{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QCTVKU55YTSVGGAS3TPOEWYXGY","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":"dd84ab3e08d55b3a439956a4074da39793c4405198cfade678193f6c88b91a54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-12-19T18:04:24Z","title_canon_sha256":"80cd2554cf84cf97b6bd24c953e616401d22e8e0d8ba3c552d7fb6141588565a"},"schema_version":"1.0","source":{"id":"1701.00514","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00514","created_at":"2026-05-18T00:53:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00514v1","created_at":"2026-05-18T00:53:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00514","created_at":"2026-05-18T00:53:29Z"},{"alias_kind":"pith_short_12","alias_value":"QCTVKU55YTSV","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QCTVKU55YTSVGGAS","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QCTVKU55","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:e7a395039a74ef726bec461747ed873a959ba2c720b1444e232d52f1c8adf687","target":"graph","created_at":"2026-05-18T00:53:29Z","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":"This paper deals with relative normalizations of skew ruled surfaces in the Euclidean space $\\mathbb{E}^{3}$. In section 2 we investigate some new formulae concerning the Pick invariant, the relative curvature, the relative mean curvature and the curvature of the relative metric of a relatively normalized ruled surface $\\varPhi$ and in section 3 we introduce some special normalizations of it. All ruled surfaces and their corresponding normalizations that make $\\varPhi$ an improper or a proper relative sphere are determined in section 4. In the last section we study ruled surfaces, which are \\e","authors_text":"Ioanna-Iris Papadopoulou, Stylianos Stamatakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-12-19T18:04:24Z","title":"Notes on relative normalizations of ruled surfaces in the three-dimensional Euclidean space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00514","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":"sha256:0e7d1e8abd4ce2343191c563072bb96440bea3394915924e5e3396d35869a59a","target":"record","created_at":"2026-05-18T00:53:29Z","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":"dd84ab3e08d55b3a439956a4074da39793c4405198cfade678193f6c88b91a54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-12-19T18:04:24Z","title_canon_sha256":"80cd2554cf84cf97b6bd24c953e616401d22e8e0d8ba3c552d7fb6141588565a"},"schema_version":"1.0","source":{"id":"1701.00514","kind":"arxiv","version":1}},"canonical_sha256":"80a75553bdc4e5531812dcdee25b1736347f68e9800a5bc3f6849d3fd0900722","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80a75553bdc4e5531812dcdee25b1736347f68e9800a5bc3f6849d3fd0900722","first_computed_at":"2026-05-18T00:53:29.074746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:29.074746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"15UP4lNUIYfDb3exBijJekRmXoItTSQl7P1kMf4u6V92IjxjuDVkpDk1GBnO1VWEFHARnTp8cFYIWSgtU1nnDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:29.075307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00514","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e7d1e8abd4ce2343191c563072bb96440bea3394915924e5e3396d35869a59a","sha256:e7a395039a74ef726bec461747ed873a959ba2c720b1444e232d52f1c8adf687"],"state_sha256":"56be64b2214450de5bb34311499ad106b0eb1e39bdfd9fcd7c4da13efecc7ffe"}