{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5HPRGOB7O453PGVWMINX7UAGT4","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":"4407c12ef407d8635b406e081c1bf27c9c55adbcf069bea9e4445da96bfd6930","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-25T20:27:42Z","title_canon_sha256":"eb9552a5a2dd5d89670ec3a4e7ca7191cafbf6607660161509b5f843f6da00df"},"schema_version":"1.0","source":{"id":"1807.09839","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09839","created_at":"2026-05-18T00:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09839v1","created_at":"2026-05-18T00:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09839","created_at":"2026-05-18T00:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"5HPRGOB7O453","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5HPRGOB7O453PGVW","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5HPRGOB7","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:b26484a938ce13c22c8b1d18281069f56b65de356648a9375b1e23387248e85f","target":"graph","created_at":"2026-05-18T00:09:46Z","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 make a systematic study of the multiplicity of the jumping points associated to the mixed multiplier ideals of a family of ideals in a complex surface with rational singularities. In particular we study the behaviour of the multiplicity by small perturbations of the jumping points. We also introduce a Poincar\\'e series for mixed multiplier ideals and prove its rationality. Finally, we study the set of divisors that contribute to the log-canonical wall.","authors_text":"Ferran Dachs-Cadefau, Josep \\`Alvarez Montaner, Maria Alberich-Carrami\\~nana, V\\'ictor Gonz\\'alez-Alonso","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-25T20:27:42Z","title":"Multiplicities of jumping points for mixed multiplier ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09839","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":"sha256:63c1014985551e3294299e96612a888c67271bf0557ea0813e24bb439db57b1b","target":"record","created_at":"2026-05-18T00:09:46Z","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":"4407c12ef407d8635b406e081c1bf27c9c55adbcf069bea9e4445da96bfd6930","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-25T20:27:42Z","title_canon_sha256":"eb9552a5a2dd5d89670ec3a4e7ca7191cafbf6607660161509b5f843f6da00df"},"schema_version":"1.0","source":{"id":"1807.09839","kind":"arxiv","version":1}},"canonical_sha256":"e9df13383f773bb79ab6621b7fd0069f27cacdc7f14057da77f85e8d900b54d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9df13383f773bb79ab6621b7fd0069f27cacdc7f14057da77f85e8d900b54d7","first_computed_at":"2026-05-18T00:09:46.441753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:46.441753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/x/vHl36w2CVadqzAtxCgh8o1sVdBbEePIH08LEt3bOBZL8ttp14tfsUE+qfVoPFcQuJodrIcdEzlqt9SyIsDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:46.442486Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.09839","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63c1014985551e3294299e96612a888c67271bf0557ea0813e24bb439db57b1b","sha256:b26484a938ce13c22c8b1d18281069f56b65de356648a9375b1e23387248e85f"],"state_sha256":"225fc7e5fd951bbcdca257149abcc73411ddccc717b5e1dd7e124f34ed39c94c"}