{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JGZTKAS2YGXMTOJDTQE4R5XW3B","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":"76da035917e5e49fa522ab1ca5a8691b699d9b21c6f95446fe150025f358b168","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-03T03:30:35Z","title_canon_sha256":"7699e9e48d5b79161ef7797b1a442d34a05fcb84bebeaa518674a8b16b5a425a"},"schema_version":"1.0","source":{"id":"1711.01013","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01013","created_at":"2026-05-17T23:57:48Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01013v4","created_at":"2026-05-17T23:57:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01013","created_at":"2026-05-17T23:57:48Z"},{"alias_kind":"pith_short_12","alias_value":"JGZTKAS2YGXM","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JGZTKAS2YGXMTOJD","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JGZTKAS2","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:e95347ac18e3c8df62ca3d509e0372bde0b73dcc1bb2096c6e118521fc7b3ada","target":"graph","created_at":"2026-05-17T23:57:48Z","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 this paper, we prove that any subset with an appropriate sub-linear horizontal growth has a non-zero stationary harmonic measure. On the other hand, we also show any subset with super-linear horizontal growth will have a $0$ stationary harmonic measure at every point. This result is fundamental to any future study of stationary DLA. As an application we prove that any possible aggregation process with growth rates proportional to the stationary harmonic measure has non zero measure at all times.","authors_text":"Eviatar B. Procaccia, Yuan Zhang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-03T03:30:35Z","title":"On sets of zero stationary harmonic measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01013","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:a7c1c73b2f94357797bb3acf8a707203dc3491ec6fa0190e028744e422558c2b","target":"record","created_at":"2026-05-17T23:57:48Z","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":"76da035917e5e49fa522ab1ca5a8691b699d9b21c6f95446fe150025f358b168","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-03T03:30:35Z","title_canon_sha256":"7699e9e48d5b79161ef7797b1a442d34a05fcb84bebeaa518674a8b16b5a425a"},"schema_version":"1.0","source":{"id":"1711.01013","kind":"arxiv","version":4}},"canonical_sha256":"49b335025ac1aec9b9239c09c8f6f6d86fceffba7a263c85856bccd57895c492","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49b335025ac1aec9b9239c09c8f6f6d86fceffba7a263c85856bccd57895c492","first_computed_at":"2026-05-17T23:57:48.823213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:48.823213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t0N7rs5olk4YLHsVOq7lqhQ3+dM7W6P9CDICMN2VE+oCY4+hfoYPYSAuHYlaASKZbSjQRygPtmGMgvP97jEgDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:48.823771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.01013","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7c1c73b2f94357797bb3acf8a707203dc3491ec6fa0190e028744e422558c2b","sha256:e95347ac18e3c8df62ca3d509e0372bde0b73dcc1bb2096c6e118521fc7b3ada"],"state_sha256":"6820a0278f8b7f300b2075f9069b1366d7b8a3b992e06fee0f4d4d9af14af6a9"}