{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NDWCMQ7FDXZI6AG6HOOJ6XPIDU","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":"d703324462100f244327180ba31b06385ccf48df14063f6aae168896739980f0","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-31T09:21:50Z","title_canon_sha256":"2b791786df36fdd6167a9dba46d078154280523425496c745351b50c7db43f88"},"schema_version":"1.0","source":{"id":"1701.00078","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00078","created_at":"2026-05-18T00:50:54Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00078v2","created_at":"2026-05-18T00:50:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00078","created_at":"2026-05-18T00:50:54Z"},{"alias_kind":"pith_short_12","alias_value":"NDWCMQ7FDXZI","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NDWCMQ7FDXZI6AG6","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NDWCMQ7F","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:64aec8d6b87569021669d927355cbbe4a3322907abc6db7135fc0c56833ee643","target":"graph","created_at":"2026-05-18T00:50:54Z","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 prove that a singular part $\\mu_s$ of a measure $\\mu$ satisfying ${\\cal A}\\mu =0$ for a linear partial differential operator ${\\cal A}$ defined on $R^d$ has the range in the intersection of kernels of the principal symbol of ${\\cal A}$ if the singular part is singular with respect to all the variables (uniformly singular) i.e. it is such that for $\\mu_s$-almost every $x\\in R^d$ there exist positive functions $\\alpha(\\epsilon), \\beta(\\epsilon)$, $\\epsilon \\in R$, satisfying $\\frac{\\alpha(\\epsilon)}{\\epsilon}\\to 0$, $ \\frac{\\epsilon}{\\beta(\\epsilon)}\\to 0$ and a set $E_\\epsilon\\subset B(\\mx,\\","authors_text":"Darko Mitrovic","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-31T09:21:50Z","title":"The structure of ${\\cal A}$-free measures with uniformly singular part"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00078","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":"sha256:43ffc4a6c5c70b3c430cdf03814d52a042c2e8ef6483a438faf8acaedeb6d69d","target":"record","created_at":"2026-05-18T00:50:54Z","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":"d703324462100f244327180ba31b06385ccf48df14063f6aae168896739980f0","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-31T09:21:50Z","title_canon_sha256":"2b791786df36fdd6167a9dba46d078154280523425496c745351b50c7db43f88"},"schema_version":"1.0","source":{"id":"1701.00078","kind":"arxiv","version":2}},"canonical_sha256":"68ec2643e51df28f00de3b9c9f5de81d3dd9768076bf93f0f2a1d14ecfa04119","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68ec2643e51df28f00de3b9c9f5de81d3dd9768076bf93f0f2a1d14ecfa04119","first_computed_at":"2026-05-18T00:50:54.285619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:54.285619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MU68toXcj+8FVvDEvtpIpASv2SeJGEGiam3XIAWzZdVr8LITKY5EONAPEbphUl+73FVauooat4G5GunxvofXAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:54.286155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00078","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43ffc4a6c5c70b3c430cdf03814d52a042c2e8ef6483a438faf8acaedeb6d69d","sha256:64aec8d6b87569021669d927355cbbe4a3322907abc6db7135fc0c56833ee643"],"state_sha256":"eaa98b362ca4e1fc327d9c401eaff7d3a64558071eace82f9fae9305b277b493"}