{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3PH7HMUPKDMP2SELDGQUP5YIZR","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":"a2a81c3e36504d8c988d9c5df4da508da9d91c56368c335f530c55a2c4b335d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-11T14:58:25Z","title_canon_sha256":"e5115d1a0c0f6aeb4df6fdd410f2d23e95e8d36e7b843597023f4d80a767b6f8"},"schema_version":"1.0","source":{"id":"1312.3196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3196","created_at":"2026-05-18T01:45:51Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3196v1","created_at":"2026-05-18T01:45:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3196","created_at":"2026-05-18T01:45:51Z"},{"alias_kind":"pith_short_12","alias_value":"3PH7HMUPKDMP","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3PH7HMUPKDMP2SEL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3PH7HMUP","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:cc84d7f9855ae1ae10004ba790cc218e4a7c73cda90d995e92a250d6364e97d0","target":"graph","created_at":"2026-05-18T01:45:51Z","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 determine all helix surfaces with parallel mean curvature vector field, which are not minimal or pseudo-umbilical, in spaces of type $M^n(c)\\times\\mathbb{R}$, where $M^n(c)$ is a simply-connected $n$-dimensional manifold with constant sectional curvature $c$.","authors_text":"Dorel Fetcu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-11T14:58:25Z","title":"A classification result for helix surfaces with parallel mean curvature in product spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3196","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":"sha256:0b73c976f994963546d45257f1520fe8aacfa778b3ebc42e4f495a4bb41f775f","target":"record","created_at":"2026-05-18T01:45:51Z","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":"a2a81c3e36504d8c988d9c5df4da508da9d91c56368c335f530c55a2c4b335d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-11T14:58:25Z","title_canon_sha256":"e5115d1a0c0f6aeb4df6fdd410f2d23e95e8d36e7b843597023f4d80a767b6f8"},"schema_version":"1.0","source":{"id":"1312.3196","kind":"arxiv","version":1}},"canonical_sha256":"dbcff3b28f50d8fd488b19a147f708cc59b7cfc44573e1716368f29c7af0bc2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbcff3b28f50d8fd488b19a147f708cc59b7cfc44573e1716368f29c7af0bc2c","first_computed_at":"2026-05-18T01:45:51.644426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:51.644426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XaECXsyi+/b5pcToBRxv+INAA53pSHxFphng69mPK19FIWMnBQFoK23Vtj59VEAxswQzSApTHBwWsXoCsN3ICg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:51.645107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b73c976f994963546d45257f1520fe8aacfa778b3ebc42e4f495a4bb41f775f","sha256:cc84d7f9855ae1ae10004ba790cc218e4a7c73cda90d995e92a250d6364e97d0"],"state_sha256":"5abe2350ba90c1d55d0bb8bb9d8a1bffb5226630600e997038f7e31fcf370e04"}