{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:R2WWL3VFEITYILZJWPCBOOFNWQ","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":"7a99cb5ddf505bff0212a4c9e1ce7c556219565bb4a0f718a641ec176eb8eadc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-12-03T10:33:58Z","title_canon_sha256":"634256d8a7f3f54f94b5e9d350da35d4a7b517599a33ce94275f075bf31ff4dc"},"schema_version":"1.0","source":{"id":"1112.0641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0641","created_at":"2026-05-18T03:53:20Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0641v1","created_at":"2026-05-18T03:53:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0641","created_at":"2026-05-18T03:53:20Z"},{"alias_kind":"pith_short_12","alias_value":"R2WWL3VFEITY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"R2WWL3VFEITYILZJ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"R2WWL3VF","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:25886075b1feab3bfc37976678bbd70a85cff2baee46b445a173bef7a76f692f","target":"graph","created_at":"2026-05-18T03:53:20Z","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 propose a continuum model to describe the molecular alignment in thin nematic shells. By contrast with previous accounts, the two-dimensional free energy, aimed at describing the physics of thin films of nematics deposited on curved substrates, is not postulated but it is deduced from the conventional three-dimensional theories of nematic liquid crystals. Both the director and the order-tensor theories are taken into account. The so-obtained surface energies exhibit extra terms compared to earlier models. These terms reflect the coupling of the geometry of the shell with the nematic order p","authors_text":"Gaetano Napoli, Luigi Vergori","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-12-03T10:33:58Z","title":"Surface free energies for nematic shells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0641","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":"sha256:4142ec265b34d755d987c48d4db24b0904ab7be052a77895eb49be34f6cbaa4a","target":"record","created_at":"2026-05-18T03:53:20Z","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":"7a99cb5ddf505bff0212a4c9e1ce7c556219565bb4a0f718a641ec176eb8eadc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2011-12-03T10:33:58Z","title_canon_sha256":"634256d8a7f3f54f94b5e9d350da35d4a7b517599a33ce94275f075bf31ff4dc"},"schema_version":"1.0","source":{"id":"1112.0641","kind":"arxiv","version":1}},"canonical_sha256":"8ead65eea52227842f29b3c41738adb4314b819a5ef5acb8aa769d8dcd15e703","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ead65eea52227842f29b3c41738adb4314b819a5ef5acb8aa769d8dcd15e703","first_computed_at":"2026-05-18T03:53:20.094609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:20.094609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xk985otJWIuYCVSwd1Fqlk1QTnr5q8XL9FHF6E+FTunRFu9ysAUuUWOFU1odRdOUPP6/TRdupGeVuN2tWBpbBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:20.095307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4142ec265b34d755d987c48d4db24b0904ab7be052a77895eb49be34f6cbaa4a","sha256:25886075b1feab3bfc37976678bbd70a85cff2baee46b445a173bef7a76f692f"],"state_sha256":"42b658589f970577935298bca661a6fdc0ecb1bdf24428008723c508819aaaaa"}