{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:A7672NHOIG4YGHDNZA6XRVQT4Y","short_pith_number":"pith:A7672NHO","schema_version":"1.0","canonical_sha256":"07fdfd34ee41b9831c6dc83d78d613e60852e05849c7994b2f1cc589c39d78bc","source":{"kind":"arxiv","id":"1703.03263","version":3},"attestation_state":"computed","paper":{"title":"A topological lower bound for the energy of a unit vector field on a closed Euclidean hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Adriana V. Nicoli, Fabiano G. B. Brito, Icaro Gon\\c{c}alves","submitted_at":"2017-03-09T13:56:44Z","abstract_excerpt":"For a unit vector field on a closed immersed Euclidean hypersurface $M^{2n+1}$, $n\\geq 1$, we exhibit a nontrivial lower bound for its energy which depends on the degree of the Gauss map of the immersion. When the hypersurface is the unit sphere $\\mathbb{S}^{2n+1}$, immersed with degree one, this lower bound corresponds to a well established value from the literature. We introduce a list of functionals $\\mathcal{B}_k$ on a compact Riemannian manifold $M^{m}$, $1\\leq k\\leq m$, and show that, when the underlying manifold is a closed hypersurface, these functionals possess similar properties rega"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.03263","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-09T13:56:44Z","cross_cats_sorted":[],"title_canon_sha256":"d005a13a82714a15b2ff08e0a0c1d457d17615ba2335f7b509a1fb3016ff6cba","abstract_canon_sha256":"840e043b7fc7effe616da96e0f82497156e5ae9f7014f74e058aeeda10a29e89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:09.106809Z","signature_b64":"W/5BAtyh5Oj4vZjZjqMRnzGl/uA65SiBoS34ISbGGyjRte6nv4QaBEhArguvyuyCNiHa2kRl6aW9DyKBYsliDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07fdfd34ee41b9831c6dc83d78d613e60852e05849c7994b2f1cc589c39d78bc","last_reissued_at":"2026-05-18T00:23:09.106253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:09.106253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A topological lower bound for the energy of a unit vector field on a closed Euclidean hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Adriana V. Nicoli, Fabiano G. B. Brito, Icaro Gon\\c{c}alves","submitted_at":"2017-03-09T13:56:44Z","abstract_excerpt":"For a unit vector field on a closed immersed Euclidean hypersurface $M^{2n+1}$, $n\\geq 1$, we exhibit a nontrivial lower bound for its energy which depends on the degree of the Gauss map of the immersion. When the hypersurface is the unit sphere $\\mathbb{S}^{2n+1}$, immersed with degree one, this lower bound corresponds to a well established value from the literature. We introduce a list of functionals $\\mathcal{B}_k$ on a compact Riemannian manifold $M^{m}$, $1\\leq k\\leq m$, and show that, when the underlying manifold is a closed hypersurface, these functionals possess similar properties rega"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03263","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.03263","created_at":"2026-05-18T00:23:09.106346+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.03263v3","created_at":"2026-05-18T00:23:09.106346+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03263","created_at":"2026-05-18T00:23:09.106346+00:00"},{"alias_kind":"pith_short_12","alias_value":"A7672NHOIG4Y","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"A7672NHOIG4YGHDN","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"A7672NHO","created_at":"2026-05-18T12:31:05.417338+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A7672NHOIG4YGHDNZA6XRVQT4Y","json":"https://pith.science/pith/A7672NHOIG4YGHDNZA6XRVQT4Y.json","graph_json":"https://pith.science/api/pith-number/A7672NHOIG4YGHDNZA6XRVQT4Y/graph.json","events_json":"https://pith.science/api/pith-number/A7672NHOIG4YGHDNZA6XRVQT4Y/events.json","paper":"https://pith.science/paper/A7672NHO"},"agent_actions":{"view_html":"https://pith.science/pith/A7672NHOIG4YGHDNZA6XRVQT4Y","download_json":"https://pith.science/pith/A7672NHOIG4YGHDNZA6XRVQT4Y.json","view_paper":"https://pith.science/paper/A7672NHO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.03263&json=true","fetch_graph":"https://pith.science/api/pith-number/A7672NHOIG4YGHDNZA6XRVQT4Y/graph.json","fetch_events":"https://pith.science/api/pith-number/A7672NHOIG4YGHDNZA6XRVQT4Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A7672NHOIG4YGHDNZA6XRVQT4Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A7672NHOIG4YGHDNZA6XRVQT4Y/action/storage_attestation","attest_author":"https://pith.science/pith/A7672NHOIG4YGHDNZA6XRVQT4Y/action/author_attestation","sign_citation":"https://pith.science/pith/A7672NHOIG4YGHDNZA6XRVQT4Y/action/citation_signature","submit_replication":"https://pith.science/pith/A7672NHOIG4YGHDNZA6XRVQT4Y/action/replication_record"}},"created_at":"2026-05-18T00:23:09.106346+00:00","updated_at":"2026-05-18T00:23:09.106346+00:00"}