{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SAPS4544TQ53D7BVJSH6LWCFLA","short_pith_number":"pith:SAPS4544","canonical_record":{"source":{"id":"1305.4889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-21T17:15:30Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"91e89ee2b364d1b9bcfdfe91a689165a6e94b913174acb5169cecd9a0e21c8d9","abstract_canon_sha256":"67fe3cdd273018b47f0bd721ee09d08858545deb2736dafba482af9e3a8cf907"},"schema_version":"1.0"},"canonical_sha256":"901f2e779c9c3bb1fc354c8fe5d84558095e36342ce5125fa20ffeda13a25ae3","source":{"kind":"arxiv","id":"1305.4889","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4889","created_at":"2026-05-18T01:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4889v1","created_at":"2026-05-18T01:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4889","created_at":"2026-05-18T01:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"SAPS4544TQ53","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SAPS4544TQ53D7BV","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SAPS4544","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SAPS4544TQ53D7BVJSH6LWCFLA","target":"record","payload":{"canonical_record":{"source":{"id":"1305.4889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-21T17:15:30Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"91e89ee2b364d1b9bcfdfe91a689165a6e94b913174acb5169cecd9a0e21c8d9","abstract_canon_sha256":"67fe3cdd273018b47f0bd721ee09d08858545deb2736dafba482af9e3a8cf907"},"schema_version":"1.0"},"canonical_sha256":"901f2e779c9c3bb1fc354c8fe5d84558095e36342ce5125fa20ffeda13a25ae3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:48.314128Z","signature_b64":"Hr6GmWvtiAUOF9bg3uzHWDJFzCCSGvwhJwKFxjiVfSQlVlYY3nUkhYzcxWSgz86U5tC6jSOZ0VKmZVmf2sJIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"901f2e779c9c3bb1fc354c8fe5d84558095e36342ce5125fa20ffeda13a25ae3","last_reissued_at":"2026-05-18T01:49:48.313616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:48.313616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.4889","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":"2026-05-18T01:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/z8QXNxQJ1f9nOf5eKDW+S8VHbGGNPd6u8BIpKo5VWuaggn9r1Lg6WTya9YWu0BzS6JqDlJiuobSZtV6v9hAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:58:54.320246Z"},"content_sha256":"a7b532cdd927b4f2941d6fd4065df3925fe642718fb97627f01bdfaf6ff0195a","schema_version":"1.0","event_id":"sha256:a7b532cdd927b4f2941d6fd4065df3925fe642718fb97627f01bdfaf6ff0195a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SAPS4544TQ53D7BVJSH6LWCFLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From microscopic theory to macroscopic theory: a systematic study on static modeling for liquid crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Jiequn Han, Pingwen Zhang, Wei Wang, Yi Luo","submitted_at":"2013-05-21T17:15:30Z","abstract_excerpt":"In this paper, we propose a systematic way of liquid crystal modeling to build connection between microscopic theory and macroscopic theory. A new Q-tensor theory based on Onsager's molecular theory which leads to liquid crystals with certain shape has been proposed. Making uniaxial assumption, we can recover the Oseen-Frank theory from the derived $Q$-tensor theory, and the Oseen-Frank model coefficients can be examined. In addition, the smectic-A phase can also be characterized by the derived macroscopic model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4889","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":"2026-05-18T01:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G1JTTFNXyG3i/c7kHwiwY39HZmcO6OykZQ6Rl+gP1AbxizD+Dt0UUNFe/huc47jdElJFhEq3f2svS67BD0yODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:58:54.320955Z"},"content_sha256":"50b278cdd8f2a5ae7bdf78b3f3ae3126b9ef9555319e437dcab0834aeab2297f","schema_version":"1.0","event_id":"sha256:50b278cdd8f2a5ae7bdf78b3f3ae3126b9ef9555319e437dcab0834aeab2297f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SAPS4544TQ53D7BVJSH6LWCFLA/bundle.json","state_url":"https://pith.science/pith/SAPS4544TQ53D7BVJSH6LWCFLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SAPS4544TQ53D7BVJSH6LWCFLA/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":"2026-06-07T04:58:54Z","links":{"resolver":"https://pith.science/pith/SAPS4544TQ53D7BVJSH6LWCFLA","bundle":"https://pith.science/pith/SAPS4544TQ53D7BVJSH6LWCFLA/bundle.json","state":"https://pith.science/pith/SAPS4544TQ53D7BVJSH6LWCFLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SAPS4544TQ53D7BVJSH6LWCFLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SAPS4544TQ53D7BVJSH6LWCFLA","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":"67fe3cdd273018b47f0bd721ee09d08858545deb2736dafba482af9e3a8cf907","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-21T17:15:30Z","title_canon_sha256":"91e89ee2b364d1b9bcfdfe91a689165a6e94b913174acb5169cecd9a0e21c8d9"},"schema_version":"1.0","source":{"id":"1305.4889","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4889","created_at":"2026-05-18T01:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4889v1","created_at":"2026-05-18T01:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4889","created_at":"2026-05-18T01:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"SAPS4544TQ53","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SAPS4544TQ53D7BV","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SAPS4544","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:50b278cdd8f2a5ae7bdf78b3f3ae3126b9ef9555319e437dcab0834aeab2297f","target":"graph","created_at":"2026-05-18T01:49:48Z","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 propose a systematic way of liquid crystal modeling to build connection between microscopic theory and macroscopic theory. A new Q-tensor theory based on Onsager's molecular theory which leads to liquid crystals with certain shape has been proposed. Making uniaxial assumption, we can recover the Oseen-Frank theory from the derived $Q$-tensor theory, and the Oseen-Frank model coefficients can be examined. In addition, the smectic-A phase can also be characterized by the derived macroscopic model.","authors_text":"Jiequn Han, Pingwen Zhang, Wei Wang, Yi Luo","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-21T17:15:30Z","title":"From microscopic theory to macroscopic theory: a systematic study on static modeling for liquid crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4889","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:a7b532cdd927b4f2941d6fd4065df3925fe642718fb97627f01bdfaf6ff0195a","target":"record","created_at":"2026-05-18T01:49:48Z","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":"67fe3cdd273018b47f0bd721ee09d08858545deb2736dafba482af9e3a8cf907","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-21T17:15:30Z","title_canon_sha256":"91e89ee2b364d1b9bcfdfe91a689165a6e94b913174acb5169cecd9a0e21c8d9"},"schema_version":"1.0","source":{"id":"1305.4889","kind":"arxiv","version":1}},"canonical_sha256":"901f2e779c9c3bb1fc354c8fe5d84558095e36342ce5125fa20ffeda13a25ae3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"901f2e779c9c3bb1fc354c8fe5d84558095e36342ce5125fa20ffeda13a25ae3","first_computed_at":"2026-05-18T01:49:48.313616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:48.313616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hr6GmWvtiAUOF9bg3uzHWDJFzCCSGvwhJwKFxjiVfSQlVlYY3nUkhYzcxWSgz86U5tC6jSOZ0VKmZVmf2sJIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:48.314128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4889","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7b532cdd927b4f2941d6fd4065df3925fe642718fb97627f01bdfaf6ff0195a","sha256:50b278cdd8f2a5ae7bdf78b3f3ae3126b9ef9555319e437dcab0834aeab2297f"],"state_sha256":"4a49f2d2eec0d5eafa664d8feda261132f98364d5d7dc0ad960dba648525cb7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSDY3YPx6CZazkzQzNtZt6kgXeMlFpM1oE/pnoB3uZZe/LfwSu+XocnIHyxJtP+F7OS1wK9LNlOlAwd4olLSBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:58:54.324557Z","bundle_sha256":"6902a9bba85f9b3a309a9d4c0b595102ef8a5e274bc40515eb8bc397024cb954"}}