{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SAV72ZCB7K5U56A6OHJ2XUIOL6","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":"2646b5c97fa55eede82e32baf92837fb15a1495dc8875890e0d3fd4e5abf2b5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-22T18:20:31Z","title_canon_sha256":"5246b654bc176944fd6afbaa813849899641fa9f984db73f0312c001016f91eb"},"schema_version":"1.0","source":{"id":"1002.4163","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4163","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4163v3","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4163","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"pith_short_12","alias_value":"SAV72ZCB7K5U","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SAV72ZCB7K5U56A6","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SAV72ZCB","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:10f0741db23f1411880d269b020a596e1e0f0b0a4ea89ffd74d1f047474ffd46","target":"graph","created_at":"2026-05-18T04:23:11Z","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":"To r ideals on a germ of smooth variety X one attaches a rational polytope in the r-dimensional Euclidean space (the LCT-polytope) that generalizes the notion of log canonical threshold in the case of one ideal. We study these polytopes, and prove a strong form of the Ascending Chain Condition in this setting: we show that if a sequence P_m of such LCT-polytopes converges to a compact subset Q in the Hausdorff metric, then Q is equal to the intersection of all but finitely many of the P_m. Furthermore, Q is an LCT-polytope.","authors_text":"Anatoly Libgober, Mircea Mustata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-22T18:20:31Z","title":"Sequences of LCT-polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4163","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":"sha256:0658ede53b97ac2df5174ef8d5f392bf0b20c3e04ab96dd9bd8971da9588a7be","target":"record","created_at":"2026-05-18T04:23:11Z","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":"2646b5c97fa55eede82e32baf92837fb15a1495dc8875890e0d3fd4e5abf2b5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-22T18:20:31Z","title_canon_sha256":"5246b654bc176944fd6afbaa813849899641fa9f984db73f0312c001016f91eb"},"schema_version":"1.0","source":{"id":"1002.4163","kind":"arxiv","version":3}},"canonical_sha256":"902bfd6441fabb4ef81e71d3abd10e5f845602305e73d7b3279851b18a1921a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"902bfd6441fabb4ef81e71d3abd10e5f845602305e73d7b3279851b18a1921a3","first_computed_at":"2026-05-18T04:23:11.752001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:11.752001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fwrXuMCP4C7toy3qucuTpUMXlcHeA4lStAzGgvYJ1ra1FTpEnGr8MWeeV9jJbJh2SmonZNFQS3peaZnFVxr4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:11.752552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.4163","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0658ede53b97ac2df5174ef8d5f392bf0b20c3e04ab96dd9bd8971da9588a7be","sha256:10f0741db23f1411880d269b020a596e1e0f0b0a4ea89ffd74d1f047474ffd46"],"state_sha256":"0833655fe6b74e384e46dee96cd045bffb89f97feee12f490732342ef5800a62"}