{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CUTPPLC6VX2E6P65GSVE2JXQV5","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":"b3860599b220adc4ef4c086d89497ab129adcb62cf0d0b6a742ac8f5c41b683e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-03T16:01:20Z","title_canon_sha256":"b88bdd2987bf2241d3ff7a7829fda1428c8ff09f147ce3e6c84fd63cd2c0b4b0"},"schema_version":"1.0","source":{"id":"1503.00987","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00987","created_at":"2026-05-18T01:26:18Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00987v3","created_at":"2026-05-18T01:26:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00987","created_at":"2026-05-18T01:26:18Z"},{"alias_kind":"pith_short_12","alias_value":"CUTPPLC6VX2E","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CUTPPLC6VX2E6P65","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CUTPPLC6","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:a243e13a1a42072a85b826fd353288a1c59405fbe60fd8826b8d1309eeca34bb","target":"graph","created_at":"2026-05-18T01:26:18Z","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 work we present the concept of $C$-semianalytic subset of a real analytic manifold and more generally of a real analytic space. $C$-semianalytic sets can be understood as the natural generalization to the semianalytic setting of global analytic sets introduced by Cartan ($C$-analytic sets for short). More precisely $S$ is a $C$-semianalytic subset of a real analytic space $(X,{\\mathcal O}_X)$ if each point of $X$ has a neighborhood $U$ such that $S\\cap U$ is a finite boolean combinations of global analytic equalities and strict inequalities on $X$. By means of paracompactness $C$-semia","authors_text":"Fabrizio Broglia, Francesca Acquistapace, Jos\\'e F. Fernando","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-03T16:01:20Z","title":"On globally defined semianalytic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00987","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:db41d003e88006f9993bcd99cfd4fe3948c21bfec3d3bf2d55e7a19a55fe651b","target":"record","created_at":"2026-05-18T01:26:18Z","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":"b3860599b220adc4ef4c086d89497ab129adcb62cf0d0b6a742ac8f5c41b683e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-03T16:01:20Z","title_canon_sha256":"b88bdd2987bf2241d3ff7a7829fda1428c8ff09f147ce3e6c84fd63cd2c0b4b0"},"schema_version":"1.0","source":{"id":"1503.00987","kind":"arxiv","version":3}},"canonical_sha256":"1526f7ac5eadf44f3fdd34aa4d26f0af458ac3f348045cc69cec4b2b54b5bb80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1526f7ac5eadf44f3fdd34aa4d26f0af458ac3f348045cc69cec4b2b54b5bb80","first_computed_at":"2026-05-18T01:26:18.622820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:18.622820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tURgZR9VbWAtB3Sms3OVcuZlv3y8Jl4vehwM5lNzyyK+U/dCCNAEEO7k0XSYbLmcbBxafdaLI4Dnqwm20noLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:18.623510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00987","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db41d003e88006f9993bcd99cfd4fe3948c21bfec3d3bf2d55e7a19a55fe651b","sha256:a243e13a1a42072a85b826fd353288a1c59405fbe60fd8826b8d1309eeca34bb"],"state_sha256":"40ac1d719b21562c4d3ff1f49af6f2f83aaff392b805c9b3c0c914acf78279b7"}