{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZIOB47UYEYSB2UCD3LS7FIC6TH","short_pith_number":"pith:ZIOB47UY","canonical_record":{"source":{"id":"1801.08326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-25T09:42:21Z","cross_cats_sorted":["math.AP","math.PR"],"title_canon_sha256":"610728423d7b82344a79853b39e2cebf7a078b0f84db3e49e9a469316d53b073","abstract_canon_sha256":"776f3315f9bf6feb91294871fd78da50628b7d0f74b7a7e42b585ac5dfd5d98c"},"schema_version":"1.0"},"canonical_sha256":"ca1c1e7e9826241d5043dae5f2a05e99f40e708aadde2dfa5864fccc9dfbbff0","source":{"kind":"arxiv","id":"1801.08326","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08326","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08326v1","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08326","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZIOB47UYEYSB","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZIOB47UYEYSB2UCD","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZIOB47UY","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZIOB47UYEYSB2UCD3LS7FIC6TH","target":"record","payload":{"canonical_record":{"source":{"id":"1801.08326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-25T09:42:21Z","cross_cats_sorted":["math.AP","math.PR"],"title_canon_sha256":"610728423d7b82344a79853b39e2cebf7a078b0f84db3e49e9a469316d53b073","abstract_canon_sha256":"776f3315f9bf6feb91294871fd78da50628b7d0f74b7a7e42b585ac5dfd5d98c"},"schema_version":"1.0"},"canonical_sha256":"ca1c1e7e9826241d5043dae5f2a05e99f40e708aadde2dfa5864fccc9dfbbff0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:06.559832Z","signature_b64":"mpPscaZod0g+DdtwjF5b0qM9q13mQEuUq0t5JgVMOVDo5i2CmjYbrjSmCOcA7Oed4/8tGVSQWFCV/fDZXjEJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca1c1e7e9826241d5043dae5f2a05e99f40e708aadde2dfa5864fccc9dfbbff0","last_reissued_at":"2026-05-18T00:25:06.559409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:06.559409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.08326","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":"2026-05-18T00:25:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wG91wybDnnY/pO4UWgafxjAUI3CcW+akPiLGa6HpLMXElTMRBHaiQx610FwoBhxo+50l8AvXROOQb5yWYHbvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:24:12.550481Z"},"content_sha256":"814f02f0dd10e66323f94dc60371bb63b14834574a0e569392bea5ff4dd15c33","schema_version":"1.0","event_id":"sha256:814f02f0dd10e66323f94dc60371bb63b14834574a0e569392bea5ff4dd15c33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZIOB47UYEYSB2UCD3LS7FIC6TH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric properties of Dirichlet forms under order isomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.FA","authors_text":"Daniel Lenz, Marcel Schmidt, Melchior Wirth","submitted_at":"2018-01-25T09:42:21Z","abstract_excerpt":"We study pairs of Dirichlet forms related by an intertwining order isomorphisms between the associated $L^2$-spaces. We consider the measurable, the topological and the geometric setting respectively. In the measurable setting, we deal with arbitrary (irreducible) Dirichlet forms and show that any intertwining order isomorphism is necessarily unitary (up to a constant). In the topological setting we deal with quasi-regular forms and show that any intertwining order isomorphism induces a quasi-homeomorphism between the underlying spaces. In the geometric setting we deal with both regular Dirich"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08326","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":"2026-05-18T00:25:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I9sSoiumafSy+hjIND0xMn2Ve8A/NpNyzYyijcshTE022A9lYIRV6PeHjnkui315H+npUQ/elKGieag+LZmlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:24:12.550834Z"},"content_sha256":"b2f5860cd8199d3b27acdb30eb5004df4ccdac8b3fb281ec9c364e04dc1676c5","schema_version":"1.0","event_id":"sha256:b2f5860cd8199d3b27acdb30eb5004df4ccdac8b3fb281ec9c364e04dc1676c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZIOB47UYEYSB2UCD3LS7FIC6TH/bundle.json","state_url":"https://pith.science/pith/ZIOB47UYEYSB2UCD3LS7FIC6TH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZIOB47UYEYSB2UCD3LS7FIC6TH/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":"2026-06-01T13:24:12Z","links":{"resolver":"https://pith.science/pith/ZIOB47UYEYSB2UCD3LS7FIC6TH","bundle":"https://pith.science/pith/ZIOB47UYEYSB2UCD3LS7FIC6TH/bundle.json","state":"https://pith.science/pith/ZIOB47UYEYSB2UCD3LS7FIC6TH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZIOB47UYEYSB2UCD3LS7FIC6TH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZIOB47UYEYSB2UCD3LS7FIC6TH","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":"776f3315f9bf6feb91294871fd78da50628b7d0f74b7a7e42b585ac5dfd5d98c","cross_cats_sorted":["math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-25T09:42:21Z","title_canon_sha256":"610728423d7b82344a79853b39e2cebf7a078b0f84db3e49e9a469316d53b073"},"schema_version":"1.0","source":{"id":"1801.08326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08326","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08326v1","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08326","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZIOB47UYEYSB","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZIOB47UYEYSB2UCD","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZIOB47UY","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:b2f5860cd8199d3b27acdb30eb5004df4ccdac8b3fb281ec9c364e04dc1676c5","target":"graph","created_at":"2026-05-18T00:25:06Z","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 pairs of Dirichlet forms related by an intertwining order isomorphisms between the associated $L^2$-spaces. We consider the measurable, the topological and the geometric setting respectively. In the measurable setting, we deal with arbitrary (irreducible) Dirichlet forms and show that any intertwining order isomorphism is necessarily unitary (up to a constant). In the topological setting we deal with quasi-regular forms and show that any intertwining order isomorphism induces a quasi-homeomorphism between the underlying spaces. In the geometric setting we deal with both regular Dirich","authors_text":"Daniel Lenz, Marcel Schmidt, Melchior Wirth","cross_cats":["math.AP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-25T09:42:21Z","title":"Geometric properties of Dirichlet forms under order isomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08326","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":"sha256:814f02f0dd10e66323f94dc60371bb63b14834574a0e569392bea5ff4dd15c33","target":"record","created_at":"2026-05-18T00:25:06Z","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":"776f3315f9bf6feb91294871fd78da50628b7d0f74b7a7e42b585ac5dfd5d98c","cross_cats_sorted":["math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-25T09:42:21Z","title_canon_sha256":"610728423d7b82344a79853b39e2cebf7a078b0f84db3e49e9a469316d53b073"},"schema_version":"1.0","source":{"id":"1801.08326","kind":"arxiv","version":1}},"canonical_sha256":"ca1c1e7e9826241d5043dae5f2a05e99f40e708aadde2dfa5864fccc9dfbbff0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca1c1e7e9826241d5043dae5f2a05e99f40e708aadde2dfa5864fccc9dfbbff0","first_computed_at":"2026-05-18T00:25:06.559409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:06.559409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mpPscaZod0g+DdtwjF5b0qM9q13mQEuUq0t5JgVMOVDo5i2CmjYbrjSmCOcA7Oed4/8tGVSQWFCV/fDZXjEJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:06.559832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:814f02f0dd10e66323f94dc60371bb63b14834574a0e569392bea5ff4dd15c33","sha256:b2f5860cd8199d3b27acdb30eb5004df4ccdac8b3fb281ec9c364e04dc1676c5"],"state_sha256":"539925642d144d94fab64e4f65cac5a25a8ac3d989139dcfb200a70beda0e886"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/AxvfehhZNvSCj+o0hzMlgfS7iYXxEOgGZeeOGjIKea8rh/ToKAmrdB+uomO5Ku9nbePhyCz6dsvUIV0/4meDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:24:12.552987Z","bundle_sha256":"448cae6bb4b285c119441cdc1a9240087cbd45ff261f2f2eb0b700f63bf524f0"}}