{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BNVNRJZ6ZFBMGMFWWOBCF34W7S","short_pith_number":"pith:BNVNRJZ6","canonical_record":{"source":{"id":"1503.02369","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2015-03-09T04:05:12Z","cross_cats_sorted":[],"title_canon_sha256":"fb2fcb0734adbe961c24ed726928584342535d5fc4d05002a9e7653addcf13ef","abstract_canon_sha256":"f51ac91ac2975d88cecf747d86f078f449e0119f46bc0350a062569f86dbcf20"},"schema_version":"1.0"},"canonical_sha256":"0b6ad8a73ec942c330b6b38222ef96fc8020819e59d1f3e15ad62f12bc3bd11c","source":{"kind":"arxiv","id":"1503.02369","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02369","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02369v1","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02369","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"BNVNRJZ6ZFBM","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BNVNRJZ6ZFBMGMFW","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BNVNRJZ6","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BNVNRJZ6ZFBMGMFWWOBCF34W7S","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02369","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2015-03-09T04:05:12Z","cross_cats_sorted":[],"title_canon_sha256":"fb2fcb0734adbe961c24ed726928584342535d5fc4d05002a9e7653addcf13ef","abstract_canon_sha256":"f51ac91ac2975d88cecf747d86f078f449e0119f46bc0350a062569f86dbcf20"},"schema_version":"1.0"},"canonical_sha256":"0b6ad8a73ec942c330b6b38222ef96fc8020819e59d1f3e15ad62f12bc3bd11c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:25.274142Z","signature_b64":"9e3FtA7cl3B1UK1BiNsUW6WG/Jy+c90H7F1ThwJwnROuqjJtb4PYdwmBl9eOonO1HxbuvcBekRTT4ZX9IQLPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b6ad8a73ec942c330b6b38222ef96fc8020819e59d1f3e15ad62f12bc3bd11c","last_reissued_at":"2026-05-18T02:25:25.273718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:25.273718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02369","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":"2026-05-18T02:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lvQ/THc8Gy8Vg4xWui81d/Jh5VpMNHTAvNggSBP1bKgzrDJD//OdFRyDI/NdCsofxpjZdybThxhfNg9K4sSqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:53:12.114240Z"},"content_sha256":"1eb1220ecb2187ee71a31e05df64800f1445a13f1a9f2244439ce6bb80002a77","schema_version":"1.0","event_id":"sha256:1eb1220ecb2187ee71a31e05df64800f1445a13f1a9f2244439ce6bb80002a77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BNVNRJZ6ZFBMGMFWWOBCF34W7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parabolic Littlewood-Paley inequality for a class of time-dependent operators of arbitrary order, and applications to higher order stochastic PDE","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim","submitted_at":"2015-03-09T04:05:12Z","abstract_excerpt":"In this paper we prove a parabolic version of the Littlewood-Paley inequality for a class of time-dependent local and non-local operators of arbitrary order, and as an application we show this inequality gives a fundamental estimate for the $L_p$-theory of the stochastic partial differential equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02369","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":"2026-05-18T02:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jrDzT3IhPbw1l/AcbvKft7H0Mr+DGKUMP7GEY9IKaKa9VLsdHXi/QtOm4Kk3docfFo7jV+BzbUekKYmLjFihBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:53:12.114640Z"},"content_sha256":"b8cb3aa079461f28753bef4222a311384773922dd00bbf5dc0effb73f1ca3f49","schema_version":"1.0","event_id":"sha256:b8cb3aa079461f28753bef4222a311384773922dd00bbf5dc0effb73f1ca3f49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNVNRJZ6ZFBMGMFWWOBCF34W7S/bundle.json","state_url":"https://pith.science/pith/BNVNRJZ6ZFBMGMFWWOBCF34W7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNVNRJZ6ZFBMGMFWWOBCF34W7S/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":"2026-05-30T15:53:12Z","links":{"resolver":"https://pith.science/pith/BNVNRJZ6ZFBMGMFWWOBCF34W7S","bundle":"https://pith.science/pith/BNVNRJZ6ZFBMGMFWWOBCF34W7S/bundle.json","state":"https://pith.science/pith/BNVNRJZ6ZFBMGMFWWOBCF34W7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNVNRJZ6ZFBMGMFWWOBCF34W7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BNVNRJZ6ZFBMGMFWWOBCF34W7S","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":"f51ac91ac2975d88cecf747d86f078f449e0119f46bc0350a062569f86dbcf20","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2015-03-09T04:05:12Z","title_canon_sha256":"fb2fcb0734adbe961c24ed726928584342535d5fc4d05002a9e7653addcf13ef"},"schema_version":"1.0","source":{"id":"1503.02369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02369","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02369v1","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02369","created_at":"2026-05-18T02:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"BNVNRJZ6ZFBM","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BNVNRJZ6ZFBMGMFW","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BNVNRJZ6","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:b8cb3aa079461f28753bef4222a311384773922dd00bbf5dc0effb73f1ca3f49","target":"graph","created_at":"2026-05-18T02:25:25Z","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":"In this paper we prove a parabolic version of the Littlewood-Paley inequality for a class of time-dependent local and non-local operators of arbitrary order, and as an application we show this inequality gives a fundamental estimate for the $L_p$-theory of the stochastic partial differential equations.","authors_text":"Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2015-03-09T04:05:12Z","title":"Parabolic Littlewood-Paley inequality for a class of time-dependent operators of arbitrary order, and applications to higher order stochastic PDE"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02369","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":"sha256:1eb1220ecb2187ee71a31e05df64800f1445a13f1a9f2244439ce6bb80002a77","target":"record","created_at":"2026-05-18T02:25:25Z","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":"f51ac91ac2975d88cecf747d86f078f449e0119f46bc0350a062569f86dbcf20","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2015-03-09T04:05:12Z","title_canon_sha256":"fb2fcb0734adbe961c24ed726928584342535d5fc4d05002a9e7653addcf13ef"},"schema_version":"1.0","source":{"id":"1503.02369","kind":"arxiv","version":1}},"canonical_sha256":"0b6ad8a73ec942c330b6b38222ef96fc8020819e59d1f3e15ad62f12bc3bd11c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b6ad8a73ec942c330b6b38222ef96fc8020819e59d1f3e15ad62f12bc3bd11c","first_computed_at":"2026-05-18T02:25:25.273718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:25.273718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9e3FtA7cl3B1UK1BiNsUW6WG/Jy+c90H7F1ThwJwnROuqjJtb4PYdwmBl9eOonO1HxbuvcBekRTT4ZX9IQLPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:25.274142Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1eb1220ecb2187ee71a31e05df64800f1445a13f1a9f2244439ce6bb80002a77","sha256:b8cb3aa079461f28753bef4222a311384773922dd00bbf5dc0effb73f1ca3f49"],"state_sha256":"6ed46e4b265f737bfa5a46bea5af2d1a038e922ee221de96eb3f89f70754a7c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qUP8RawQC4r5R02cAzYyvvCqRciqz6/rmiWklAWKznHuP9BmPrV811ZzA/OY/B1o9tu948IUyJ/vC94JL7yWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:53:12.117111Z","bundle_sha256":"105c27424a0870884453e3da24fe265f064b3e573d93a8df7e3dace475974d9e"}}