{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7T5QSQJWILSVN26FWFQK77NEJJ","short_pith_number":"pith:7T5QSQJW","canonical_record":{"source":{"id":"1403.7608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-29T09:10:13Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"64bc5105f51257a990b1d7c59bc5955ee141f7fd398a166fb67607db1643d194","abstract_canon_sha256":"10f579cebc39be4ecb414ff65872c03a8d71ae9be0db33af84aa794ffe8c1dac"},"schema_version":"1.0"},"canonical_sha256":"fcfb09413642e556ebc5b160affda44a484d22bc928a0830c30429708a055a5a","source":{"kind":"arxiv","id":"1403.7608","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7608","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7608v1","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7608","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"pith_short_12","alias_value":"7T5QSQJWILSV","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7T5QSQJWILSVN26F","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7T5QSQJW","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7T5QSQJWILSVN26FWFQK77NEJJ","target":"record","payload":{"canonical_record":{"source":{"id":"1403.7608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-29T09:10:13Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"64bc5105f51257a990b1d7c59bc5955ee141f7fd398a166fb67607db1643d194","abstract_canon_sha256":"10f579cebc39be4ecb414ff65872c03a8d71ae9be0db33af84aa794ffe8c1dac"},"schema_version":"1.0"},"canonical_sha256":"fcfb09413642e556ebc5b160affda44a484d22bc928a0830c30429708a055a5a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:19.020324Z","signature_b64":"qg9HQPkfh53fAAcF/Ts/DZuo1rJc3yDuqdIy5CmkkXoiM4amGqNI4rDfbS20siM5jLMjItFIVw5VvektSknrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcfb09413642e556ebc5b160affda44a484d22bc928a0830c30429708a055a5a","last_reissued_at":"2026-05-18T02:55:19.019908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:19.019908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.7608","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":"2026-05-18T02:55:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7n90pTYD/QQ8WUS1CNl4q20lMP/bLRnd3cbrLjfGopCeVy99c3NVlHTLTmj0ooR/yQkyAxjFp4fqIedmAXOBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:17:07.586063Z"},"content_sha256":"40c8b7958fc1e9b64062fdd74f2f288103d258a5bd74a8d01ebfe87aee4b360d","schema_version":"1.0","event_id":"sha256:40c8b7958fc1e9b64062fdd74f2f288103d258a5bd74a8d01ebfe87aee4b360d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7T5QSQJWILSVN26FWFQK77NEJJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Density estimates for vector minimizers and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Giorgio Fusco, Nicholas D. Alikakos","submitted_at":"2014-03-29T09:10:13Z","abstract_excerpt":"We extend the Caffarelli-Cordoba estimates to the vector case in two ways, one of which has no scalar counterpart, and we give a few applications for minimal solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7608","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":"2026-05-18T02:55:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sXeyAj7VIoBhu6rSWNWXovnup5Dd+FuHfTbjrETplpZzhEMncEuvDaaloyYpYE9m+2PGPlfNhGx9OD/xraAZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:17:07.586429Z"},"content_sha256":"c83f710c13c488ac32c96e030a127eeed962e9ef251e7f7a3eba2fb607e1d91f","schema_version":"1.0","event_id":"sha256:c83f710c13c488ac32c96e030a127eeed962e9ef251e7f7a3eba2fb607e1d91f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7T5QSQJWILSVN26FWFQK77NEJJ/bundle.json","state_url":"https://pith.science/pith/7T5QSQJWILSVN26FWFQK77NEJJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7T5QSQJWILSVN26FWFQK77NEJJ/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":"2026-06-23T21:17:07Z","links":{"resolver":"https://pith.science/pith/7T5QSQJWILSVN26FWFQK77NEJJ","bundle":"https://pith.science/pith/7T5QSQJWILSVN26FWFQK77NEJJ/bundle.json","state":"https://pith.science/pith/7T5QSQJWILSVN26FWFQK77NEJJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7T5QSQJWILSVN26FWFQK77NEJJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7T5QSQJWILSVN26FWFQK77NEJJ","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":"10f579cebc39be4ecb414ff65872c03a8d71ae9be0db33af84aa794ffe8c1dac","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-29T09:10:13Z","title_canon_sha256":"64bc5105f51257a990b1d7c59bc5955ee141f7fd398a166fb67607db1643d194"},"schema_version":"1.0","source":{"id":"1403.7608","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7608","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7608v1","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7608","created_at":"2026-05-18T02:55:19Z"},{"alias_kind":"pith_short_12","alias_value":"7T5QSQJWILSV","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7T5QSQJWILSVN26F","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7T5QSQJW","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:c83f710c13c488ac32c96e030a127eeed962e9ef251e7f7a3eba2fb607e1d91f","target":"graph","created_at":"2026-05-18T02:55:19Z","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 extend the Caffarelli-Cordoba estimates to the vector case in two ways, one of which has no scalar counterpart, and we give a few applications for minimal solutions.","authors_text":"Giorgio Fusco, Nicholas D. Alikakos","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-29T09:10:13Z","title":"Density estimates for vector minimizers and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7608","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":"sha256:40c8b7958fc1e9b64062fdd74f2f288103d258a5bd74a8d01ebfe87aee4b360d","target":"record","created_at":"2026-05-18T02:55:19Z","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":"10f579cebc39be4ecb414ff65872c03a8d71ae9be0db33af84aa794ffe8c1dac","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-29T09:10:13Z","title_canon_sha256":"64bc5105f51257a990b1d7c59bc5955ee141f7fd398a166fb67607db1643d194"},"schema_version":"1.0","source":{"id":"1403.7608","kind":"arxiv","version":1}},"canonical_sha256":"fcfb09413642e556ebc5b160affda44a484d22bc928a0830c30429708a055a5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcfb09413642e556ebc5b160affda44a484d22bc928a0830c30429708a055a5a","first_computed_at":"2026-05-18T02:55:19.019908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:19.019908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qg9HQPkfh53fAAcF/Ts/DZuo1rJc3yDuqdIy5CmkkXoiM4amGqNI4rDfbS20siM5jLMjItFIVw5VvektSknrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:19.020324Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7608","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40c8b7958fc1e9b64062fdd74f2f288103d258a5bd74a8d01ebfe87aee4b360d","sha256:c83f710c13c488ac32c96e030a127eeed962e9ef251e7f7a3eba2fb607e1d91f"],"state_sha256":"b12e2f1cc6ba605c8551b3af7ca31df93aea0be773762a73a4b5a10f30d9b8bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z17vz/AmFmYTcY9i/hpytaT8AokfU0qRmwJLiG1UbT8xg/Au1sqA7BcLrs/qYvA+rok6qSy11yDkagYjyECNDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:17:07.588406Z","bundle_sha256":"577009ee782aa3ecaa2dad281090105bc579ee82bc2b3602484677f9bee3e0e4"}}