{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TJN7UHRA6WCQZJHAAPJ4CPNDXX","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":"8eba6a162dad6b1d3db8721e9bfcd352b71d8cce6d948d001167e34d6b99a588","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-24T03:54:41Z","title_canon_sha256":"956b7b1c6b900a7f981074c582a62fbde2a1412fa6a08ffbe4a4cdfcde200a31"},"schema_version":"1.0","source":{"id":"1805.09499","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09499","created_at":"2026-05-18T00:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09499v1","created_at":"2026-05-18T00:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09499","created_at":"2026-05-18T00:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"TJN7UHRA6WCQ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TJN7UHRA6WCQZJHA","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TJN7UHRA","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:6c4db891b00185809a82844991cb8dbf457b8bfafa8b53c688c84b423c05c3b5","target":"graph","created_at":"2026-05-18T00:15:03Z","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":"It is shown in [10] that a regular and local Dirichlet form on an interval can be represented by so-called effective intervals with scale functions. This paper focuses on how to operate on effective intervals to obtain regular Dirichlet subspaces. The first result is a complete characterization for a Dirichlet form to be a regular subspace of such a Dirichlet form in terms of effective intervals. Then we give an explicit road map how to obtain all regular Dirichlet subspaces from a local and regular Dirichlet form on an interval, by a series of intuitive operations on the effective intervals i","authors_text":"Jiangang Ying, Liping Li, Wenjie Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-24T03:54:41Z","title":"Effective intervals and regular Dirichlet subspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09499","kind":"arxiv","version":1},"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:ef4e4c734693764a32c58ad757be8386db9ef613239e9ea2c53c78fb0fffedd2","target":"record","created_at":"2026-05-18T00:15:03Z","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":"8eba6a162dad6b1d3db8721e9bfcd352b71d8cce6d948d001167e34d6b99a588","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-24T03:54:41Z","title_canon_sha256":"956b7b1c6b900a7f981074c582a62fbde2a1412fa6a08ffbe4a4cdfcde200a31"},"schema_version":"1.0","source":{"id":"1805.09499","kind":"arxiv","version":1}},"canonical_sha256":"9a5bfa1e20f5850ca4e003d3c13da3bdedf09b20919f13ca18b744e305c35211","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a5bfa1e20f5850ca4e003d3c13da3bdedf09b20919f13ca18b744e305c35211","first_computed_at":"2026-05-18T00:15:03.748457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:03.748457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4JYaQRRyGx5wqjhmHNbPOLf05K6Ohi2y6CyFogbp5Q3zv8bStGJoBoHe60VyYq2iGgKFEzKpAwwL078SiFluCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:03.748963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09499","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef4e4c734693764a32c58ad757be8386db9ef613239e9ea2c53c78fb0fffedd2","sha256:6c4db891b00185809a82844991cb8dbf457b8bfafa8b53c688c84b423c05c3b5"],"state_sha256":"22d335c76c9b8d3bf52c5dc1b54cd88f04b3f3a15a933221b73470290bc06056"}