{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RM5XAYZB6FVQ4M7IMXKBUZ5AF7","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":"3625bc6ee6e7c319c89e2210987a36b1f26393afad14c16125b1f51093c94518","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-28T10:02:52Z","title_canon_sha256":"14ed5756639a3a2a27cfb8ec0f545c410054c81693bb8802cf9e1a0a9171117e"},"schema_version":"1.0","source":{"id":"1712.10319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.10319","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"arxiv_version","alias_value":"1712.10319v1","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.10319","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"pith_short_12","alias_value":"RM5XAYZB6FVQ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RM5XAYZB6FVQ4M7I","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RM5XAYZB","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:ab283b65ea51ed2b8b761967785f933264d671a5e984f96416c5b7d86eb88dce","target":"graph","created_at":"2026-05-18T00:27:03Z","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 deal with hypersurfaces in the framework of the $n$-dimensional relative differential geometry.  We consider a hypersurface $\\varPhi$ of $\\mathbb{R}^{n+1}$ with position vector field $\\mathbf{x}$, which is relatively normalized by a relative normalization $\\mathbf{y}$. Then $\\mathbf{y}$ is also a relative normalization of every member of the one-parameter family $\\mathcal{F}$ of hypersurfaces $\\varPhi_\\mu$ with position vector field $$\\mathbf{x}_\\mu = \\mathbf{x} + \\mu \\, \\mathbf{y},$$ where $\\mu$ is a real constant. We call every hypersurface $\\varPhi_\\mu \\in \\mathcal{F}$ relatively paralle","authors_text":"Ioannis Kaffas, Stylianos Stamatakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-28T10:02:52Z","title":"On the shape operator of relatively parallel hypersurfaces in the $n$-dimensional relative differential geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10319","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:d8703c9d4733aeda936f9d472ab93253dfa3761e0aa3a1d51cf31b468a61f385","target":"record","created_at":"2026-05-18T00:27:03Z","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":"3625bc6ee6e7c319c89e2210987a36b1f26393afad14c16125b1f51093c94518","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-28T10:02:52Z","title_canon_sha256":"14ed5756639a3a2a27cfb8ec0f545c410054c81693bb8802cf9e1a0a9171117e"},"schema_version":"1.0","source":{"id":"1712.10319","kind":"arxiv","version":1}},"canonical_sha256":"8b3b706321f16b0e33e865d41a67a02ffff09f9b533da7d36f886ee4727dbc57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b3b706321f16b0e33e865d41a67a02ffff09f9b533da7d36f886ee4727dbc57","first_computed_at":"2026-05-18T00:27:03.449849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:03.449849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RQEvXrds+A2fCTOzbYEYEyMfHHzh7vta8+Vw0+2t7IHz/yhBEMZTgD3WVCLSMrQFnPOks8c5X6O47+bNfVNDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:03.450450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.10319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8703c9d4733aeda936f9d472ab93253dfa3761e0aa3a1d51cf31b468a61f385","sha256:ab283b65ea51ed2b8b761967785f933264d671a5e984f96416c5b7d86eb88dce"],"state_sha256":"b763bb93dcf226d164e2da01ff8361513ad2a43d5b643066a992cd3a3709f3db"}