{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:I4F3BVMORV64LWYLDYGVYOQT6T","short_pith_number":"pith:I4F3BVMO","canonical_record":{"source":{"id":"2403.20274","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-29T16:29:07Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"0d912dfc9f53c0feab9ec189f73341bfbbf9e6b2e53869228a6f10c4c4139056","abstract_canon_sha256":"525c9b15a6956b81cef1f44f6f1af07213fbea653ef34a2038cc061f4393a88e"},"schema_version":"1.0"},"canonical_sha256":"470bb0d58e8d7dc5db0b1e0d5c3a13f4c28e843aff714f37029afd08777ffc81","source":{"kind":"arxiv","id":"2403.20274","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.20274","created_at":"2026-07-05T09:28:48Z"},{"alias_kind":"arxiv_version","alias_value":"2403.20274v2","created_at":"2026-07-05T09:28:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.20274","created_at":"2026-07-05T09:28:48Z"},{"alias_kind":"pith_short_12","alias_value":"I4F3BVMORV64","created_at":"2026-07-05T09:28:48Z"},{"alias_kind":"pith_short_16","alias_value":"I4F3BVMORV64LWYL","created_at":"2026-07-05T09:28:48Z"},{"alias_kind":"pith_short_8","alias_value":"I4F3BVMO","created_at":"2026-07-05T09:28:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:I4F3BVMORV64LWYLDYGVYOQT6T","target":"record","payload":{"canonical_record":{"source":{"id":"2403.20274","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-29T16:29:07Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"0d912dfc9f53c0feab9ec189f73341bfbbf9e6b2e53869228a6f10c4c4139056","abstract_canon_sha256":"525c9b15a6956b81cef1f44f6f1af07213fbea653ef34a2038cc061f4393a88e"},"schema_version":"1.0"},"canonical_sha256":"470bb0d58e8d7dc5db0b1e0d5c3a13f4c28e843aff714f37029afd08777ffc81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:28:48.818340Z","signature_b64":"GnrixDsgSfUqk+z+bx9SZq2rswUKz2+X2k+eJXfVQLxLTgONQZKACu+VqXYd97IqIW2dk+30SWwP6s/OgVjZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"470bb0d58e8d7dc5db0b1e0d5c3a13f4c28e843aff714f37029afd08777ffc81","last_reissued_at":"2026-07-05T09:28:48.817799Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:28:48.817799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.20274","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:28:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Be8wOJrPJZtWHZx7UDkbsM85XC9XpI9dRvL9u8ZcwBDtFRmku7Qw9ZFXEwPltvz4pTZGbYvIbZ3rNFHvd2myBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T13:09:14.508422Z"},"content_sha256":"e9751e1bbb906a1fd7f0a9cb3894dfd12049b66218638935ddfb3852dae63094","schema_version":"1.0","event_id":"sha256:e9751e1bbb906a1fd7f0a9cb3894dfd12049b66218638935ddfb3852dae63094"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:I4F3BVMORV64LWYLDYGVYOQT6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical Particle in Nematic Liquid Crystal with a Magnetic Field and Planar Anchoring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Dean Louizos, Dominik Stantejsky, Lia Bronsard","submitted_at":"2024-03-29T16:29:07Z","abstract_excerpt":"We study minimizers of the Landau-de Gennes energy in $\\mathbb{R}^3\\setminus B_1(0)$ with external magnetic field in the large particle limit. We impose strong tangential anchoring and uniaxiality of the $Q-$tensor on the boundary. We derive a lower bound for the energy in terms of the boundary condition and show in the extreme cases of strong and weak magnetic field strength that the longitudinal director field is energy minimizing, indicating the presence of two half-point defects, so called boojums, at two opposite points of the sphere. Using a recovery sequence, we show that the energy bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.20274","kind":"arxiv","version":2},"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/2403.20274/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":"2026-07-05T09:28:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2YINSuKbiDqNOAsssQK5YN0ef7E5tyLckWhT0E1xxQ11LpzSqeqsnszZxxbawn5ZetFvWVYkzAmARiRwle7JDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T13:09:14.508800Z"},"content_sha256":"65df9078724eb5d0a10f1dd4d6852b3bfbf285de12b5bcce804c4f5b0708d93c","schema_version":"1.0","event_id":"sha256:65df9078724eb5d0a10f1dd4d6852b3bfbf285de12b5bcce804c4f5b0708d93c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4F3BVMORV64LWYLDYGVYOQT6T/bundle.json","state_url":"https://pith.science/pith/I4F3BVMORV64LWYLDYGVYOQT6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4F3BVMORV64LWYLDYGVYOQT6T/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":"2026-07-06T13:09:14Z","links":{"resolver":"https://pith.science/pith/I4F3BVMORV64LWYLDYGVYOQT6T","bundle":"https://pith.science/pith/I4F3BVMORV64LWYLDYGVYOQT6T/bundle.json","state":"https://pith.science/pith/I4F3BVMORV64LWYLDYGVYOQT6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4F3BVMORV64LWYLDYGVYOQT6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:I4F3BVMORV64LWYLDYGVYOQT6T","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":"525c9b15a6956b81cef1f44f6f1af07213fbea653ef34a2038cc061f4393a88e","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-29T16:29:07Z","title_canon_sha256":"0d912dfc9f53c0feab9ec189f73341bfbbf9e6b2e53869228a6f10c4c4139056"},"schema_version":"1.0","source":{"id":"2403.20274","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.20274","created_at":"2026-07-05T09:28:48Z"},{"alias_kind":"arxiv_version","alias_value":"2403.20274v2","created_at":"2026-07-05T09:28:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.20274","created_at":"2026-07-05T09:28:48Z"},{"alias_kind":"pith_short_12","alias_value":"I4F3BVMORV64","created_at":"2026-07-05T09:28:48Z"},{"alias_kind":"pith_short_16","alias_value":"I4F3BVMORV64LWYL","created_at":"2026-07-05T09:28:48Z"},{"alias_kind":"pith_short_8","alias_value":"I4F3BVMO","created_at":"2026-07-05T09:28:48Z"}],"graph_snapshots":[{"event_id":"sha256:65df9078724eb5d0a10f1dd4d6852b3bfbf285de12b5bcce804c4f5b0708d93c","target":"graph","created_at":"2026-07-05T09:28:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.20274/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study minimizers of the Landau-de Gennes energy in $\\mathbb{R}^3\\setminus B_1(0)$ with external magnetic field in the large particle limit. We impose strong tangential anchoring and uniaxiality of the $Q-$tensor on the boundary. We derive a lower bound for the energy in terms of the boundary condition and show in the extreme cases of strong and weak magnetic field strength that the longitudinal director field is energy minimizing, indicating the presence of two half-point defects, so called boojums, at two opposite points of the sphere. Using a recovery sequence, we show that the energy bou","authors_text":"Dean Louizos, Dominik Stantejsky, Lia Bronsard","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-29T16:29:07Z","title":"Spherical Particle in Nematic Liquid Crystal with a Magnetic Field and Planar Anchoring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.20274","kind":"arxiv","version":2},"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:e9751e1bbb906a1fd7f0a9cb3894dfd12049b66218638935ddfb3852dae63094","target":"record","created_at":"2026-07-05T09:28:48Z","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":"525c9b15a6956b81cef1f44f6f1af07213fbea653ef34a2038cc061f4393a88e","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-29T16:29:07Z","title_canon_sha256":"0d912dfc9f53c0feab9ec189f73341bfbbf9e6b2e53869228a6f10c4c4139056"},"schema_version":"1.0","source":{"id":"2403.20274","kind":"arxiv","version":2}},"canonical_sha256":"470bb0d58e8d7dc5db0b1e0d5c3a13f4c28e843aff714f37029afd08777ffc81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"470bb0d58e8d7dc5db0b1e0d5c3a13f4c28e843aff714f37029afd08777ffc81","first_computed_at":"2026-07-05T09:28:48.817799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:28:48.817799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GnrixDsgSfUqk+z+bx9SZq2rswUKz2+X2k+eJXfVQLxLTgONQZKACu+VqXYd97IqIW2dk+30SWwP6s/OgVjZCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:28:48.818340Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.20274","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9751e1bbb906a1fd7f0a9cb3894dfd12049b66218638935ddfb3852dae63094","sha256:65df9078724eb5d0a10f1dd4d6852b3bfbf285de12b5bcce804c4f5b0708d93c"],"state_sha256":"62ebef46dd2c0f525c952b8856e874d11b563166e5ddeb6b60dfebcbb6e35bb4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"so6RWwTtQQqJYisEFyT5+X4PfAvtwv78b+V9JlEkSb0bLaFGtGCOY4NECdV5EzhdpeN6TGFmpt8g44QBc7sgAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T13:09:14.510787Z","bundle_sha256":"236fe6fbdce38d5b473f5ba3f3c0cd848c7d3573eba44cd2acfe7353f05fcf7f"}}