{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NL7IDPICDFWI72JPRH2HNRA4P7","short_pith_number":"pith:NL7IDPIC","canonical_record":{"source":{"id":"1606.06575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-21T14:00:52Z","cross_cats_sorted":[],"title_canon_sha256":"11ebf4e4e27f2099fcb52124c753ad6321cd3bf03c6c8ba5aa53ff3377ddab8f","abstract_canon_sha256":"aa88cece96bfeafbd9780a673f233305bde3277feb67eb425f80d9f07465785f"},"schema_version":"1.0"},"canonical_sha256":"6afe81bd02196c8fe92f89f476c41c7fea1fc7299d7e80074a922e5b2377fb4d","source":{"kind":"arxiv","id":"1606.06575","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06575","created_at":"2026-05-18T01:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06575v1","created_at":"2026-05-18T01:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06575","created_at":"2026-05-18T01:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"NL7IDPICDFWI","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NL7IDPICDFWI72JP","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NL7IDPIC","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NL7IDPICDFWI72JPRH2HNRA4P7","target":"record","payload":{"canonical_record":{"source":{"id":"1606.06575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-21T14:00:52Z","cross_cats_sorted":[],"title_canon_sha256":"11ebf4e4e27f2099fcb52124c753ad6321cd3bf03c6c8ba5aa53ff3377ddab8f","abstract_canon_sha256":"aa88cece96bfeafbd9780a673f233305bde3277feb67eb425f80d9f07465785f"},"schema_version":"1.0"},"canonical_sha256":"6afe81bd02196c8fe92f89f476c41c7fea1fc7299d7e80074a922e5b2377fb4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:09.192405Z","signature_b64":"yFYdn2FzzzzegdZwa7m/DeWOQnRn23nl53+sVTGZ+eTlFeBUaE2qVE0yw2pnEGgHZtYpInyQA8WuozPz0EOJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6afe81bd02196c8fe92f89f476c41c7fea1fc7299d7e80074a922e5b2377fb4d","last_reissued_at":"2026-05-18T01:12:09.191921Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:09.191921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.06575","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zbkPX9UcpcW9hiRwe2sXcLYoWbBURbT/JQmc+eahuhZ+e6GCRxClnwrHPt2mJAP2wbrUQ23yto1Lyk8Abd9pAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:08:05.938881Z"},"content_sha256":"3f955708c872c31522c0abf8e721be5457f54c3f4cf1dfe36d2a47a1e9c33b46","schema_version":"1.0","event_id":"sha256:3f955708c872c31522c0abf8e721be5457f54c3f4cf1dfe36d2a47a1e9c33b46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NL7IDPICDFWI72JPRH2HNRA4P7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Order Reconstruction for Nematics on Squares and Regular Polygons: A Landau-de Gennes Study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amy Spicer, Apala Majumdar, Giacomo Canevari","submitted_at":"2016-06-21T14:00:52Z","abstract_excerpt":"We construct an order reconstruction (OR)-type Landau-de Gennes critical point on a square domain of edge length $\\lambda$, motivated by the well order reconstruction solution numerically reported by Kralj and Majumdar. The OR critical point is distinguished by an uniaxial cross with negative scalar order parameter along the square diagonals. The OR critical point is defined in terms of a saddle-type critical point of an associated scalar variational problem. The OR-type critical point is globally stable for small $\\lambda$ and undergoes a supercritical pitchfork bifurcation in the associated "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06575","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Np4eftEhQQuUeLb9KoWo4J5Zk9Jqf7mkEvOBiRa8iAPaw2RbunQOz3R7EYSI7dW7XZOlFjXzPW6zw9WwgCKCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:08:05.939500Z"},"content_sha256":"d6b197ace2cd8c2d591d3bd3a7be6d732ef13d62dc377a5642f831de5a96d9a4","schema_version":"1.0","event_id":"sha256:d6b197ace2cd8c2d591d3bd3a7be6d732ef13d62dc377a5642f831de5a96d9a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NL7IDPICDFWI72JPRH2HNRA4P7/bundle.json","state_url":"https://pith.science/pith/NL7IDPICDFWI72JPRH2HNRA4P7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NL7IDPICDFWI72JPRH2HNRA4P7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T21:08:05Z","links":{"resolver":"https://pith.science/pith/NL7IDPICDFWI72JPRH2HNRA4P7","bundle":"https://pith.science/pith/NL7IDPICDFWI72JPRH2HNRA4P7/bundle.json","state":"https://pith.science/pith/NL7IDPICDFWI72JPRH2HNRA4P7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NL7IDPICDFWI72JPRH2HNRA4P7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NL7IDPICDFWI72JPRH2HNRA4P7","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":"aa88cece96bfeafbd9780a673f233305bde3277feb67eb425f80d9f07465785f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-21T14:00:52Z","title_canon_sha256":"11ebf4e4e27f2099fcb52124c753ad6321cd3bf03c6c8ba5aa53ff3377ddab8f"},"schema_version":"1.0","source":{"id":"1606.06575","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06575","created_at":"2026-05-18T01:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06575v1","created_at":"2026-05-18T01:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06575","created_at":"2026-05-18T01:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"NL7IDPICDFWI","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NL7IDPICDFWI72JP","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NL7IDPIC","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:d6b197ace2cd8c2d591d3bd3a7be6d732ef13d62dc377a5642f831de5a96d9a4","target":"graph","created_at":"2026-05-18T01:12:09Z","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 construct an order reconstruction (OR)-type Landau-de Gennes critical point on a square domain of edge length $\\lambda$, motivated by the well order reconstruction solution numerically reported by Kralj and Majumdar. The OR critical point is distinguished by an uniaxial cross with negative scalar order parameter along the square diagonals. The OR critical point is defined in terms of a saddle-type critical point of an associated scalar variational problem. The OR-type critical point is globally stable for small $\\lambda$ and undergoes a supercritical pitchfork bifurcation in the associated ","authors_text":"Amy Spicer, Apala Majumdar, Giacomo Canevari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-21T14:00:52Z","title":"Order Reconstruction for Nematics on Squares and Regular Polygons: A Landau-de Gennes Study"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06575","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":"sha256:3f955708c872c31522c0abf8e721be5457f54c3f4cf1dfe36d2a47a1e9c33b46","target":"record","created_at":"2026-05-18T01:12:09Z","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":"aa88cece96bfeafbd9780a673f233305bde3277feb67eb425f80d9f07465785f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-21T14:00:52Z","title_canon_sha256":"11ebf4e4e27f2099fcb52124c753ad6321cd3bf03c6c8ba5aa53ff3377ddab8f"},"schema_version":"1.0","source":{"id":"1606.06575","kind":"arxiv","version":1}},"canonical_sha256":"6afe81bd02196c8fe92f89f476c41c7fea1fc7299d7e80074a922e5b2377fb4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6afe81bd02196c8fe92f89f476c41c7fea1fc7299d7e80074a922e5b2377fb4d","first_computed_at":"2026-05-18T01:12:09.191921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:09.191921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yFYdn2FzzzzegdZwa7m/DeWOQnRn23nl53+sVTGZ+eTlFeBUaE2qVE0yw2pnEGgHZtYpInyQA8WuozPz0EOJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:09.192405Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06575","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f955708c872c31522c0abf8e721be5457f54c3f4cf1dfe36d2a47a1e9c33b46","sha256:d6b197ace2cd8c2d591d3bd3a7be6d732ef13d62dc377a5642f831de5a96d9a4"],"state_sha256":"4008cf98b47650084fa200238946befdbcc4308981ebb9bd6d8803232b1c0ec8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9nFGPuEbarqaeGKxAFSOvTYC1WHbEAn4PSoCDOHx/fuyitwwKM2ytMddEBWoO6ZnwJHn7/JVeIZftEPFv4VeCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:08:05.942040Z","bundle_sha256":"9f7838741001c967bb50031017075c1503055208070d6e6bc64bdf71d14dcb4a"}}