{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V4UDUTUGRRPNZRN6ZV2FJ35ZDU","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":"e184306a493403612ad9ebe2357771f1c830fa4fe4f4fa1849510f6a6c7f4fb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-17T15:37:29Z","title_canon_sha256":"f4ce22815e6c2070dfeeee2c997cc25579d9db3cada0d723a5fa4f52c84fd8f9"},"schema_version":"1.0","source":{"id":"1804.06326","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06326","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06326v4","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06326","created_at":"2026-05-17T23:45:15Z"},{"alias_kind":"pith_short_12","alias_value":"V4UDUTUGRRPN","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"V4UDUTUGRRPNZRN6","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"V4UDUTUG","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:b95631f1a661b88a8d851f6902df25c094d9c32ed5037fc01dc80ae5742f7b5c","target":"graph","created_at":"2026-05-17T23:45:15Z","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 define a class of singularity on arbitrary pairs of a normal variety and an effective $\\mathbb{R}$-divisor on it, which we call pseudo-lc in this paper. This is a generalization of the usual lc singularity of pairs and log canonical singularity of normal varieties introduced by de Fernex and Hacon. By giving examples of pseudo-lc pairs which are not lc or log canonical in the sense of de Fernex--Hacon's paper, we show that pseudo-lc singularity is a strictly extended notion of those singularities. We prove that pseudo-lc pairs admit a small lc modification. We also discuss a criterion of lo","authors_text":"Kenta Hashizume","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-17T15:37:29Z","title":"A class of singularity of arbitrary pairs and log canonicalizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06326","kind":"arxiv","version":4},"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:bf7d898dbf7c99cd1f93bcc72bcc17c0e1ee439f36558fe88b8bad4e98632d04","target":"record","created_at":"2026-05-17T23:45:15Z","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":"e184306a493403612ad9ebe2357771f1c830fa4fe4f4fa1849510f6a6c7f4fb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-17T15:37:29Z","title_canon_sha256":"f4ce22815e6c2070dfeeee2c997cc25579d9db3cada0d723a5fa4f52c84fd8f9"},"schema_version":"1.0","source":{"id":"1804.06326","kind":"arxiv","version":4}},"canonical_sha256":"af283a4e868c5edcc5becd7454efb91d3188280b0a9d132cd2250d3d8571b7a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af283a4e868c5edcc5becd7454efb91d3188280b0a9d132cd2250d3d8571b7a9","first_computed_at":"2026-05-17T23:45:15.508399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:15.508399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yvGOhn5/bS6umhsM4B47G/X4M+cTBKqY+G9uUD32yKcHl3x0QavpEORz3vC13i4sInWxh4a50wpJfYx8q8ouAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:15.509058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06326","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf7d898dbf7c99cd1f93bcc72bcc17c0e1ee439f36558fe88b8bad4e98632d04","sha256:b95631f1a661b88a8d851f6902df25c094d9c32ed5037fc01dc80ae5742f7b5c"],"state_sha256":"ca652f8dd706d374baa12328fe8154d9f955bb47b6b335528af522a772dbe21d"}