{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZXDECZUSREOINJ3AXYLA5EXBGH","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":"866dde07f7e38ab7a579169575590ca24a996a9aae5b514c10171489014df01e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-05T17:08:38Z","title_canon_sha256":"15b8a7e3ca383f6315fe79d99640f841521e079487c48fa107456f59c4e292eb"},"schema_version":"1.0","source":{"id":"1811.01847","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01847","created_at":"2026-05-17T23:55:03Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01847v2","created_at":"2026-05-17T23:55:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01847","created_at":"2026-05-17T23:55:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZXDECZUSREOI","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZXDECZUSREOINJ3A","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZXDECZUS","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:ea53649e51b420dff2ff589d569e6c7942ca3e7d2a9aa225b287c86b5d655548","target":"graph","created_at":"2026-05-17T23:55:03Z","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 establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first-order systems and all second-order scalar operators. In particular, our general theorem provides a new proof of the rectifiability results for functions of bounded variations (BV) and functions of bounded deformation (BD). For divergence-free tensors we obtain refinements and new proofs of several known results on the rectifiability of varifolds and defect measures.","authors_text":"Adolfo Arroyo-Rabasa, Filip Rindler, Guido De Philippis, Jonas Hirsch","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-05T17:08:38Z","title":"Dimensional estimates and rectifiability for measures satisfying linear PDE constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01847","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":"sha256:22538a5b22665f00d44ccf46b8b3d0e60844182d4992378fb0313594af672fc0","target":"record","created_at":"2026-05-17T23:55:03Z","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":"866dde07f7e38ab7a579169575590ca24a996a9aae5b514c10171489014df01e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-05T17:08:38Z","title_canon_sha256":"15b8a7e3ca383f6315fe79d99640f841521e079487c48fa107456f59c4e292eb"},"schema_version":"1.0","source":{"id":"1811.01847","kind":"arxiv","version":2}},"canonical_sha256":"cdc6416692891c86a760be160e92e131cffe442ed75de14a0868545edf3c5000","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdc6416692891c86a760be160e92e131cffe442ed75de14a0868545edf3c5000","first_computed_at":"2026-05-17T23:55:03.154304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:03.154304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3AUeCb45+3LHk/7IXJvqU494nHjTsqPXaQa8dVgXb3yr67IKr84JCuZBaks8ZU0LfueBDJ+QArCeGs9l8aaAAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:03.154723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01847","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22538a5b22665f00d44ccf46b8b3d0e60844182d4992378fb0313594af672fc0","sha256:ea53649e51b420dff2ff589d569e6c7942ca3e7d2a9aa225b287c86b5d655548"],"state_sha256":"20dbbd5d6d317e1037667620abfeda662fb0ba3d5ac3bf53f2b907464a032207"}