{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QENPCJFLJRJFN2US7NZ24636I6","short_pith_number":"pith:QENPCJFL","canonical_record":{"source":{"id":"1312.7778","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-30T17:00:18Z","cross_cats_sorted":["math.AC","math.CV"],"title_canon_sha256":"52eca98e0cb45fe8d30635623da9cf387f89f719f8a2dcdc804d536fc5710980","abstract_canon_sha256":"2d0b1763e75334635b1aeca661972b4e8530a4f6740f203d861b4052f8be535b"},"schema_version":"1.0"},"canonical_sha256":"811af124ab4c5256ea92fb73ae7b7e47a97fd2c6095ea9d2d820e7e4f2a9f437","source":{"kind":"arxiv","id":"1312.7778","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7778","created_at":"2026-05-18T02:54:37Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7778v3","created_at":"2026-05-18T02:54:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7778","created_at":"2026-05-18T02:54:37Z"},{"alias_kind":"pith_short_12","alias_value":"QENPCJFLJRJF","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QENPCJFLJRJFN2US","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QENPCJFL","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QENPCJFLJRJFN2US7NZ24636I6","target":"record","payload":{"canonical_record":{"source":{"id":"1312.7778","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-30T17:00:18Z","cross_cats_sorted":["math.AC","math.CV"],"title_canon_sha256":"52eca98e0cb45fe8d30635623da9cf387f89f719f8a2dcdc804d536fc5710980","abstract_canon_sha256":"2d0b1763e75334635b1aeca661972b4e8530a4f6740f203d861b4052f8be535b"},"schema_version":"1.0"},"canonical_sha256":"811af124ab4c5256ea92fb73ae7b7e47a97fd2c6095ea9d2d820e7e4f2a9f437","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:37.640952Z","signature_b64":"4QQcvtPY28RJxeJNUa9dUfw4+i/HHxrZEjIt/xPRa5z+sojdfVdvOKveUXUzCFc1+1fes9taQp3ovi9BEWSrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"811af124ab4c5256ea92fb73ae7b7e47a97fd2c6095ea9d2d820e7e4f2a9f437","last_reissued_at":"2026-05-18T02:54:37.640283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:37.640283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.7778","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":"2026-05-18T02:54:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FDJenC4WcOnsNebTq1HuIVpCZP0oV8wrCFXy8huTOfTL50JeYypnOYJ25x/TPogbQSjKz9lj3repiojngdAgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:07:45.562451Z"},"content_sha256":"0b2bf86080944165bb2cb85336427f44ec6a69898d2e27d2f93f4f92b349a71b","schema_version":"1.0","event_id":"sha256:0b2bf86080944165bb2cb85336427f44ec6a69898d2e27d2f93f4f92b349a71b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QENPCJFLJRJFN2US7NZ24636I6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Castelnuovo--Mumford Regularity and Log-canonical Thresholds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CV"],"primary_cat":"math.AG","authors_text":"Alex K\\\"uronya, Norbert Pintye","submitted_at":"2013-12-30T17:00:18Z","abstract_excerpt":"We prove a sharp inequality relating the Castelnuovo--Mumford regularity of a coherent ideal sheaf to its log-canonical threshold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7778","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":""},"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":"2026-05-18T02:54:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+onRkBS8l3bX5XkpKqBtLILHrOyYuFIzjr4OAkNsNv+tsIse0Cr9ZiQa0vH3462EHwsAT7ynsBNVGQMOiVG2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:07:45.563137Z"},"content_sha256":"3eddd9191702ab684af99b14dea4ac68ef94adcc2c9074cf8a43aeaebee7d57e","schema_version":"1.0","event_id":"sha256:3eddd9191702ab684af99b14dea4ac68ef94adcc2c9074cf8a43aeaebee7d57e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QENPCJFLJRJFN2US7NZ24636I6/bundle.json","state_url":"https://pith.science/pith/QENPCJFLJRJFN2US7NZ24636I6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QENPCJFLJRJFN2US7NZ24636I6/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":"2026-06-10T13:07:45Z","links":{"resolver":"https://pith.science/pith/QENPCJFLJRJFN2US7NZ24636I6","bundle":"https://pith.science/pith/QENPCJFLJRJFN2US7NZ24636I6/bundle.json","state":"https://pith.science/pith/QENPCJFLJRJFN2US7NZ24636I6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QENPCJFLJRJFN2US7NZ24636I6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QENPCJFLJRJFN2US7NZ24636I6","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":"2d0b1763e75334635b1aeca661972b4e8530a4f6740f203d861b4052f8be535b","cross_cats_sorted":["math.AC","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-30T17:00:18Z","title_canon_sha256":"52eca98e0cb45fe8d30635623da9cf387f89f719f8a2dcdc804d536fc5710980"},"schema_version":"1.0","source":{"id":"1312.7778","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7778","created_at":"2026-05-18T02:54:37Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7778v3","created_at":"2026-05-18T02:54:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7778","created_at":"2026-05-18T02:54:37Z"},{"alias_kind":"pith_short_12","alias_value":"QENPCJFLJRJF","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QENPCJFLJRJFN2US","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QENPCJFL","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:3eddd9191702ab684af99b14dea4ac68ef94adcc2c9074cf8a43aeaebee7d57e","target":"graph","created_at":"2026-05-18T02:54:37Z","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 prove a sharp inequality relating the Castelnuovo--Mumford regularity of a coherent ideal sheaf to its log-canonical threshold.","authors_text":"Alex K\\\"uronya, Norbert Pintye","cross_cats":["math.AC","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-30T17:00:18Z","title":"Castelnuovo--Mumford Regularity and Log-canonical Thresholds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7778","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":"sha256:0b2bf86080944165bb2cb85336427f44ec6a69898d2e27d2f93f4f92b349a71b","target":"record","created_at":"2026-05-18T02:54:37Z","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":"2d0b1763e75334635b1aeca661972b4e8530a4f6740f203d861b4052f8be535b","cross_cats_sorted":["math.AC","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-30T17:00:18Z","title_canon_sha256":"52eca98e0cb45fe8d30635623da9cf387f89f719f8a2dcdc804d536fc5710980"},"schema_version":"1.0","source":{"id":"1312.7778","kind":"arxiv","version":3}},"canonical_sha256":"811af124ab4c5256ea92fb73ae7b7e47a97fd2c6095ea9d2d820e7e4f2a9f437","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"811af124ab4c5256ea92fb73ae7b7e47a97fd2c6095ea9d2d820e7e4f2a9f437","first_computed_at":"2026-05-18T02:54:37.640283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:37.640283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4QQcvtPY28RJxeJNUa9dUfw4+i/HHxrZEjIt/xPRa5z+sojdfVdvOKveUXUzCFc1+1fes9taQp3ovi9BEWSrAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:37.640952Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7778","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b2bf86080944165bb2cb85336427f44ec6a69898d2e27d2f93f4f92b349a71b","sha256:3eddd9191702ab684af99b14dea4ac68ef94adcc2c9074cf8a43aeaebee7d57e"],"state_sha256":"6c2d6f174ba3a293cf1e25e69f5c26b1ed5bbfb028a3467d5c5593898c340d60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T7MddUe73RD6WxsGicGc/zSjY7UxXW5uRT8O6Iy91/08Tpn9y7rtwqRHjTuIMrGYwaTCTIUKMGaBQyplfKWVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T13:07:45.567117Z","bundle_sha256":"ced15a740a3bd14f25fae2ae5f5c068e86d09bd5f06b053e4d53bde019633b96"}}