{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5KTUSRX2F5RTDL7XI2N3KTNNID","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":"dca14b763aa86b741f6f2b9dfead46d412cd607353c96c93f79ac326c98de33b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T23:31:05Z","title_canon_sha256":"fbaa92df3a53278ce82fc19c19ff81f6441debb90aca494c1e742e43e0259e45"},"schema_version":"1.0","source":{"id":"1404.6290","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6290","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6290v3","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6290","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"5KTUSRX2F5RT","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5KTUSRX2F5RTDL7X","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5KTUSRX2","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:82c173860e9afd154d264081053f3ae912ca1ae5dce5fa7e58612f120962b10a","target":"graph","created_at":"2026-05-18T00:47:29Z","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 stochastic processes on complete, locally compact tree-like metric spaces $(T,r)$ on their \"natural scale\" with boundedly finite speed measure $\\nu$. Given a triple $(T,r,\\nu)$ such a speed-$\\nu$ motion on $(T,r)$ can be characterized as the unique strong Markov process which if restricted to compact subtrees satisfies for all $x,y\\in T$ and all positive, bounded measurable $f$, \\[ \\mathbb{E}^x [ \\int^{\\tau_y}_0\\mathrm{d}s\\, f(X_s) ]\n  = 2\\int_T\\nu(\\mathrm{d}z)\\, r(y,c(x,y,z))f(z)\n  < \\infty, \\] where $c(x,y,z)$ denotes the branch point generated by $x,y,z$. If $(T,r)$ is a discret","authors_text":"Anita Winter, Siva Athreya, Wolfgang L\\\"ohr","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T23:31:05Z","title":"Invariance principle for variable speed random walks on trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6290","kind":"arxiv","version":3},"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:dddfa87b70d3f27c0708beb9e50c4788d17da1ced40e0b1a66348867ab60efe3","target":"record","created_at":"2026-05-18T00:47:29Z","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":"dca14b763aa86b741f6f2b9dfead46d412cd607353c96c93f79ac326c98de33b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-24T23:31:05Z","title_canon_sha256":"fbaa92df3a53278ce82fc19c19ff81f6441debb90aca494c1e742e43e0259e45"},"schema_version":"1.0","source":{"id":"1404.6290","kind":"arxiv","version":3}},"canonical_sha256":"eaa74946fa2f6331aff7469bb54dad40f3e9201b560f57e4fbb4e726a720d5e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eaa74946fa2f6331aff7469bb54dad40f3e9201b560f57e4fbb4e726a720d5e5","first_computed_at":"2026-05-18T00:47:29.803843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:29.803843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"94MwkeCmzYc2aa3Jr1XHByx6mYVkGTo/jbf0T7CvOfFDQCkGpi2xtQgRhEIYhxSwRYJwQ008u/5bGd2TcFf1Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:29.804307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6290","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dddfa87b70d3f27c0708beb9e50c4788d17da1ced40e0b1a66348867ab60efe3","sha256:82c173860e9afd154d264081053f3ae912ca1ae5dce5fa7e58612f120962b10a"],"state_sha256":"a236f7a79e0fc775c42eb4d5801a90878c9fffb54019015e4e161c8e0a985b68"}