{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6SZ727EAJ33KLXBWNXQWYTHGAQ","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":"6ba9f091d0e8dc6041c399af00c8b1d4f69e223867ff4a3ec5e9b15cc5fe1245","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-07-17T16:12:37Z","title_canon_sha256":"c21e6a33530001c364a1c6ad70df79bfb8cd12145177cb33706ad3409dd765a2"},"schema_version":"1.0","source":{"id":"1507.05015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05015","created_at":"2026-05-18T01:36:42Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05015v1","created_at":"2026-05-18T01:36:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05015","created_at":"2026-05-18T01:36:42Z"},{"alias_kind":"pith_short_12","alias_value":"6SZ727EAJ33K","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6SZ727EAJ33KLXBW","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6SZ727EA","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:4f8e921b67f15080387c75e63f09c127299acf5b4ba64b3a723f38db9c4c0b11","target":"graph","created_at":"2026-05-18T01:36:42Z","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 study injective versions of the characterization of sets potentially in a Wadge class of Borel sets, for the first Borel and Lavrentieff classes. We also study the case of oriented graphs in terms of continuous homomorphisms, injective or not.","authors_text":"Dominique Lecomte, Rafael Zamora (IMJ)","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-07-17T16:12:37Z","title":"Injective tests of low complexity in the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05015","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":"sha256:0f0a20770edd21654963f23750d4297079bee3c7ea33b4c54e7953dc77632500","target":"record","created_at":"2026-05-18T01:36:42Z","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":"6ba9f091d0e8dc6041c399af00c8b1d4f69e223867ff4a3ec5e9b15cc5fe1245","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-07-17T16:12:37Z","title_canon_sha256":"c21e6a33530001c364a1c6ad70df79bfb8cd12145177cb33706ad3409dd765a2"},"schema_version":"1.0","source":{"id":"1507.05015","kind":"arxiv","version":1}},"canonical_sha256":"f4b3fd7c804ef6a5dc366de16c4ce60419d6abf2375c0498fc3c26c25b889523","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4b3fd7c804ef6a5dc366de16c4ce60419d6abf2375c0498fc3c26c25b889523","first_computed_at":"2026-05-18T01:36:42.165905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:42.165905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eIMxdCbQ9G1v38W8nIgY67vejQLUHxk/fHqJG5q9AEVaYfdqHYADRy8rUoEDGjSiuXP1LyOvz03w7VYzMvsHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:42.166513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f0a20770edd21654963f23750d4297079bee3c7ea33b4c54e7953dc77632500","sha256:4f8e921b67f15080387c75e63f09c127299acf5b4ba64b3a723f38db9c4c0b11"],"state_sha256":"90f58551b5e3290ea5a8f1cec1fad4de1e1838f838c0116bba03b9290cac451c"}