{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TUWNMC4KKQZCSTLQSKRTOGKQKX","short_pith_number":"pith:TUWNMC4K","canonical_record":{"source":{"id":"1402.3185","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T15:44:33Z","cross_cats_sorted":[],"title_canon_sha256":"f61ea04a5a22aa3b0c09180443c1c2773437c6e6d864076b421ecc824cee3560","abstract_canon_sha256":"310b70c4e86170e6f4b4e3692db52a0db454991377486bc59ac6e894e1bf2391"},"schema_version":"1.0"},"canonical_sha256":"9d2cd60b8a5432294d7092a337195055d7a96fcd1228e93156f32b8e1e7ca5ae","source":{"kind":"arxiv","id":"1402.3185","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3185","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3185v2","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3185","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"pith_short_12","alias_value":"TUWNMC4KKQZC","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TUWNMC4KKQZCSTLQ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TUWNMC4K","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TUWNMC4KKQZCSTLQSKRTOGKQKX","target":"record","payload":{"canonical_record":{"source":{"id":"1402.3185","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T15:44:33Z","cross_cats_sorted":[],"title_canon_sha256":"f61ea04a5a22aa3b0c09180443c1c2773437c6e6d864076b421ecc824cee3560","abstract_canon_sha256":"310b70c4e86170e6f4b4e3692db52a0db454991377486bc59ac6e894e1bf2391"},"schema_version":"1.0"},"canonical_sha256":"9d2cd60b8a5432294d7092a337195055d7a96fcd1228e93156f32b8e1e7ca5ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:14.262134Z","signature_b64":"B3R1HBgfpr4casgr2IhIhtIAEeOVtYxTWzbjpSSAsy6AOWQ8bRWfghx9HssTl3CR4y21OYFEiEIZzTHerVZWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d2cd60b8a5432294d7092a337195055d7a96fcd1228e93156f32b8e1e7ca5ae","last_reissued_at":"2026-05-18T02:45:14.261494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:14.261494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.3185","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5KJ6q0z3qCWvCwnJM8axs2q8bj3T8O/f8Q1tVvHQohB16e4M1aJvLYW609XmH470IJPU5unOMLoK+822P/HhBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T14:24:44.725946Z"},"content_sha256":"88c830b86eac97ae907e8a9a4c2791c8fec6b14fcef6ca3811517268668d14b0","schema_version":"1.0","event_id":"sha256:88c830b86eac97ae907e8a9a4c2791c8fec6b14fcef6ca3811517268668d14b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TUWNMC4KKQZCSTLQSKRTOGKQKX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The L^p-Poincar\\'e inequality for analytic Ornstein-Uhlenbeck operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jan van Neerven","submitted_at":"2014-02-13T15:44:33Z","abstract_excerpt":"Consider the linear stochastic evolution equation dU(t) = AU(t) + dW_H(t), t\\ge 0, where A generates a C_0-semigroup on a Banach space E and W_H is a cylindrical Brownian motion in a continuously embedded Hilbert subspace H of E. Under the assumption that the solutions to this equation admit an invariant measure \\mu_\\infty we prove that if the associated Ornstein-Uhlenbeck semigroup is analytic and has compact resolvent, then the Poincar\\'e inequality \\n f - \\overline f\\n_{L^p(E,\\mu_\\infty)} \\le \\n D_H f\\n_{L^p(E,\\mu_\\infty)} holds for all 1<p<\\infty. Here \\overline f denotes the average of f "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3185","kind":"arxiv","version":2},"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":"2026-05-18T02:45:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mx11XMQJUWYNcD0+4N6mu3tcFv0/PqHhbZOFAyzGJVxzT/xKVLY+TFK4mqPec2UY17hpMZ3uyf0nGCn0zdrYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T14:24:44.726293Z"},"content_sha256":"e18fd3c7d066b03e6a7f8e504ea54ed5c71447870df01b7a145a8280ca3af0e8","schema_version":"1.0","event_id":"sha256:e18fd3c7d066b03e6a7f8e504ea54ed5c71447870df01b7a145a8280ca3af0e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TUWNMC4KKQZCSTLQSKRTOGKQKX/bundle.json","state_url":"https://pith.science/pith/TUWNMC4KKQZCSTLQSKRTOGKQKX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TUWNMC4KKQZCSTLQSKRTOGKQKX/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":"2026-07-04T14:24:44Z","links":{"resolver":"https://pith.science/pith/TUWNMC4KKQZCSTLQSKRTOGKQKX","bundle":"https://pith.science/pith/TUWNMC4KKQZCSTLQSKRTOGKQKX/bundle.json","state":"https://pith.science/pith/TUWNMC4KKQZCSTLQSKRTOGKQKX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TUWNMC4KKQZCSTLQSKRTOGKQKX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TUWNMC4KKQZCSTLQSKRTOGKQKX","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":"310b70c4e86170e6f4b4e3692db52a0db454991377486bc59ac6e894e1bf2391","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T15:44:33Z","title_canon_sha256":"f61ea04a5a22aa3b0c09180443c1c2773437c6e6d864076b421ecc824cee3560"},"schema_version":"1.0","source":{"id":"1402.3185","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3185","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3185v2","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3185","created_at":"2026-05-18T02:45:14Z"},{"alias_kind":"pith_short_12","alias_value":"TUWNMC4KKQZC","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TUWNMC4KKQZCSTLQ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TUWNMC4K","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:e18fd3c7d066b03e6a7f8e504ea54ed5c71447870df01b7a145a8280ca3af0e8","target":"graph","created_at":"2026-05-18T02:45:14Z","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":"Consider the linear stochastic evolution equation dU(t) = AU(t) + dW_H(t), t\\ge 0, where A generates a C_0-semigroup on a Banach space E and W_H is a cylindrical Brownian motion in a continuously embedded Hilbert subspace H of E. Under the assumption that the solutions to this equation admit an invariant measure \\mu_\\infty we prove that if the associated Ornstein-Uhlenbeck semigroup is analytic and has compact resolvent, then the Poincar\\'e inequality \\n f - \\overline f\\n_{L^p(E,\\mu_\\infty)} \\le \\n D_H f\\n_{L^p(E,\\mu_\\infty)} holds for all 1<p<\\infty. Here \\overline f denotes the average of f ","authors_text":"Jan van Neerven","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T15:44:33Z","title":"The L^p-Poincar\\'e inequality for analytic Ornstein-Uhlenbeck operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3185","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":"sha256:88c830b86eac97ae907e8a9a4c2791c8fec6b14fcef6ca3811517268668d14b0","target":"record","created_at":"2026-05-18T02:45:14Z","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":"310b70c4e86170e6f4b4e3692db52a0db454991377486bc59ac6e894e1bf2391","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T15:44:33Z","title_canon_sha256":"f61ea04a5a22aa3b0c09180443c1c2773437c6e6d864076b421ecc824cee3560"},"schema_version":"1.0","source":{"id":"1402.3185","kind":"arxiv","version":2}},"canonical_sha256":"9d2cd60b8a5432294d7092a337195055d7a96fcd1228e93156f32b8e1e7ca5ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d2cd60b8a5432294d7092a337195055d7a96fcd1228e93156f32b8e1e7ca5ae","first_computed_at":"2026-05-18T02:45:14.261494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:14.261494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3R1HBgfpr4casgr2IhIhtIAEeOVtYxTWzbjpSSAsy6AOWQ8bRWfghx9HssTl3CR4y21OYFEiEIZzTHerVZWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:14.262134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3185","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88c830b86eac97ae907e8a9a4c2791c8fec6b14fcef6ca3811517268668d14b0","sha256:e18fd3c7d066b03e6a7f8e504ea54ed5c71447870df01b7a145a8280ca3af0e8"],"state_sha256":"b447d3f4774e1f14a38756e5254e77be1f0a5c90c00f64e997e2c166e1f36a0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RpL8s1ouqR0941YoDgw1JJ7D8eDKOQjctDkrZlso8gieh4MrkNm5waA32eMTY3H9YHk6IV9jgGEahmToqUMkCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T14:24:44.728331Z","bundle_sha256":"509532a007b55c3a2a35307cc474a5d0959fd01e3a8f40d8ffb0ef941e8e882a"}}