{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JLPT6JGXYMPFO6UC2EVWJBRDAQ","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":"3278dcd814b780cc5aacc8c0e6da67c4aabf2f306ff4d8249f28931af1a24bb1","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-16T07:40:21Z","title_canon_sha256":"ef1ff6a292e07e9f42b0116a44a0db52ac7c92364776ec94e1ca5b6c4f408c35"},"schema_version":"1.0","source":{"id":"1304.4352","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4352","created_at":"2026-05-18T01:31:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4352v4","created_at":"2026-05-18T01:31:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4352","created_at":"2026-05-18T01:31:21Z"},{"alias_kind":"pith_short_12","alias_value":"JLPT6JGXYMPF","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JLPT6JGXYMPFO6UC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JLPT6JGX","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:6ba88c1aa014a655ca038280f94e25280404da62de9325d4a44463994a084e3e","target":"graph","created_at":"2026-05-18T01:31:21Z","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":"We study mean value properties of harmonic functions in metric measure spaces. The metric measure spaces we consider have a doubling measure and support a (1,1)- Poincar\\'e inequality. The notion of harmonicity is based on the Dirichlet form defined in terms of a Cheeger differentiable structure. By studying fine properties of the Green function on balls, we characterize harmonic functions in terms of a mean value property. As a consequence, we obtain a detailed description of Poisson kernels. We shall also obtain a Gauss-Green type formula for sets of finite perimeter which posses a Minkowski","authors_text":"Michele Miranda Jr., Nageswari Shanmugalingam, Niko Marola","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-16T07:40:21Z","title":"Boundary measures, generalized Gauss-Green formulas, and mean value property in metric measure spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4352","kind":"arxiv","version":4},"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":"sha256:05266f3ead99f9517c725a7e4fdf30dc58b0021d835cfa2f0c3c0944b48db66e","target":"record","created_at":"2026-05-18T01:31:21Z","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":"3278dcd814b780cc5aacc8c0e6da67c4aabf2f306ff4d8249f28931af1a24bb1","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-16T07:40:21Z","title_canon_sha256":"ef1ff6a292e07e9f42b0116a44a0db52ac7c92364776ec94e1ca5b6c4f408c35"},"schema_version":"1.0","source":{"id":"1304.4352","kind":"arxiv","version":4}},"canonical_sha256":"4adf3f24d7c31e577a82d12b64862304313e3292a3aa8e4ee819490f62cc17cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4adf3f24d7c31e577a82d12b64862304313e3292a3aa8e4ee819490f62cc17cd","first_computed_at":"2026-05-18T01:31:21.669328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:21.669328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OWmmAWgRPNByJb9EVUeR2kAgAt3IjOBjqglWFRuBnOTgBNvgc8YYsSahWFI5K0awFjpaPwrtBs2e6J/AYub0Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:21.669779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4352","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05266f3ead99f9517c725a7e4fdf30dc58b0021d835cfa2f0c3c0944b48db66e","sha256:6ba88c1aa014a655ca038280f94e25280404da62de9325d4a44463994a084e3e"],"state_sha256":"c7ae0990cdc2a7b77c3b719afa26ed7e5acbf8e858b236eb353d6fefe1dbf92d"}