{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VXMMXXON6Y2FEHWKRNAS325HC6","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":"0fa6341fafc0beb6b0d949689a5677c87dba181f3e6680bb0996dd7b6cd3a437","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-09T08:54:01Z","title_canon_sha256":"44d989c05bc6a4e6d4e6cfc8c3cee1c593ccd8efe0b833c92cf806e680155405"},"schema_version":"1.0","source":{"id":"1808.03060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03060","created_at":"2026-05-18T00:08:30Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03060v1","created_at":"2026-05-18T00:08:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03060","created_at":"2026-05-18T00:08:30Z"},{"alias_kind":"pith_short_12","alias_value":"VXMMXXON6Y2F","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VXMMXXON6Y2FEHWK","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VXMMXXON","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:5b701b4ec69331d9a3c8dfc068bfdb2caafa87144001af370e575bac5539d204","target":"graph","created_at":"2026-05-18T00:08:30Z","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 review the notion of shape tensor of an embedded manifold, which efficiently combines intrinsic and extrinsic geometry, and allows for intuitive understanding of some basic concepts of classical differential geometry, such as parallel transport, covariant differentiation, and curvature. We introduce shape-minimizing curves, i.e., curves between given two points that minimize integrated value of the shape tensor magnitude.","authors_text":"Vaclav Zatloukal","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-09T08:54:01Z","title":"Shape tensor and geometry of embedded manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03060","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:f0a38bcdf471b0c0a56e90d0401101874bbc1d10aa6d125ece3ce8598a9f8b79","target":"record","created_at":"2026-05-18T00:08:30Z","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":"0fa6341fafc0beb6b0d949689a5677c87dba181f3e6680bb0996dd7b6cd3a437","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-09T08:54:01Z","title_canon_sha256":"44d989c05bc6a4e6d4e6cfc8c3cee1c593ccd8efe0b833c92cf806e680155405"},"schema_version":"1.0","source":{"id":"1808.03060","kind":"arxiv","version":1}},"canonical_sha256":"add8cbddcdf634521eca8b412deba717bc24deaf40fb1a4a4ed8f987349fb211","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"add8cbddcdf634521eca8b412deba717bc24deaf40fb1a4a4ed8f987349fb211","first_computed_at":"2026-05-18T00:08:30.299672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:30.299672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eb2ermjSqQGQ5tQz7FZlvsX2eQHrKl/Et9hVNcfiYZHR3p3OcuVLVCJQZ0mr6l6mcXU4mIn4FPez+zkFq0PtBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:30.300389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.03060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0a38bcdf471b0c0a56e90d0401101874bbc1d10aa6d125ece3ce8598a9f8b79","sha256:5b701b4ec69331d9a3c8dfc068bfdb2caafa87144001af370e575bac5539d204"],"state_sha256":"7b7dba6bf9401b4aa818e0c44a639aec0a96cde81f265dfd124c6e94445bcfda"}