{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VCS6E5H7DRIHTI6MNROV6ROVTT","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":"bcd0a68a841b5169826075e842bf2f8718c638879cbcefa791ed936c9d2e0fc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-12-13T21:07:22Z","title_canon_sha256":"634f17d1fb8bea99597502c81e36e1e2afe2a3e4a49f9787e5fbd9720b815a0f"},"schema_version":"1.0","source":{"id":"1012.2877","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2877","created_at":"2026-05-18T04:33:26Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2877v1","created_at":"2026-05-18T04:33:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2877","created_at":"2026-05-18T04:33:26Z"},{"alias_kind":"pith_short_12","alias_value":"VCS6E5H7DRIH","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VCS6E5H7DRIHTI6M","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VCS6E5H7","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:b115ceef0e29d22095df2e193de2bc0c4427ca4552cc806794a3985921b25a58","target":"graph","created_at":"2026-05-18T04:33:26Z","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 consider a generalization of the Riesz operator in $R^d$ and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version of $T1$ theorem for Calder\\'on-Zygmund operators in metric spaces. We extend two versions of Calder\\'on-Zygmund capacities in $R^d$ to metric spaces and establish their equivalence (under certain conditions). As an application, we extend the known relations between $s$-Riesz capacities, $0<s<d$, and the capacities in Nonlinear Potential Theory, to the case $s=0$.","authors_text":"David R. Adams, Vladimir Eiderman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-12-13T21:07:22Z","title":"Singular operators with antisymmetric kernels, related capacities, and Wolff potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2877","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":"sha256:91ed5bcbf5091ab5af2b75de90ff5ce564d10a79652fa99c17150da4560dc762","target":"record","created_at":"2026-05-18T04:33:26Z","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":"bcd0a68a841b5169826075e842bf2f8718c638879cbcefa791ed936c9d2e0fc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-12-13T21:07:22Z","title_canon_sha256":"634f17d1fb8bea99597502c81e36e1e2afe2a3e4a49f9787e5fbd9720b815a0f"},"schema_version":"1.0","source":{"id":"1012.2877","kind":"arxiv","version":1}},"canonical_sha256":"a8a5e274ff1c5079a3cc6c5d5f45d59ce9bf63dbb2d038d76d9cd0f4f8e7c13d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8a5e274ff1c5079a3cc6c5d5f45d59ce9bf63dbb2d038d76d9cd0f4f8e7c13d","first_computed_at":"2026-05-18T04:33:26.480434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:26.480434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5lA0I/HQ0E0kG0l4+Fyx9eRmqmIKdwG56R1nMUwbYDTxaRwJfryLOUO+vnjFPImvnyrMd9Zd2fHbYv4WZUsODw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:26.481227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2877","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91ed5bcbf5091ab5af2b75de90ff5ce564d10a79652fa99c17150da4560dc762","sha256:b115ceef0e29d22095df2e193de2bc0c4427ca4552cc806794a3985921b25a58"],"state_sha256":"29e768ef1c0d8f2ea3898bc9c7521b1c802a5ae8f46a6afc03205fcf5badbce1"}