6c81f8b63c83a53eee0e57adb6e165","abstract_canon_sha256":"f64eab263265c9cbb9ef9fe407eea9f7c0884d0aa674f6f8204672c684696f21"},"schema_version":"1.0"},"canonical_sha256":"d410234f6924166204dd81bd628f108e79a23bf99e61aa8d28c1cfd699076b9c","source":{"kind":"arxiv","id":"2103.01417","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.01417","created_at":"2026-07-05T04:47:06Z"},{"alias_kind":"arxiv_version","alias_value":"2103.01417v2","created_at":"2026-07-05T04:47:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.01417","created_at":"2026-07-05T04:47:06Z"},{"alias_kind":"pith_short_12","alias_value":"2QICGT3JEQLG","created_at":"2026-07-05T04:47:06Z"},{"alias_kind":"pith_short_16","alias_value":"2QICGT3JEQLGEBG5","created_at":"2026-07-05T04:47:06Z"},{"alias_kind":"pith_short_8","alias_value":"2QICGT3J","created_at":"2026-07-05T04:47:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:2QICGT3JEQLGEBG5QG6WFDYQRZ","target":"record","payload":{"canonical_record":{"source":{"id":"2103.01417","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-03-02T02:04:51Z","cross_cats_sorted":[],"title_canon_sha256":"6ce4fc74dd7a034434369228c18859c38a6c81f8b63c83a53eee0e57adb6e165","abstract_canon_sha256":"f64eab263265c9cbb9ef9fe407eea9f7c0884d0aa674f6f8204672c684696f21"},"schema_version":"1.0"},"canonical_sha256":"d410234f6924166204dd81bd628f108e79a23bf99e61aa8d28c1cfd699076b9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:47:06.890539Z","signature_b64":"Zmr1N+JOhj/V+UfjEGJv3h3xxlrYMSz+IyqIhxm+VNeWlbMkzITj0BjI0ykayvgt5iQOisdmPP+IozEpmtUUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d410234f6924166204dd81bd628f108e79a23bf99e61aa8d28c1cfd699076b9c","last_reissued_at":"2026-07-05T04:47:06.890057Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:47:06.890057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.01417","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":"2026-07-05T04:47:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zxBJY+9cuugu2JbSzO5TI+tMmy/PXgBbNFiRysMzUCEKyKS6+hgAP45Heh66Hr+hG+22YLmD7+Y92+eVZgukBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T22:47:25.130338Z"},"content_sha256":"972b90103be581fdbeb85cba3271318184cb33ef4b8e0f45c94e89d9ecddd915","schema_version":"1.0","event_id":"sha256:972b90103be581fdbeb85cba3271318184cb33ef4b8e0f45c94e89d9ecddd915"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:2QICGT3JEQLGEBG5QG6WFDYQRZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of log canonical modifications and its applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kenta Hashizume, Osamu Fujino","submitted_at":"2021-03-02T02:04:51Z","abstract_excerpt":"The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some suitable assumptions. It recovers Kawakita's inversion of adjunction on log canonicity in full generality. We also discuss the existence of semi-log canonical modifications for demi-normal pairs and construct dlt blow-ups with several extra good properties. As applications, we study lengths of extremal rational curves and so on."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.01417","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.01417/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":"2026-07-05T04:47:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DnJwyXfNm4WxShLA5yD5CQmW3yER7+vKaXmz+jQ0ZbQ9+szX6H3eJfjSWQxuvCET0Nb4KdCFPDcW/ypYbuxTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T22:47:25.130838Z"},"content_sha256":"2a50e0a842a111089c831b2627c75709296f62d3381dfbfca7957d73bf6aa40d","schema_version":"1.0","event_id":"sha256:2a50e0a842a111089c831b2627c75709296f62d3381dfbfca7957d73bf6aa40d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2QICGT3JEQLGEBG5QG6WFDYQRZ/bundle.json","state_url":"https://pith.science/pith/2QICGT3JEQLGEBG5QG6WFDYQRZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2QICGT3JEQLGEBG5QG6WFDYQRZ/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":"2026-08-10T22:47:25Z","links":{"resolver":"https://pith.science/pith/2QICGT3JEQLGEBG5QG6WFDYQRZ","bundle":"https://pith.science/pith/2QICGT3JEQLGEBG5QG6WFDYQRZ/bundle.json","state":"https://pith.science/pith/2QICGT3JEQLGEBG5QG6WFDYQRZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2QICGT3JEQLGEBG5QG6WFDYQRZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:2QICGT3JEQLGEBG5QG6WFDYQRZ","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":"f64eab263265c9cbb9ef9fe407eea9f7c0884d0aa674f6f8204672c684696f21","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-03-02T02:04:51Z","title_canon_sha256":"6ce4fc74dd7a034434369228c18859c38a6c81f8b63c83a53eee0e57adb6e165"},"schema_version":"1.0","source":{"id":"2103.01417","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.01417","created_at":"2026-07-05T04:47:06Z"},{"alias_kind":"arxiv_version","alias_value":"2103.01417v2","created_at":"2026-07-05T04:47:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.01417","created_at":"2026-07-05T04:47:06Z"},{"alias_kind":"pith_short_12","alias_value":"2QICGT3JEQLG","created_at":"2026-07-05T04:47:06Z"},{"alias_kind":"pith_short_16","alias_value":"2QICGT3JEQLGEBG5","created_at":"2026-07-05T04:47:06Z"},{"alias_kind":"pith_short_8","alias_value":"2QICGT3J","created_at":"2026-07-05T04:47:06Z"}],"graph_snapshots":[{"event_id":"sha256:2a50e0a842a111089c831b2627c75709296f62d3381dfbfca7957d73bf6aa40d","target":"graph","created_at":"2026-07-05T04:47:06Z","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/2103.01417/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some suitable assumptions. It recovers Kawakita's inversion of adjunction on log canonicity in full generality. We also discuss the existence of semi-log canonical modifications for demi-normal pairs and construct dlt blow-ups with several extra good properties. As applications, we study lengths of extremal rational curves and so on.","authors_text":"Kenta Hashizume, Osamu Fujino","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-03-02T02:04:51Z","title":"Existence of log canonical modifications and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.01417","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":"sha256:972b90103be581fdbeb85cba3271318184cb33ef4b8e0f45c94e89d9ecddd915","target":"record","created_at":"2026-07-05T04:47:06Z","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":"f64eab263265c9cbb9ef9fe407eea9f7c0884d0aa674f6f8204672c684696f21","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-03-02T02:04:51Z","title_canon_sha256":"6ce4fc74dd7a034434369228c18859c38a6c81f8b63c83a53eee0e57adb6e165"},"schema_version":"1.0","source":{"id":"2103.01417","kind":"arxiv","version":2}},"canonical_sha256":"d410234f6924166204dd81bd628f108e79a23bf99e61aa8d28c1cfd699076b9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d410234f6924166204dd81bd628f108e79a23bf99e61aa8d28c1cfd699076b9c","first_computed_at":"2026-07-05T04:47:06.890057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:47:06.890057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zmr1N+JOhj/V+UfjEGJv3h3xxlrYMSz+IyqIhxm+VNeWlbMkzITj0BjI0ykayvgt5iQOisdmPP+IozEpmtUUCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:47:06.890539Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.01417","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:972b90103be581fdbeb85cba3271318184cb33ef4b8e0f45c94e89d9ecddd915","sha256:2a50e0a842a111089c831b2627c75709296f62d3381dfbfca7957d73bf6aa40d"],"state_sha256":"b384bbf1240ebd87ffda5e1d8cf568587dede904ac73d16ade20e36ee7848121"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTr5OJo8zsK8y4AIRf9MDpWlSoNMA4AMDW7Rv+avI0nrao/imxa4/FZr2MQQ0me3pE76HlYur+fqr81EDayLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T22:47:25.134597Z","bundle_sha256":"e4bab60689f687a8b13a584a0d2c4cbf0f31a1cee639183540f8d39b3dd167f5"}}