{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZOTCFPV2IZYNZ3SGB57XVD34GK","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":"c6b636bb097305daf9d1db96901f07a2958f94275fba9fb9918b008bb886ff3c","cross_cats_sorted":["cond-mat.soft"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-06-28T14:52:00Z","title_canon_sha256":"192945ff1860ee9a1a65077c26cfb49f15b734cd81d942ba45c59234b83c1734"},"schema_version":"1.0","source":{"id":"1806.11018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.11018","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"arxiv_version","alias_value":"1806.11018v1","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.11018","created_at":"2026-05-18T00:12:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZOTCFPV2IZYN","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZOTCFPV2IZYNZ3SG","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZOTCFPV2","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:45bab5bf156d21380d17f6c0b9a8668ea56a9419b0fa882ff177f96b6a15eaa3","target":"graph","created_at":"2026-05-18T00:12:07Z","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":"These lectures focus on bifurcation analysis as a tool for studying phase transitions that occur in models of liquid-crystalline systems. We show how this approach bridges the gap between the phenomenological Landau theory and the --- often intractable --- full statistical mechanical treatment. Employing a `toy model' as a tutorial example the various ingredients of the technique are presented. Special attention is paid to the way in which one obtains information on the relation between the characteristics of the assumed interparticle interactions (shape, symmetry ...) and global properties of","authors_text":"Bela M. Mulder","cross_cats":["cond-mat.soft"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-06-28T14:52:00Z","title":"Bifurcation Analysis of Liquid Crystal Phase Transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11018","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:bf5553a56c62b7ba3550f8e08b2cd24a652bac44f1970be4ed77d710e1b6b72e","target":"record","created_at":"2026-05-18T00:12:07Z","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":"c6b636bb097305daf9d1db96901f07a2958f94275fba9fb9918b008bb886ff3c","cross_cats_sorted":["cond-mat.soft"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-06-28T14:52:00Z","title_canon_sha256":"192945ff1860ee9a1a65077c26cfb49f15b734cd81d942ba45c59234b83c1734"},"schema_version":"1.0","source":{"id":"1806.11018","kind":"arxiv","version":1}},"canonical_sha256":"cba622beba4670dcee460f7f7a8f7c32979bf7e0340fa22213dba8a4e93e15e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cba622beba4670dcee460f7f7a8f7c32979bf7e0340fa22213dba8a4e93e15e1","first_computed_at":"2026-05-18T00:12:07.237238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:07.237238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lc21jHD28yL+/CR7K9jXrxLfz1TshXS/DBDF706YP54U11mNYwoBHOsu6TEw9xsv5tyrQLudLYjjOvhp/s50Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:07.237723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.11018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf5553a56c62b7ba3550f8e08b2cd24a652bac44f1970be4ed77d710e1b6b72e","sha256:45bab5bf156d21380d17f6c0b9a8668ea56a9419b0fa882ff177f96b6a15eaa3"],"state_sha256":"311f8f56b8b6286d1a23769c2ff713e26d0d4f7f0d3ea3a7d983b848c62ac52b"}