{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CYEV6CVGF7KGATS5KLBCSSMP5T","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":"dfdc13dbee65397fbaa2900a4246e551b1e8cbac5f58c3b443f2827e17e3adb9","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-01-28T12:07:14Z","title_canon_sha256":"e01353b36decb6f8362385e7f91b0a9341dc485eafd393017b15a93a16b6f438"},"schema_version":"1.0","source":{"id":"1601.07734","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07734","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07734v1","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07734","created_at":"2026-05-18T01:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"CYEV6CVGF7KG","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CYEV6CVGF7KGATS5","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CYEV6CVG","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:224475fa780631b51bc4b365cfd483991e13772d2a708355ca180fd46941eea6","target":"graph","created_at":"2026-05-18T01:21:42Z","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":"In this paper we prove some results on the covering morphisms of internal groupoids. We also give a result on the coverings of the crossed modules of groups with operations.","authors_text":"H. Fulya Ak{\\i}z, Nazmiye Alemdar, Osman Mucuk, Tun\\c{c}ar \\c{S}ahan","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-01-28T12:07:14Z","title":"Coverings of internal groupoids and crossed modules in the category of groups with operations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07734","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":"sha256:3da214c77053b29a4f608a00244810aedd110a8a638dd0cd4259e91310fa6f0e","target":"record","created_at":"2026-05-18T01:21:42Z","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":"dfdc13dbee65397fbaa2900a4246e551b1e8cbac5f58c3b443f2827e17e3adb9","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-01-28T12:07:14Z","title_canon_sha256":"e01353b36decb6f8362385e7f91b0a9341dc485eafd393017b15a93a16b6f438"},"schema_version":"1.0","source":{"id":"1601.07734","kind":"arxiv","version":1}},"canonical_sha256":"16095f0aa62fd4604e5d52c229498fecf8118104e878b9abd2a3bf51696dedb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16095f0aa62fd4604e5d52c229498fecf8118104e878b9abd2a3bf51696dedb6","first_computed_at":"2026-05-18T01:21:42.327920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:42.327920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"As15UoomyIVTO1Ea4oyn7EPZ67JmJe5zNJnxiRKmL8upeHuWPJDzaqjSTWxm+A9h5dKtXWSCW5quYPWcNE0yDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:42.328434Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07734","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3da214c77053b29a4f608a00244810aedd110a8a638dd0cd4259e91310fa6f0e","sha256:224475fa780631b51bc4b365cfd483991e13772d2a708355ca180fd46941eea6"],"state_sha256":"d257196f07800af76bf9c40ab3c1b58c90b78f6372760f77c146eadd40b89602"}