{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:D3U6O5UVM3I5C3VMEZCOTPU6E7","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":"125152a1f836dc21502d4dafbd6de84b358ba1b7bae6b3f2a82c79d1ea495194","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-12T18:10:15Z","title_canon_sha256":"f6c9db5af3baeec7066b42c3b0c6e1f68d300a9e24cc2c465bc2e171fcf35d3b"},"schema_version":"1.0","source":{"id":"1411.3264","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3264","created_at":"2026-05-18T02:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3264v2","created_at":"2026-05-18T02:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3264","created_at":"2026-05-18T02:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"D3U6O5UVM3I5","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D3U6O5UVM3I5C3VM","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D3U6O5UV","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:5c1bc64e32b34ad5aa8bf1d842c707876c3c511ff363dae842aad6ecb4ba1526","target":"graph","created_at":"2026-05-18T02:32:45Z","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":"The paper is concerned with various issues surrounding the mathematical description of defects in models of liquid crystals, drawing on experience from solid mechanics. The roles played by a suitable choice of function space and by the growth properties of the free-energy density are highlighted. Models in which the director can jump across surfaces are formulated, and their relevance for nematic elastomers, order reconstruction and smectic A thin films discussed.","authors_text":"J. M. Ball, S. J. Bedford","cross_cats":["cond-mat.soft"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-12T18:10:15Z","title":"Discontinuous order parameters in liquid crystal theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3264","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":"sha256:410d272f0154f03450493221940fa6d9202b5f5578c9accbf20fbcf24ca0eaf8","target":"record","created_at":"2026-05-18T02:32:45Z","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":"125152a1f836dc21502d4dafbd6de84b358ba1b7bae6b3f2a82c79d1ea495194","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-12T18:10:15Z","title_canon_sha256":"f6c9db5af3baeec7066b42c3b0c6e1f68d300a9e24cc2c465bc2e171fcf35d3b"},"schema_version":"1.0","source":{"id":"1411.3264","kind":"arxiv","version":2}},"canonical_sha256":"1ee9e7769566d1d16eac2644e9be9e27e298b3981122b10ee38f301a3ff45bd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ee9e7769566d1d16eac2644e9be9e27e298b3981122b10ee38f301a3ff45bd9","first_computed_at":"2026-05-18T02:32:45.637241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:45.637241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q2jRp1ikHpcF+HgbGai8VjiWJXhlgrKzyCbPEW3BHEiVBhpeuCyhCTqDgVj6TRllHiemxuR0yYNBUXHsJ2p2Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:45.637820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3264","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:410d272f0154f03450493221940fa6d9202b5f5578c9accbf20fbcf24ca0eaf8","sha256:5c1bc64e32b34ad5aa8bf1d842c707876c3c511ff363dae842aad6ecb4ba1526"],"state_sha256":"fbb953da1a9bcbd7a06c4f9fb26cfa3e32628b2d05b01dc00babdc63535dcc99"}