{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XKYFLPROPQ7KD3KLG2HXTY55JO","short_pith_number":"pith:XKYFLPRO","canonical_record":{"source":{"id":"1301.1180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-07T13:10:23Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"908998355b3bb77d90e45da0ba36faa2cbaa24808d1599c0700a0c1937f4fa15","abstract_canon_sha256":"dbf49df5e24656f66fe35cb1dd1b0404d374891764edac37c13cc411671bbc4a"},"schema_version":"1.0"},"canonical_sha256":"bab055be2e7c3ea1ed4b368f79e3bd4bbf1555a23427073fe8b5beb83d28af53","source":{"kind":"arxiv","id":"1301.1180","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1180","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1180v1","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1180","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"XKYFLPROPQ7K","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XKYFLPROPQ7KD3KL","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XKYFLPRO","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XKYFLPROPQ7KD3KLG2HXTY55JO","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-07T13:10:23Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"908998355b3bb77d90e45da0ba36faa2cbaa24808d1599c0700a0c1937f4fa15","abstract_canon_sha256":"dbf49df5e24656f66fe35cb1dd1b0404d374891764edac37c13cc411671bbc4a"},"schema_version":"1.0"},"canonical_sha256":"bab055be2e7c3ea1ed4b368f79e3bd4bbf1555a23427073fe8b5beb83d28af53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:04.855898Z","signature_b64":"eUFktMKbapuEP1L0uYCoycIpeixixby4DIrjWPnv6jDJmVIppbasJmvGG0VQs9xcTO3bmASxOXatEXXwvVfdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bab055be2e7c3ea1ed4b368f79e3bd4bbf1555a23427073fe8b5beb83d28af53","last_reissued_at":"2026-05-18T01:18:04.855180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:04.855180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1180","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":"2026-05-18T01:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yrygeo44izr9/HChe6WWlGjPUFA9wzbqQ3iDDXrllhzJ740MLI/Jr7lIcekt3doeIMBrB/12igOfGaiqaHEhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:11:06.425251Z"},"content_sha256":"e5b864882f4986aeb312c8a92c3292018453bdd1d12f1fc902b33ad0038b94ef","schema_version":"1.0","event_id":"sha256:e5b864882f4986aeb312c8a92c3292018453bdd1d12f1fc902b33ad0038b94ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XKYFLPROPQ7KD3KLG2HXTY55JO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Lq(Lp)-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NA"],"primary_cat":"math.PR","authors_text":"Felix Lindner, Kijung Lee, Kyeong-Hun Kim, Petru A. Cioica","submitted_at":"2013-01-07T13:10:23Z","abstract_excerpt":"We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains $O \\subset R^d$ with both theoretical and numerical purpose. We use N.V. Krylov's framework of stochastic parabolic weighted Sobolev spaces $\\mathfrak{H}^{\\gamma,q}_{p,\\theta}(O;T)$. The summability parameters p and q in space and time may differ. Existence and uniqueness of solutions in these spaces is established and the H\\\"older regularity in time is analysed. Moreover, we prove a general embedding of weighted Lp(O)-Sobolev spaces into the scale of Besov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1180","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":"2026-05-18T01:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8B2KJrWYD0vw62TzsR7XCnjhOEzFlnqQNeqApEGb8Xhk3HVVpIneLIXq+Ly3FYvYtf1UwvanaHUe7xdPCqJNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:11:06.425931Z"},"content_sha256":"e40cadf0eb0319a43ea86e59366948b98797ae20f191887c92f9769e27d80a43","schema_version":"1.0","event_id":"sha256:e40cadf0eb0319a43ea86e59366948b98797ae20f191887c92f9769e27d80a43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XKYFLPROPQ7KD3KLG2HXTY55JO/bundle.json","state_url":"https://pith.science/pith/XKYFLPROPQ7KD3KLG2HXTY55JO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XKYFLPROPQ7KD3KLG2HXTY55JO/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":"2026-05-27T02:11:06Z","links":{"resolver":"https://pith.science/pith/XKYFLPROPQ7KD3KLG2HXTY55JO","bundle":"https://pith.science/pith/XKYFLPROPQ7KD3KLG2HXTY55JO/bundle.json","state":"https://pith.science/pith/XKYFLPROPQ7KD3KLG2HXTY55JO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XKYFLPROPQ7KD3KLG2HXTY55JO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XKYFLPROPQ7KD3KLG2HXTY55JO","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":"dbf49df5e24656f66fe35cb1dd1b0404d374891764edac37c13cc411671bbc4a","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-07T13:10:23Z","title_canon_sha256":"908998355b3bb77d90e45da0ba36faa2cbaa24808d1599c0700a0c1937f4fa15"},"schema_version":"1.0","source":{"id":"1301.1180","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1180","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1180v1","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1180","created_at":"2026-05-18T01:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"XKYFLPROPQ7K","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XKYFLPROPQ7KD3KL","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XKYFLPRO","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:e40cadf0eb0319a43ea86e59366948b98797ae20f191887c92f9769e27d80a43","target":"graph","created_at":"2026-05-18T01:18:04Z","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 investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains $O \\subset R^d$ with both theoretical and numerical purpose. We use N.V. Krylov's framework of stochastic parabolic weighted Sobolev spaces $\\mathfrak{H}^{\\gamma,q}_{p,\\theta}(O;T)$. The summability parameters p and q in space and time may differ. Existence and uniqueness of solutions in these spaces is established and the H\\\"older regularity in time is analysed. Moreover, we prove a general embedding of weighted Lp(O)-Sobolev spaces into the scale of Besov","authors_text":"Felix Lindner, Kijung Lee, Kyeong-Hun Kim, Petru A. Cioica","cross_cats":["math.AP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-07T13:10:23Z","title":"On the Lq(Lp)-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1180","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:e5b864882f4986aeb312c8a92c3292018453bdd1d12f1fc902b33ad0038b94ef","target":"record","created_at":"2026-05-18T01:18:04Z","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":"dbf49df5e24656f66fe35cb1dd1b0404d374891764edac37c13cc411671bbc4a","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-07T13:10:23Z","title_canon_sha256":"908998355b3bb77d90e45da0ba36faa2cbaa24808d1599c0700a0c1937f4fa15"},"schema_version":"1.0","source":{"id":"1301.1180","kind":"arxiv","version":1}},"canonical_sha256":"bab055be2e7c3ea1ed4b368f79e3bd4bbf1555a23427073fe8b5beb83d28af53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bab055be2e7c3ea1ed4b368f79e3bd4bbf1555a23427073fe8b5beb83d28af53","first_computed_at":"2026-05-18T01:18:04.855180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:04.855180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eUFktMKbapuEP1L0uYCoycIpeixixby4DIrjWPnv6jDJmVIppbasJmvGG0VQs9xcTO3bmASxOXatEXXwvVfdAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:04.855898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1180","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5b864882f4986aeb312c8a92c3292018453bdd1d12f1fc902b33ad0038b94ef","sha256:e40cadf0eb0319a43ea86e59366948b98797ae20f191887c92f9769e27d80a43"],"state_sha256":"1db06b4ecec23b144c08cc1da02c49d7d3bde70f4a45688e710a55b6999c8070"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CE8aS4UxMU1QJiznTg3RPZZcsWuHiHi/qn5GRtKb1fuBKFA657oh2xmzm++/bJU2IvKmDXpWYvAIERN7YBCiAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:11:06.429511Z","bundle_sha256":"c2ecf0e7c4dba60b7bfbfa8ef945accbe5ccaedc298d7dfbc780576214566ec5"}}