{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QHJGVAP7ZXMR5VHTKSF3HNYK2U","short_pith_number":"pith:QHJGVAP7","canonical_record":{"source":{"id":"1412.3355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-12-10T16:27:51Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"eb03ed0f2b02ea9955234ee68eefedbdc1689cf668941293a80c829aa8199415","abstract_canon_sha256":"d002d6c49cde512a56a3148e3a69c3c4555cd5693b770557f9a94b8b2c44aaa7"},"schema_version":"1.0"},"canonical_sha256":"81d26a81ffcdd91ed4f3548bb3b70ad52d6d2eb85afe5d85a8ceedcb3432dc63","source":{"kind":"arxiv","id":"1412.3355","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3355","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3355v1","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3355","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"QHJGVAP7ZXMR","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QHJGVAP7ZXMR5VHT","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QHJGVAP7","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QHJGVAP7ZXMR5VHTKSF3HNYK2U","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-12-10T16:27:51Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"eb03ed0f2b02ea9955234ee68eefedbdc1689cf668941293a80c829aa8199415","abstract_canon_sha256":"d002d6c49cde512a56a3148e3a69c3c4555cd5693b770557f9a94b8b2c44aaa7"},"schema_version":"1.0"},"canonical_sha256":"81d26a81ffcdd91ed4f3548bb3b70ad52d6d2eb85afe5d85a8ceedcb3432dc63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:36.884979Z","signature_b64":"f6ewJ4CMRlcZi0hd92CKZdSxgs9wuTcnzXu43dL9fMdVI83mZb/oagWz8n1zghLCcHNuhWgj79C7yry+fl6+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81d26a81ffcdd91ed4f3548bb3b70ad52d6d2eb85afe5d85a8ceedcb3432dc63","last_reissued_at":"2026-05-18T02:31:36.884450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:36.884450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3355","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6uBCkQqoS6Ww4BXA2xgDVg/3h1ICgP4RB6xSsAc8/pKq7yPhhkbA2rFrlf94nRbZq7Fx0J1Flx6KYTnKY6WRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:50:05.201161Z"},"content_sha256":"7959cfe64b534ec850531f9f7b10cba584d727f0edbd1d13860ea50ba3eebd2d","schema_version":"1.0","event_id":"sha256:7959cfe64b534ec850531f9f7b10cba584d727f0edbd1d13860ea50ba3eebd2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QHJGVAP7ZXMR5VHTKSF3HNYK2U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global properties of Dirichlet forms in terms of Green's formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.FA","authors_text":"Daniel Lenz, Jun Masamune, Marcel Schmidt, Matthias Keller, Sebastian Haeseler","submitted_at":"2014-12-10T16:27:51Z","abstract_excerpt":"We study global properties of Dirichlet forms such as uniqueness of the Dirichlet extension, stochastic completeness and recurrence. We characterize these properties by means of vanishing of a boundary term in Green's formula for functions from suitable function spaces and suitable operators arising from extensions of the underlying form. We first present results in the framework of general Dirichlet forms on $\\sigma$-finite measure spaces. For regular Dirichlet forms our results can be strengthened as all operators from the previous considerations turn out to be restrictions of a single opera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3355","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kizv79rOUKW12+sZ21wfGeM9NQ3oq/xfHZ0dAuG2IcCki6Qw2u0CpjvmoemyTRuvtVOL6zS41HDr+JGaGtWEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:50:05.201539Z"},"content_sha256":"e509827cc83302331c2ec3ba8c3afaa46cbbe382b0e34938026ce2de47bd42e8","schema_version":"1.0","event_id":"sha256:e509827cc83302331c2ec3ba8c3afaa46cbbe382b0e34938026ce2de47bd42e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHJGVAP7ZXMR5VHTKSF3HNYK2U/bundle.json","state_url":"https://pith.science/pith/QHJGVAP7ZXMR5VHTKSF3HNYK2U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHJGVAP7ZXMR5VHTKSF3HNYK2U/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T21:50:05Z","links":{"resolver":"https://pith.science/pith/QHJGVAP7ZXMR5VHTKSF3HNYK2U","bundle":"https://pith.science/pith/QHJGVAP7ZXMR5VHTKSF3HNYK2U/bundle.json","state":"https://pith.science/pith/QHJGVAP7ZXMR5VHTKSF3HNYK2U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHJGVAP7ZXMR5VHTKSF3HNYK2U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QHJGVAP7ZXMR5VHTKSF3HNYK2U","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":"d002d6c49cde512a56a3148e3a69c3c4555cd5693b770557f9a94b8b2c44aaa7","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-12-10T16:27:51Z","title_canon_sha256":"eb03ed0f2b02ea9955234ee68eefedbdc1689cf668941293a80c829aa8199415"},"schema_version":"1.0","source":{"id":"1412.3355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3355","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3355v1","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3355","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"QHJGVAP7ZXMR","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QHJGVAP7ZXMR5VHT","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QHJGVAP7","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:e509827cc83302331c2ec3ba8c3afaa46cbbe382b0e34938026ce2de47bd42e8","target":"graph","created_at":"2026-05-18T02:31:36Z","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 study global properties of Dirichlet forms such as uniqueness of the Dirichlet extension, stochastic completeness and recurrence. We characterize these properties by means of vanishing of a boundary term in Green's formula for functions from suitable function spaces and suitable operators arising from extensions of the underlying form. We first present results in the framework of general Dirichlet forms on $\\sigma$-finite measure spaces. For regular Dirichlet forms our results can be strengthened as all operators from the previous considerations turn out to be restrictions of a single opera","authors_text":"Daniel Lenz, Jun Masamune, Marcel Schmidt, Matthias Keller, Sebastian Haeseler","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-12-10T16:27:51Z","title":"Global properties of Dirichlet forms in terms of Green's formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3355","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":"sha256:7959cfe64b534ec850531f9f7b10cba584d727f0edbd1d13860ea50ba3eebd2d","target":"record","created_at":"2026-05-18T02:31:36Z","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":"d002d6c49cde512a56a3148e3a69c3c4555cd5693b770557f9a94b8b2c44aaa7","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-12-10T16:27:51Z","title_canon_sha256":"eb03ed0f2b02ea9955234ee68eefedbdc1689cf668941293a80c829aa8199415"},"schema_version":"1.0","source":{"id":"1412.3355","kind":"arxiv","version":1}},"canonical_sha256":"81d26a81ffcdd91ed4f3548bb3b70ad52d6d2eb85afe5d85a8ceedcb3432dc63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81d26a81ffcdd91ed4f3548bb3b70ad52d6d2eb85afe5d85a8ceedcb3432dc63","first_computed_at":"2026-05-18T02:31:36.884450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:36.884450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f6ewJ4CMRlcZi0hd92CKZdSxgs9wuTcnzXu43dL9fMdVI83mZb/oagWz8n1zghLCcHNuhWgj79C7yry+fl6+Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:36.884979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7959cfe64b534ec850531f9f7b10cba584d727f0edbd1d13860ea50ba3eebd2d","sha256:e509827cc83302331c2ec3ba8c3afaa46cbbe382b0e34938026ce2de47bd42e8"],"state_sha256":"92c453b2b0eea793267898ef842933946504d37918cb974f3a2711fe07d41366"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RfPt3G9wlQIM9a4yvc1Q1HpQM3FbXMEgr00AB7UvV19eR+DzWWva7u28lSkjU7Gux0uVhMJrQrMVUq7DOJocBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:50:05.203523Z","bundle_sha256":"24f4281c5cbf16f990710d33fdaa17240cbc3eb17984bb8781e6d76efd4a55f2"}}