{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:O4JAR76QYB7VZ6MCHRJ3QJBRUT","short_pith_number":"pith:O4JAR76Q","canonical_record":{"source":{"id":"1004.5170","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-29T01:09:23Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"a670694446378d9b3eec60a239b638e90a8dc5e6c9754ea6e48c591b28ac409f","abstract_canon_sha256":"a929d517b2c444b9fd8ccb133b886bb11dea1bc1a2927da4d9d0f0017ac127c3"},"schema_version":"1.0"},"canonical_sha256":"771208ffd0c07f5cf9823c53b82431a4c48cc31e966cd3bd3e6f8f0f8fd8e29e","source":{"kind":"arxiv","id":"1004.5170","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5170","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5170v2","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5170","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"pith_short_12","alias_value":"O4JAR76QYB7V","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"O4JAR76QYB7VZ6MC","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"O4JAR76Q","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:O4JAR76QYB7VZ6MCHRJ3QJBRUT","target":"record","payload":{"canonical_record":{"source":{"id":"1004.5170","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-29T01:09:23Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"a670694446378d9b3eec60a239b638e90a8dc5e6c9754ea6e48c591b28ac409f","abstract_canon_sha256":"a929d517b2c444b9fd8ccb133b886bb11dea1bc1a2927da4d9d0f0017ac127c3"},"schema_version":"1.0"},"canonical_sha256":"771208ffd0c07f5cf9823c53b82431a4c48cc31e966cd3bd3e6f8f0f8fd8e29e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:15.185107Z","signature_b64":"m3gN5LQ+KqcR93ltgqZp6OnXwFk2u0Qc1AQo91hKmJdgM7r0+ApfjCLHQ0A2DCbYijQi6ANZfA85xH6GyZS1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"771208ffd0c07f5cf9823c53b82431a4c48cc31e966cd3bd3e6f8f0f8fd8e29e","last_reissued_at":"2026-05-18T02:24:15.184456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:15.184456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.5170","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":"2026-05-18T02:24:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M9WAV1ukmvAhDCdOtJdQBhW57zG4hZ8WOuv+PZ9ycOSMwjBDxUbOVtx+L/fc96bVkb+HiT/Tk1FB2h9WMBlWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:19:00.381201Z"},"content_sha256":"b05456dca9c3f13df224e7fd914ae5c150b7319fe4bd033f2d0bdb203ab3d3ae","schema_version":"1.0","event_id":"sha256:b05456dca9c3f13df224e7fd914ae5c150b7319fe4bd033f2d0bdb203ab3d3ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:O4JAR76QYB7VZ6MCHRJ3QJBRUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Supplements to non-lc ideal sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Karl Schwede, Osamu Fujino, Shunsuke Takagi","submitted_at":"2010-04-29T01:09:23Z","abstract_excerpt":"We consider various definitions of non-lc ideal sheaves -- generalizations of the multiplier ideal sheaf which define the non-lc (non-log canonical) locus. We introduce the maximal non-lc ideal sheaf and intermediate non-lc ideal sheaves and consider the restriction theorem for these ideal sheaves. We also begin the development of the theory of a characteristic p>0 analog of maximal non-lc ideals, utilizing some recent work of Blickle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5170","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":""},"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":"2026-05-18T02:24:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NOwaanhfBm97Vq6k/feLdrOvULtS6efTqm1a6csGzqh2kguk2855aWn5sJeYNfP3SFHihURhuw4LN8xPC9/VAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:19:00.381560Z"},"content_sha256":"26f5361f6f65bb402d9db04e46598352724a51df8d50b61c53d474ddcb2f00c7","schema_version":"1.0","event_id":"sha256:26f5361f6f65bb402d9db04e46598352724a51df8d50b61c53d474ddcb2f00c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4JAR76QYB7VZ6MCHRJ3QJBRUT/bundle.json","state_url":"https://pith.science/pith/O4JAR76QYB7VZ6MCHRJ3QJBRUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4JAR76QYB7VZ6MCHRJ3QJBRUT/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":"2026-06-29T12:19:00Z","links":{"resolver":"https://pith.science/pith/O4JAR76QYB7VZ6MCHRJ3QJBRUT","bundle":"https://pith.science/pith/O4JAR76QYB7VZ6MCHRJ3QJBRUT/bundle.json","state":"https://pith.science/pith/O4JAR76QYB7VZ6MCHRJ3QJBRUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4JAR76QYB7VZ6MCHRJ3QJBRUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:O4JAR76QYB7VZ6MCHRJ3QJBRUT","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":"a929d517b2c444b9fd8ccb133b886bb11dea1bc1a2927da4d9d0f0017ac127c3","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-29T01:09:23Z","title_canon_sha256":"a670694446378d9b3eec60a239b638e90a8dc5e6c9754ea6e48c591b28ac409f"},"schema_version":"1.0","source":{"id":"1004.5170","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5170","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5170v2","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5170","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"pith_short_12","alias_value":"O4JAR76QYB7V","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"O4JAR76QYB7VZ6MC","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"O4JAR76Q","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:26f5361f6f65bb402d9db04e46598352724a51df8d50b61c53d474ddcb2f00c7","target":"graph","created_at":"2026-05-18T02:24:15Z","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"},"paper":{"abstract_excerpt":"We consider various definitions of non-lc ideal sheaves -- generalizations of the multiplier ideal sheaf which define the non-lc (non-log canonical) locus. We introduce the maximal non-lc ideal sheaf and intermediate non-lc ideal sheaves and consider the restriction theorem for these ideal sheaves. We also begin the development of the theory of a characteristic p>0 analog of maximal non-lc ideals, utilizing some recent work of Blickle.","authors_text":"Karl Schwede, Osamu Fujino, Shunsuke Takagi","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-29T01:09:23Z","title":"Supplements to non-lc ideal sheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5170","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:b05456dca9c3f13df224e7fd914ae5c150b7319fe4bd033f2d0bdb203ab3d3ae","target":"record","created_at":"2026-05-18T02:24:15Z","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":"a929d517b2c444b9fd8ccb133b886bb11dea1bc1a2927da4d9d0f0017ac127c3","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-29T01:09:23Z","title_canon_sha256":"a670694446378d9b3eec60a239b638e90a8dc5e6c9754ea6e48c591b28ac409f"},"schema_version":"1.0","source":{"id":"1004.5170","kind":"arxiv","version":2}},"canonical_sha256":"771208ffd0c07f5cf9823c53b82431a4c48cc31e966cd3bd3e6f8f0f8fd8e29e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"771208ffd0c07f5cf9823c53b82431a4c48cc31e966cd3bd3e6f8f0f8fd8e29e","first_computed_at":"2026-05-18T02:24:15.184456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:15.184456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m3gN5LQ+KqcR93ltgqZp6OnXwFk2u0Qc1AQo91hKmJdgM7r0+ApfjCLHQ0A2DCbYijQi6ANZfA85xH6GyZS1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:15.185107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5170","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b05456dca9c3f13df224e7fd914ae5c150b7319fe4bd033f2d0bdb203ab3d3ae","sha256:26f5361f6f65bb402d9db04e46598352724a51df8d50b61c53d474ddcb2f00c7"],"state_sha256":"368eb3f7aec02939a3ece5941a612a3a435859d84fb1d3c3202c1921a49d2ccc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HlCDWJt2CpAYVs45ZXoG5mgIq4ww46C0wLwVO8xzF93Ty1+j/KhmyqiITWJcSJDJrOeE13HUlZuZv5PgtmpfAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T12:19:00.383382Z","bundle_sha256":"e0c17eb6e930188eef5969c206719d06112a58525654347aff472b00df4926d3"}}