{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DF37CBF5RZ373E5QFWHYKV3UKE","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":"312739526319ebb3710a806fa61333fb322550f8fa69ce3384e872a3c7e5f310","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-05T05:27:06Z","title_canon_sha256":"11943777d97c1b4a1d3ab63203c8a0091790f3b01cb3545fa980e0f2a7d1a9f7"},"schema_version":"1.0","source":{"id":"1412.1896","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1896","created_at":"2026-05-18T01:15:38Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1896v2","created_at":"2026-05-18T01:15:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1896","created_at":"2026-05-18T01:15:38Z"},{"alias_kind":"pith_short_12","alias_value":"DF37CBF5RZ37","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DF37CBF5RZ373E5Q","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DF37CBF5","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:aabe48c2b65a1e482b26d843e33e41178d06c3ee3fa8f721fdb22913e8e9707e","target":"graph","created_at":"2026-05-18T01:15:38Z","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":"The main purpose of this paper is to explore the structure of regular subspaces of 1-dim Brownian motion. As outlined in \\cite{FMG} every such regular subspace can be characterized by a measure-dense set $G$. When $G$ is open, $F=G^c$ is the boundary of $G$ and, before leaving $G$, the diffusion associated with the regular subspace is nothing but Brownian motion. Their traces on $F$ still inherit the inclusion relation, in other words, the trace Dirichlet form of regular subspace on $F$ is still a regular subspace of trace Dirichlet form of one-dimensional Brownian motion on $F$. Moreover we h","authors_text":"Jiangang Ying, Liping Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-05T05:27:06Z","title":"On structure of regular Dirichlet subspaces for one-dimensional Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1896","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":"sha256:55338ee9e6624862f07cbaf8e5075fa6c9f99e7f4980bf3656c69e5eb41e1a89","target":"record","created_at":"2026-05-18T01:15:38Z","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":"312739526319ebb3710a806fa61333fb322550f8fa69ce3384e872a3c7e5f310","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-05T05:27:06Z","title_canon_sha256":"11943777d97c1b4a1d3ab63203c8a0091790f3b01cb3545fa980e0f2a7d1a9f7"},"schema_version":"1.0","source":{"id":"1412.1896","kind":"arxiv","version":2}},"canonical_sha256":"1977f104bd8e77fd93b02d8f855774512f4a58d63df4402029c284059d3c7f4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1977f104bd8e77fd93b02d8f855774512f4a58d63df4402029c284059d3c7f4d","first_computed_at":"2026-05-18T01:15:38.881435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:38.881435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uW9Vcq4vT2WHWEIMyCJWtjwgoGPAUrGS+kj3m1OjbMvDaVzKc6zPH/Ol1+akVoGfjKDa2rkpbI4Fy+FvhXg2BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:38.882179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1896","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55338ee9e6624862f07cbaf8e5075fa6c9f99e7f4980bf3656c69e5eb41e1a89","sha256:aabe48c2b65a1e482b26d843e33e41178d06c3ee3fa8f721fdb22913e8e9707e"],"state_sha256":"3a8c1ec69ecb07b7929b7f7e9b5540db1191e2b0ee5d74f5e9db2c02731808e6"}