{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4R44OVBRJB55RJJF5TQ65PP5IQ","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":"9e192393d0dba7c7a486f361a6b8820b1c359ac2a0258273ada8f38ef218735f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-03T13:39:45Z","title_canon_sha256":"d106916ec9677d6144f7edda9fe89d5dd75d2a18a9946ed743701df4d551d64e"},"schema_version":"1.0","source":{"id":"1012.0739","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0739","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0739v2","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0739","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"pith_short_12","alias_value":"4R44OVBRJB55","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4R44OVBRJB55RJJF","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4R44OVBR","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:a7d022acf7997aeb368fd667d7c97685f79760d043027d00bbdeea2143fff8e6","target":"graph","created_at":"2026-05-18T04:34:08Z","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":"Consider a metric graph G with set of vertices V. Assume that for every vertex in V one is given a Wentzell boundary condition. It is shown how one can construct the paths of a Brownian motion on G such that its generator - viewed as an operator on the space of continuous functions vanishing at infinity - has a domain consisting of twice continuously differentiable functions satisfying these boundary conditions.","authors_text":"J\\\"urgen Potthoff, Robert Schrader, Vadim Kostrykin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-03T13:39:45Z","title":"Brownian Motions on Metric Graphs III - Construction: General Metric Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0739","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":"sha256:0cfb214f34cfc4ef4988b17ef3edb30dd247e22af94fe06a45d324d501bd9ce2","target":"record","created_at":"2026-05-18T04:34:08Z","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":"9e192393d0dba7c7a486f361a6b8820b1c359ac2a0258273ada8f38ef218735f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-03T13:39:45Z","title_canon_sha256":"d106916ec9677d6144f7edda9fe89d5dd75d2a18a9946ed743701df4d551d64e"},"schema_version":"1.0","source":{"id":"1012.0739","kind":"arxiv","version":2}},"canonical_sha256":"e479c75431487bd8a525ece1eebdfd440d497f3e2d0cff500ae8bf7d7aeb4e3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e479c75431487bd8a525ece1eebdfd440d497f3e2d0cff500ae8bf7d7aeb4e3c","first_computed_at":"2026-05-18T04:34:08.524888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:08.524888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EoYY7Jzwso6mB6LzaVM1NqT8uv1e97cpsA6ZbsFREemsxYoqaGRPX9CSU5mrWIdXLn6tujBYk+txEzRjl8vWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:08.525423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0739","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cfb214f34cfc4ef4988b17ef3edb30dd247e22af94fe06a45d324d501bd9ce2","sha256:a7d022acf7997aeb368fd667d7c97685f79760d043027d00bbdeea2143fff8e6"],"state_sha256":"12a7a57d0ce97e36dadf5cb694ff249dd58d16f1683e7cdf5fa7e70d430e081c"}