{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZTAXK22GNSNOSE5DDRH7BQGMT7","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":"3b7db9f142df5e747a0f41b4288f4783ec434766f15ec9b873e2bbafd037cebe","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-21T12:36:38Z","title_canon_sha256":"4b383198d33919a19295eedac55178bfa62f360f501ee4c19a71a700ef6503f5"},"schema_version":"1.0","source":{"id":"1608.01343","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01343","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01343v2","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01343","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZTAXK22GNSNO","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZTAXK22GNSNOSE5D","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZTAXK22G","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:3f41fdcc1af42c9fd434fd754cf6162ff60a8a7dd3938ec94588a4cbd67357c0","target":"graph","created_at":"2026-05-18T00:38:39Z","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 consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient-flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite-element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and ","authors_text":"Axel Voigt, Ingo Nitschke, Michael Nestler, Simon Praetorius","cross_cats":["cond-mat.soft","math-ph","math.MP","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-21T12:36:38Z","title":"Orientational order on surfaces - the coupling of topology, geometry, and dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01343","kind":"arxiv","version":2},"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:fcf585f8d2c4172b0835762b433fd011a6e9bc70b85f3ea8aa0897de76d5d27c","target":"record","created_at":"2026-05-18T00:38:39Z","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":"3b7db9f142df5e747a0f41b4288f4783ec434766f15ec9b873e2bbafd037cebe","cross_cats_sorted":["cond-mat.soft","math-ph","math.MP","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-07-21T12:36:38Z","title_canon_sha256":"4b383198d33919a19295eedac55178bfa62f360f501ee4c19a71a700ef6503f5"},"schema_version":"1.0","source":{"id":"1608.01343","kind":"arxiv","version":2}},"canonical_sha256":"ccc1756b466c9ae913a31c4ff0c0cc9fcf883f4ff8b941e9ccb904023d6776d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccc1756b466c9ae913a31c4ff0c0cc9fcf883f4ff8b941e9ccb904023d6776d4","first_computed_at":"2026-05-18T00:38:39.952484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:39.952484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZGNvTxwCIJ2OO9zxB1RAHZJhmZ8hf01wnimtTc8j3LqbaPchru6zMXKcJvQ5YUpX2GbVVEOM8je6Ue4oeSxCCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:39.952959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01343","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcf585f8d2c4172b0835762b433fd011a6e9bc70b85f3ea8aa0897de76d5d27c","sha256:3f41fdcc1af42c9fd434fd754cf6162ff60a8a7dd3938ec94588a4cbd67357c0"],"state_sha256":"a07ba50ed0dce3beb886605b0b0b2871888cd009c211999b6724ac4fe4c65b7d"}