{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7SJPBP7YD3G4LETMWUF4Q25IQ4","short_pith_number":"pith:7SJPBP7Y","canonical_record":{"source":{"id":"2608.04908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-05T14:35:42Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"8b20ddd39d0edde5763e3604ba616ca7d3f5513161227a9be9742dd6af0edc0b","abstract_canon_sha256":"3d6c3940500dbfa4533dc97e097af8b9f156ba8511967fd58aa3734a241b3ddd"},"schema_version":"1.0"},"canonical_sha256":"fc92f0bff81ecdc5926cb50bc86ba8871a3073ae980ece7c1f9089a714b7329d","source":{"kind":"arxiv","id":"2608.04908","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04908","created_at":"2026-08-06T01:47:40Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04908v1","created_at":"2026-08-06T01:47:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04908","created_at":"2026-08-06T01:47:40Z"},{"alias_kind":"pith_short_12","alias_value":"7SJPBP7YD3G4","created_at":"2026-08-06T01:47:40Z"},{"alias_kind":"pith_short_16","alias_value":"7SJPBP7YD3G4LETM","created_at":"2026-08-06T01:47:40Z"},{"alias_kind":"pith_short_8","alias_value":"7SJPBP7Y","created_at":"2026-08-06T01:47:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7SJPBP7YD3G4LETMWUF4Q25IQ4","target":"record","payload":{"canonical_record":{"source":{"id":"2608.04908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-05T14:35:42Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"8b20ddd39d0edde5763e3604ba616ca7d3f5513161227a9be9742dd6af0edc0b","abstract_canon_sha256":"3d6c3940500dbfa4533dc97e097af8b9f156ba8511967fd58aa3734a241b3ddd"},"schema_version":"1.0"},"canonical_sha256":"fc92f0bff81ecdc5926cb50bc86ba8871a3073ae980ece7c1f9089a714b7329d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:47:40.839830Z","signature_b64":"u3NzZlkqfGXQdnXI2CWc8hCbOpsF0a+nucTecqPRPPjDWEla5nbwRCtcMxq2qwkJfh6u8Zbb073CoE7kuQ5mAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc92f0bff81ecdc5926cb50bc86ba8871a3073ae980ece7c1f9089a714b7329d","last_reissued_at":"2026-08-06T01:47:40.838410Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:47:40.838410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.04908","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":"2026-08-06T01:47:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8DE0dJOZQ8FzdalNyQHqp4p46znuOSGiXjyHeY5Uf1cexekpO1ONW87JyLd+8CVaPTrnclnIzzNN3ENZ2A6NBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T03:23:37.414179Z"},"content_sha256":"f41661934684defbd936a2ecc0662601b13d8bf23953158002a4d16e32ab0e77","schema_version":"1.0","event_id":"sha256:f41661934684defbd936a2ecc0662601b13d8bf23953158002a4d16e32ab0e77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7SJPBP7YD3G4LETMWUF4Q25IQ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the absence of point defects in biaxial Landau--de Gennes models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.AP","authors_text":"Haotong Fu, Huaijie Wang, Wei Wang, Zhifei Zhang","submitted_at":"2026-08-05T14:35:42Z","abstract_excerpt":"We study local minimizers of a sextic-potential Landau--de Gennes energy for nematic liquid crystals in the small-elastic-constant limit. Under the uniform energy and $L^\\infty$ bounds, these minimizers converge to a locally energy-minimizing harmonic map $\\mathbf{Q}_0$ into a biaxial vacuum manifold. The main result of this paper is that such a limiting map $\\mathbf{Q}_0$ has no interior point singularities. The proof relies on a geometric identification of the lifted Frobenius metric on the universal cover $\\mathbb{S}^3$ with a rescaled Berger metric. For a hypothetical tangent cone at a poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04908","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.04908/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-06T01:47:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u6EKf0aOmgBFJzNhBzGtlO9rM7yU5l7fEUoQCSBZR0GPo+eksg3Sq7J8RagoB6zqXsn7+q2fI8o8vbQ2uZcGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T03:23:37.415092Z"},"content_sha256":"2f44cd370d5f6f352eca19160aa58676efe6a28640458688dd9b975afa5bcfeb","schema_version":"1.0","event_id":"sha256:2f44cd370d5f6f352eca19160aa58676efe6a28640458688dd9b975afa5bcfeb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SJPBP7YD3G4LETMWUF4Q25IQ4/bundle.json","state_url":"https://pith.science/pith/7SJPBP7YD3G4LETMWUF4Q25IQ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SJPBP7YD3G4LETMWUF4Q25IQ4/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":"2026-08-19T03:23:37Z","links":{"resolver":"https://pith.science/pith/7SJPBP7YD3G4LETMWUF4Q25IQ4","bundle":"https://pith.science/pith/7SJPBP7YD3G4LETMWUF4Q25IQ4/bundle.json","state":"https://pith.science/pith/7SJPBP7YD3G4LETMWUF4Q25IQ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SJPBP7YD3G4LETMWUF4Q25IQ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7SJPBP7YD3G4LETMWUF4Q25IQ4","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":"3d6c3940500dbfa4533dc97e097af8b9f156ba8511967fd58aa3734a241b3ddd","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-05T14:35:42Z","title_canon_sha256":"8b20ddd39d0edde5763e3604ba616ca7d3f5513161227a9be9742dd6af0edc0b"},"schema_version":"1.0","source":{"id":"2608.04908","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04908","created_at":"2026-08-06T01:47:40Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04908v1","created_at":"2026-08-06T01:47:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04908","created_at":"2026-08-06T01:47:40Z"},{"alias_kind":"pith_short_12","alias_value":"7SJPBP7YD3G4","created_at":"2026-08-06T01:47:40Z"},{"alias_kind":"pith_short_16","alias_value":"7SJPBP7YD3G4LETM","created_at":"2026-08-06T01:47:40Z"},{"alias_kind":"pith_short_8","alias_value":"7SJPBP7Y","created_at":"2026-08-06T01:47:40Z"}],"graph_snapshots":[{"event_id":"sha256:2f44cd370d5f6f352eca19160aa58676efe6a28640458688dd9b975afa5bcfeb","target":"graph","created_at":"2026-08-06T01:47:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.04908/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study local minimizers of a sextic-potential Landau--de Gennes energy for nematic liquid crystals in the small-elastic-constant limit. Under the uniform energy and $L^\\infty$ bounds, these minimizers converge to a locally energy-minimizing harmonic map $\\mathbf{Q}_0$ into a biaxial vacuum manifold. The main result of this paper is that such a limiting map $\\mathbf{Q}_0$ has no interior point singularities. The proof relies on a geometric identification of the lifted Frobenius metric on the universal cover $\\mathbb{S}^3$ with a rescaled Berger metric. For a hypothetical tangent cone at a poi","authors_text":"Haotong Fu, Huaijie Wang, Wei Wang, Zhifei Zhang","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-05T14:35:42Z","title":"On the absence of point defects in biaxial Landau--de Gennes models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04908","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:f41661934684defbd936a2ecc0662601b13d8bf23953158002a4d16e32ab0e77","target":"record","created_at":"2026-08-06T01:47:40Z","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":"3d6c3940500dbfa4533dc97e097af8b9f156ba8511967fd58aa3734a241b3ddd","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-05T14:35:42Z","title_canon_sha256":"8b20ddd39d0edde5763e3604ba616ca7d3f5513161227a9be9742dd6af0edc0b"},"schema_version":"1.0","source":{"id":"2608.04908","kind":"arxiv","version":1}},"canonical_sha256":"fc92f0bff81ecdc5926cb50bc86ba8871a3073ae980ece7c1f9089a714b7329d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc92f0bff81ecdc5926cb50bc86ba8871a3073ae980ece7c1f9089a714b7329d","first_computed_at":"2026-08-06T01:47:40.838410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-06T01:47:40.838410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u3NzZlkqfGXQdnXI2CWc8hCbOpsF0a+nucTecqPRPPjDWEla5nbwRCtcMxq2qwkJfh6u8Zbb073CoE7kuQ5mAA==","signature_status":"signed_v1","signed_at":"2026-08-06T01:47:40.839830Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.04908","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f41661934684defbd936a2ecc0662601b13d8bf23953158002a4d16e32ab0e77","sha256:2f44cd370d5f6f352eca19160aa58676efe6a28640458688dd9b975afa5bcfeb"],"state_sha256":"e55bdc210f1baed94bb534007e408b7976917baace25225c63eb2ae4b19d0d87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"447dH/DR6zwntCyUnz2X9qyjOBu7W8UWe1hbRZllj4UQTt36hiFU450vr6KQDl4BXWxPw59uvXXPCtAF0umiDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T03:23:37.420766Z","bundle_sha256":"0780eb00568b1da05a062cecdc3ee137c4d7586d6141d641c5bb0d10d3d30305"}}