{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:FEXCV7TZSCI4VRSU7GRUZ5MI22","short_pith_number":"pith:FEXCV7TZ","schema_version":"1.0","canonical_sha256":"292e2afe799091cac654f9a34cf588d6ac2b182cc0884972aebd0e2968f622e4","source":{"kind":"arxiv","id":"1806.00453","version":3},"attestation_state":"computed","paper":{"title":"Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Ivan I. Smalyukh, Jung-Shen B. Tai","submitted_at":"2018-06-01T17:20:04Z","abstract_excerpt":"Two-dimensional topological solitons, commonly called Skyrmions, are extensively studied in solid-state magnetic nanostructures and promise many spintronics applications. However, three-dimensional topological solitons dubbed hopfions have not been demonstrated as stable spatially localized structures in solid-state magnetic materials. Here we model the existence of such static solitons with different Hopf index values in noncentrosymmetric solid magnetic nanostructures with a perpendicular interfacial magnetic anisotropy. We show how this surface anisotropy, along with the Dzyaloshinskii-Mori"},"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":"1806.00453","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2018-06-01T17:20:04Z","cross_cats_sorted":[],"title_canon_sha256":"b6340fc27fa0ace6d78910342850a2019ff7246fae57aa0feac3ff48217a6134","abstract_canon_sha256":"838e6ea02043de7612a966d43ff89b8c945ea37732d235becb69e43023800a25"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:48.858263Z","signature_b64":"G2UQKTNqEBy0EVfP//HwutHQXxcJ6/pv3zGxQ2Ih1+IhafWYC8r9PXIO1DljXVKBYc07TQmzat7YJJKEzd0JAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"292e2afe799091cac654f9a34cf588d6ac2b182cc0884972aebd0e2968f622e4","last_reissued_at":"2026-05-18T00:01:48.857753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:48.857753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Ivan I. Smalyukh, Jung-Shen B. Tai","submitted_at":"2018-06-01T17:20:04Z","abstract_excerpt":"Two-dimensional topological solitons, commonly called Skyrmions, are extensively studied in solid-state magnetic nanostructures and promise many spintronics applications. However, three-dimensional topological solitons dubbed hopfions have not been demonstrated as stable spatially localized structures in solid-state magnetic materials. Here we model the existence of such static solitons with different Hopf index values in noncentrosymmetric solid magnetic nanostructures with a perpendicular interfacial magnetic anisotropy. We show how this surface anisotropy, along with the Dzyaloshinskii-Mori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00453","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":"1806.00453","created_at":"2026-05-18T00:01:48.857832+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.00453v3","created_at":"2026-05-18T00:01:48.857832+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00453","created_at":"2026-05-18T00:01:48.857832+00:00"},{"alias_kind":"pith_short_12","alias_value":"FEXCV7TZSCI4","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"FEXCV7TZSCI4VRSU","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"FEXCV7TZ","created_at":"2026-05-18T12:32:22.470017+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/FEXCV7TZSCI4VRSU7GRUZ5MI22","json":"https://pith.science/pith/FEXCV7TZSCI4VRSU7GRUZ5MI22.json","graph_json":"https://pith.science/api/pith-number/FEXCV7TZSCI4VRSU7GRUZ5MI22/graph.json","events_json":"https://pith.science/api/pith-number/FEXCV7TZSCI4VRSU7GRUZ5MI22/events.json","paper":"https://pith.science/paper/FEXCV7TZ"},"agent_actions":{"view_html":"https://pith.science/pith/FEXCV7TZSCI4VRSU7GRUZ5MI22","download_json":"https://pith.science/pith/FEXCV7TZSCI4VRSU7GRUZ5MI22.json","view_paper":"https://pith.science/paper/FEXCV7TZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.00453&json=true","fetch_graph":"https://pith.science/api/pith-number/FEXCV7TZSCI4VRSU7GRUZ5MI22/graph.json","fetch_events":"https://pith.science/api/pith-number/FEXCV7TZSCI4VRSU7GRUZ5MI22/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FEXCV7TZSCI4VRSU7GRUZ5MI22/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FEXCV7TZSCI4VRSU7GRUZ5MI22/action/storage_attestation","attest_author":"https://pith.science/pith/FEXCV7TZSCI4VRSU7GRUZ5MI22/action/author_attestation","sign_citation":"https://pith.science/pith/FEXCV7TZSCI4VRSU7GRUZ5MI22/action/citation_signature","submit_replication":"https://pith.science/pith/FEXCV7TZSCI4VRSU7GRUZ5MI22/action/replication_record"}},"created_at":"2026-05-18T00:01:48.857832+00:00","updated_at":"2026-05-18T00:01:48.857832+00:00"}