{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DD2HGY7BMAAL7MBTQDWM6TANXJ","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":"8d5d48831e7b73ce41d21ad3dee88d939daf43a90907e81bd9fbd9d0da62e0d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-11T13:54:05Z","title_canon_sha256":"e2024f627e793c08a73ee97cc0ab68e661bfbcd89965d451f833c2fc93124c48"},"schema_version":"1.0","source":{"id":"1903.04302","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04302","created_at":"2026-05-17T23:51:21Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04302v2","created_at":"2026-05-17T23:51:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04302","created_at":"2026-05-17T23:51:21Z"},{"alias_kind":"pith_short_12","alias_value":"DD2HGY7BMAAL","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DD2HGY7BMAAL7MBT","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DD2HGY7B","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:2b9a53896851ed023bcb8773a2f0fb444ede90761db12049f1fd479fdf0070a5","target":"graph","created_at":"2026-05-17T23:51:21Z","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":"In the existing language for tensor calculus on RCD spaces, tensor fields are only defined m-a.e.. In this paper we introduce the concept of tensor field defined `2-capacity-a.e.' and discuss in which sense Sobolev vector fields have a 2-capacity-a.e. uniquely defined quasi-continuous representative.","authors_text":"Cl\\'ement Debin, Enrico Pasqualetto, Nicola Gigli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-11T13:54:05Z","title":"Quasi-continuous vector fields on RCD spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04302","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":"sha256:5dba671d9737157c758888ceba15e37627b25dd924333ac50e63a2546e3df2bf","target":"record","created_at":"2026-05-17T23:51:21Z","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":"8d5d48831e7b73ce41d21ad3dee88d939daf43a90907e81bd9fbd9d0da62e0d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-03-11T13:54:05Z","title_canon_sha256":"e2024f627e793c08a73ee97cc0ab68e661bfbcd89965d451f833c2fc93124c48"},"schema_version":"1.0","source":{"id":"1903.04302","kind":"arxiv","version":2}},"canonical_sha256":"18f47363e16000bfb03380eccf4c0dba478777a09d570a0d82a8d5c35749f301","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18f47363e16000bfb03380eccf4c0dba478777a09d570a0d82a8d5c35749f301","first_computed_at":"2026-05-17T23:51:21.038142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:21.038142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ujHHbE0+c4ROEVi2NtF0hy1HyAZVhxbbCWk49S7d/Olm3FeKN0ZjOVcWPFNIpMdOxekmsTJcxutcs/h2FBCCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:21.038787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.04302","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dba671d9737157c758888ceba15e37627b25dd924333ac50e63a2546e3df2bf","sha256:2b9a53896851ed023bcb8773a2f0fb444ede90761db12049f1fd479fdf0070a5"],"state_sha256":"8d5d1dc4e4eb80835a7e3f7bc5e43ba012e79728a3075f92b440218fbfd8e08f"}