{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ABZ6PHP3PKJA7J2PGPIPMUVXDZ","short_pith_number":"pith:ABZ6PHP3","canonical_record":{"source":{"id":"1312.4471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-16T19:22:33Z","cross_cats_sorted":[],"title_canon_sha256":"f085df52fc6854f47ed5c5426d5b5f0ad1efc4f36fb06c094d510f2aa4ee6038","abstract_canon_sha256":"e3908590a383a2e75946e8e3c48d32b32fe0f8fe3cfea8fb1e982e3f62181297"},"schema_version":"1.0"},"canonical_sha256":"0073e79dfb7a920fa74f33d0f652b71e74e35cead234aa43852129c0c319f57c","source":{"kind":"arxiv","id":"1312.4471","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4471","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4471v1","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4471","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"ABZ6PHP3PKJA","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ABZ6PHP3PKJA7J2P","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ABZ6PHP3","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ABZ6PHP3PKJA7J2PGPIPMUVXDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-16T19:22:33Z","cross_cats_sorted":[],"title_canon_sha256":"f085df52fc6854f47ed5c5426d5b5f0ad1efc4f36fb06c094d510f2aa4ee6038","abstract_canon_sha256":"e3908590a383a2e75946e8e3c48d32b32fe0f8fe3cfea8fb1e982e3f62181297"},"schema_version":"1.0"},"canonical_sha256":"0073e79dfb7a920fa74f33d0f652b71e74e35cead234aa43852129c0c319f57c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:24.681923Z","signature_b64":"o0vHuFQUaINcvlfoZTFAK5uDjqh/vOtGusJTj7ykFgpQPSLoaxfYu6D7UtoNTbCf8KjMTFEGyy53jffuqxtQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0073e79dfb7a920fa74f33d0f652b71e74e35cead234aa43852129c0c319f57c","last_reissued_at":"2026-05-18T03:04:24.681133Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:24.681133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4471","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":"2026-05-18T03:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zHZp/xGEKEUbwxLI3yHkpb2vEP4FX2Iwh9AVR9F6BTZazj4boOqaWnkXCBq288LVmeBmhJCDzqICk5qUcC0wCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:38:44.348791Z"},"content_sha256":"216a0b6f1e03d470994cabd3d1e26fa043c80dd5cebba1e60acb88370ef2753e","schema_version":"1.0","event_id":"sha256:216a0b6f1e03d470994cabd3d1e26fa043c80dd5cebba1e60acb88370ef2753e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ABZ6PHP3PKJA7J2PGPIPMUVXDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partial regularity for minimizers of singular energy functionals, with application to liquid crystal models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hung Tran, Lawrence C. Evans, Olivier Kneuss","submitted_at":"2013-12-16T19:22:33Z","abstract_excerpt":"We study the partial regularity of minimizers for certain singular functionals in the calculus of variations, motivated by Ball and Majumdar's recent modification [BM] of the Landau-de Gennes energy functional."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4471","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":"2026-05-18T03:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DgWbg4GlG83B4zNkuASRZj7FXeD38Sr8NwH8oFeMBKXU4++eYxeGB7N0uEuMwZcFjb5nSY4RNiz0yPxTFhfTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:38:44.349129Z"},"content_sha256":"df6bcf8cc9e05efc9638528cca7614f1ed8745deb264b59869024086234d8590","schema_version":"1.0","event_id":"sha256:df6bcf8cc9e05efc9638528cca7614f1ed8745deb264b59869024086234d8590"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABZ6PHP3PKJA7J2PGPIPMUVXDZ/bundle.json","state_url":"https://pith.science/pith/ABZ6PHP3PKJA7J2PGPIPMUVXDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABZ6PHP3PKJA7J2PGPIPMUVXDZ/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":"2026-06-03T22:38:44Z","links":{"resolver":"https://pith.science/pith/ABZ6PHP3PKJA7J2PGPIPMUVXDZ","bundle":"https://pith.science/pith/ABZ6PHP3PKJA7J2PGPIPMUVXDZ/bundle.json","state":"https://pith.science/pith/ABZ6PHP3PKJA7J2PGPIPMUVXDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABZ6PHP3PKJA7J2PGPIPMUVXDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ABZ6PHP3PKJA7J2PGPIPMUVXDZ","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":"e3908590a383a2e75946e8e3c48d32b32fe0f8fe3cfea8fb1e982e3f62181297","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-16T19:22:33Z","title_canon_sha256":"f085df52fc6854f47ed5c5426d5b5f0ad1efc4f36fb06c094d510f2aa4ee6038"},"schema_version":"1.0","source":{"id":"1312.4471","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4471","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4471v1","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4471","created_at":"2026-05-18T03:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"ABZ6PHP3PKJA","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ABZ6PHP3PKJA7J2P","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ABZ6PHP3","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:df6bcf8cc9e05efc9638528cca7614f1ed8745deb264b59869024086234d8590","target":"graph","created_at":"2026-05-18T03:04:24Z","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 study the partial regularity of minimizers for certain singular functionals in the calculus of variations, motivated by Ball and Majumdar's recent modification [BM] of the Landau-de Gennes energy functional.","authors_text":"Hung Tran, Lawrence C. Evans, Olivier Kneuss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-16T19:22:33Z","title":"Partial regularity for minimizers of singular energy functionals, with application to liquid crystal models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4471","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":"sha256:216a0b6f1e03d470994cabd3d1e26fa043c80dd5cebba1e60acb88370ef2753e","target":"record","created_at":"2026-05-18T03:04:24Z","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":"e3908590a383a2e75946e8e3c48d32b32fe0f8fe3cfea8fb1e982e3f62181297","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-16T19:22:33Z","title_canon_sha256":"f085df52fc6854f47ed5c5426d5b5f0ad1efc4f36fb06c094d510f2aa4ee6038"},"schema_version":"1.0","source":{"id":"1312.4471","kind":"arxiv","version":1}},"canonical_sha256":"0073e79dfb7a920fa74f33d0f652b71e74e35cead234aa43852129c0c319f57c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0073e79dfb7a920fa74f33d0f652b71e74e35cead234aa43852129c0c319f57c","first_computed_at":"2026-05-18T03:04:24.681133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:24.681133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o0vHuFQUaINcvlfoZTFAK5uDjqh/vOtGusJTj7ykFgpQPSLoaxfYu6D7UtoNTbCf8KjMTFEGyy53jffuqxtQDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:24.681923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4471","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:216a0b6f1e03d470994cabd3d1e26fa043c80dd5cebba1e60acb88370ef2753e","sha256:df6bcf8cc9e05efc9638528cca7614f1ed8745deb264b59869024086234d8590"],"state_sha256":"a2df0216a10b8119f8a7e8c574e705eae8b7d2d9e8892fadaccf0378298c9b8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JfaSTcZT2piwvgH8QkkkdewdBlfL76gMyVwbp/Ff2Ue1lHQIvyTvojvd+aOPrU0xwiD2Rv9QzX0JPYGFcuRGBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T22:38:44.351148Z","bundle_sha256":"112e9966fbd427530ddbe24e9e8a7f3aed12546108b9f3e53089811ec0ba64be"}}