{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:N55VQDGAGJHDTVS4WAWOUOCHCM","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":"95984a92180b9d21e7675f462134ac54b972ca3c1a723b18d0800d3d49bdeb90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-03-17T23:51:44Z","title_canon_sha256":"67f545356737a5e38bdad93490b0746ded83f1a166386480094d98dc03762649"},"schema_version":"1.0","source":{"id":"1903.07202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07202","created_at":"2026-05-17T23:51:03Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07202v1","created_at":"2026-05-17T23:51:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07202","created_at":"2026-05-17T23:51:03Z"},{"alias_kind":"pith_short_12","alias_value":"N55VQDGAGJHD","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N55VQDGAGJHDTVS4","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N55VQDGA","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:07e501234316d3d302e28f1aa2dd4e02d8f501edc1a92bc687d06acee4b26542","target":"graph","created_at":"2026-05-17T23:51:03Z","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":"In this paper we study $(\\epsilon,\\delta)$-lc singularites, i.e. $\\epsilon$-lc singularities admitting a $\\delta$-plt blow-up. We prove that $n$-dimensional $(\\epsilon,\\delta)$-lc singularities are bounded up to a deformation, and $2$-dimensional $(\\epsilon,\\delta)$-lc singularities form a bounded family. Furthermore, we give an example which shows that $(\\epsilon,\\delta)$-lc singularities are not bounded in higher dimensions, even in the analytic sense.","authors_text":"Jihao Liu, Jingjun Han, Joaqu\\'in Moraga","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-03-17T23:51:44Z","title":"Bounded deformations of $(\\epsilon,\\delta)$-log canonical singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07202","kind":"arxiv","version":1},"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":"sha256:7e569a2b531292131f120c210d1ac04a4cd29c1aba03212699fcdb393c7f53c4","target":"record","created_at":"2026-05-17T23:51:03Z","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":"95984a92180b9d21e7675f462134ac54b972ca3c1a723b18d0800d3d49bdeb90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-03-17T23:51:44Z","title_canon_sha256":"67f545356737a5e38bdad93490b0746ded83f1a166386480094d98dc03762649"},"schema_version":"1.0","source":{"id":"1903.07202","kind":"arxiv","version":1}},"canonical_sha256":"6f7b580cc0324e39d65cb02cea384713189ecc23def1d9d77d8b7a048616d771","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f7b580cc0324e39d65cb02cea384713189ecc23def1d9d77d8b7a048616d771","first_computed_at":"2026-05-17T23:51:03.954653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:03.954653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dcSjbKuOK1rXnTIdzGciSKkajbZA2WWgcfArm9pC1fPXReTGOhoAWj5J6cNxXcjZdDXTgtaszywyqm0tBxifBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:03.955284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e569a2b531292131f120c210d1ac04a4cd29c1aba03212699fcdb393c7f53c4","sha256:07e501234316d3d302e28f1aa2dd4e02d8f501edc1a92bc687d06acee4b26542"],"state_sha256":"0a0645c9265ccfee2b7375ab84d4fee61fcca1fae7718b31b6bbe716a9246d38"}