{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NIQUHWS2UN3N3CXQ4EEDSR7Q4S","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":"d1360baa099957e059d4ab30e3e2ba4c2410b51fdfe2134ae3e3345278c23af4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-31T13:45:41Z","title_canon_sha256":"48a4e6b6ee99115604361b554ef477f72ce3d2f17f2e0a67ab2c8fa944ed7d84"},"schema_version":"1.0","source":{"id":"1809.01034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.01034","created_at":"2026-05-18T00:06:31Z"},{"alias_kind":"arxiv_version","alias_value":"1809.01034v1","created_at":"2026-05-18T00:06:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01034","created_at":"2026-05-18T00:06:31Z"},{"alias_kind":"pith_short_12","alias_value":"NIQUHWS2UN3N","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NIQUHWS2UN3N3CXQ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NIQUHWS2","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:5143025551e3fa675bc9a0c330f6dfcb331970c59a6c6fc6b487cd81bf5a682a","target":"graph","created_at":"2026-05-18T00:06:31Z","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":"In this paper we describe domain walls appearing in a thin, nematic liquid crystal sample subject to an external field with intensity close to the Fr\\'eedericksz transition threshold. Using the gradient theory of the phase transition adopted to this situation, we show that depending on the parameters of the system, domain walls occur in the bistable region or at the border between the bistable and the monostable region.","authors_text":"Marcel G. Clerc, Michal Kowalczyk, Panayotis Smyrnelis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-31T13:45:41Z","title":"Gradient theory of domain walls in thin, nematic liquid crystals films"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01034","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":"sha256:3307e91ebee5802ca57a292f3c8e5c6ba650834e5eb8cb390940c19827187a09","target":"record","created_at":"2026-05-18T00:06:31Z","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":"d1360baa099957e059d4ab30e3e2ba4c2410b51fdfe2134ae3e3345278c23af4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-31T13:45:41Z","title_canon_sha256":"48a4e6b6ee99115604361b554ef477f72ce3d2f17f2e0a67ab2c8fa944ed7d84"},"schema_version":"1.0","source":{"id":"1809.01034","kind":"arxiv","version":1}},"canonical_sha256":"6a2143da5aa376dd8af0e1083947f0e48ac74ec3cb60b0a830a47c4b5fc95377","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a2143da5aa376dd8af0e1083947f0e48ac74ec3cb60b0a830a47c4b5fc95377","first_computed_at":"2026-05-18T00:06:31.873919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:31.873919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eWgYicFfQIu9zszrI4AMWhoEXzv/CMdLDrz9GHMhvl42GLjIv6d1OMG0uuRmRtV0CwKMyLHV4WyqeNDL8PmJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:31.874280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.01034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3307e91ebee5802ca57a292f3c8e5c6ba650834e5eb8cb390940c19827187a09","sha256:5143025551e3fa675bc9a0c330f6dfcb331970c59a6c6fc6b487cd81bf5a682a"],"state_sha256":"ad893ef6346061e0f68ae3e03cfac28214ecf8f47e5d37ce8e1dd4fae49d2d64"}