{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:25P47K2PDYRKHMBXGGY7I3XBCP","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":"295962112ae17aefc243840ae04ddb7b9ee2d66cc4596c7324408b6597d4c4a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-29T14:10:51Z","title_canon_sha256":"001cc2e407b82f2223b71fe8f1d6e588baf982df390bcea3a7094b5819b48a9b"},"schema_version":"1.0","source":{"id":"1904.12726","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12726","created_at":"2026-05-17T23:47:24Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12726v2","created_at":"2026-05-17T23:47:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12726","created_at":"2026-05-17T23:47:24Z"},{"alias_kind":"pith_short_12","alias_value":"25P47K2PDYRK","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"25P47K2PDYRKHMBX","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"25P47K2P","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:ddca41cb2eb00e6b2cf1e55843e59f4f6b38f007b5f106e9700d906174030896","target":"graph","created_at":"2026-05-17T23:47:24Z","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":"Within the framework of balayage spaces (the analytical equivalent of nice Hunt processes), we prove equicontinuity of bounded families of harmonic functions and apply it to obtain criteria for compactness of potential kernels.","authors_text":"Wolfhard Hansen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-29T14:10:51Z","title":"Equicontinuity of harmonic functions and compactness of potential kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12726","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:e72ae4f78d914ff60bcc2ec772eef39740128d42d293abe61b86282888086859","target":"record","created_at":"2026-05-17T23:47:24Z","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":"295962112ae17aefc243840ae04ddb7b9ee2d66cc4596c7324408b6597d4c4a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-29T14:10:51Z","title_canon_sha256":"001cc2e407b82f2223b71fe8f1d6e588baf982df390bcea3a7094b5819b48a9b"},"schema_version":"1.0","source":{"id":"1904.12726","kind":"arxiv","version":2}},"canonical_sha256":"d75fcfab4f1e22a3b03731b1f46ee113db57a3f841ea059fe71bb786374fab01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d75fcfab4f1e22a3b03731b1f46ee113db57a3f841ea059fe71bb786374fab01","first_computed_at":"2026-05-17T23:47:24.596245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:24.596245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D4cyEwc+QjzcEI6OFGQPu46h2D8MT6nY50+86NENeDQW/FwKVXd2LtCo7maGFJ91VPn5ysS9K7RMm8Fz4RxzDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:24.596968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.12726","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e72ae4f78d914ff60bcc2ec772eef39740128d42d293abe61b86282888086859","sha256:ddca41cb2eb00e6b2cf1e55843e59f4f6b38f007b5f106e9700d906174030896"],"state_sha256":"593672890f0f7e4d817341e286efe35d61bed65856ab1cd69d3b242240809925"}