{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UYZSEP4VVPW7BZRFVXWE4JJ5VX","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":"37a71d865076010375ebf2ecd4b1d2ded8eab28104906ee3bbe35286bf43f0ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-02-03T02:22:42Z","title_canon_sha256":"6b221d6ba660e39aabde79cf1f4132088715a9d51710039a2e4045afe62af630"},"schema_version":"1.0","source":{"id":"1602.01167","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01167","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01167v1","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01167","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"UYZSEP4VVPW7","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UYZSEP4VVPW7BZRF","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UYZSEP4V","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:7dbdfa1741d270513c47d153fb52959474d52f383779c953da49c3db55a59f07","target":"graph","created_at":"2026-05-18T01:21:23Z","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":"Let $\\ce$ be a Dirichlet form on $L_2(X\\,;\\mu)$ where $(X,\\mu)$ is locally compact $\\sigma$-compact measure space. Assume $\\ce$ is inner regular, i.e.\\ regular in restriction to functions of compact support, and local in the sense that\n  $\\ce(\\varphi,\\psi)=0$ for all $\\varphi, \\psi\\in D(\\ce)$ with $\\varphi\\,\\psi=0$. We construct two Dirichlet forms $\\ce_m$ and $\\ce_M$ such that $\\ce_m\\leq \\ce\\leq \\ce_M$. These forms are potentially the smallest and largest such Dirichlet forms. In particular $\\ce_m\\supseteq \\ce_M$, $(\\ce_M)_m=\\ce_m$ and $(\\ce_m)_M=\\ce_M$. We analyze the family of local, inner ","authors_text":"Derek W. Robinson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-02-03T02:22:42Z","title":"On extensions of local Dirichlet forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01167","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:ac6899b70ec3f0b6a5c7b15b916c81c363cb4140c08e266b8afa68bfcd62997c","target":"record","created_at":"2026-05-18T01:21:23Z","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":"37a71d865076010375ebf2ecd4b1d2ded8eab28104906ee3bbe35286bf43f0ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-02-03T02:22:42Z","title_canon_sha256":"6b221d6ba660e39aabde79cf1f4132088715a9d51710039a2e4045afe62af630"},"schema_version":"1.0","source":{"id":"1602.01167","kind":"arxiv","version":1}},"canonical_sha256":"a633223f95abedf0e625adec4e253dadd3f590cf0f8553956fa338204091e545","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a633223f95abedf0e625adec4e253dadd3f590cf0f8553956fa338204091e545","first_computed_at":"2026-05-18T01:21:23.425765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:23.425765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tfrhF1VJifoPNMiw1Ta0ZhBum4TDhSAIqJVPxyd+BpS5CXWPX8NROpxF0CUykDJeyT2fXVQFewgvtfkmOVKtCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:23.426295Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01167","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac6899b70ec3f0b6a5c7b15b916c81c363cb4140c08e266b8afa68bfcd62997c","sha256:7dbdfa1741d270513c47d153fb52959474d52f383779c953da49c3db55a59f07"],"state_sha256":"4d92fed7f39936dfeee5f014db30a3865b4d23959fce5ffd4645243c5c02615c"}