{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:I6EOVDPQQ3O3EUYV7HONJIDP7V","short_pith_number":"pith:I6EOVDPQ","canonical_record":{"source":{"id":"1905.07545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-18T07:29:14Z","cross_cats_sorted":[],"title_canon_sha256":"cc1b31d603e49c301f3269173773e2e0041cafaa26f956fdb7014e094d5e31d8","abstract_canon_sha256":"00aa6cee36472a6fe9bb6be2cb8db5b5d655cd37697fb7e6649a5e0b98854e84"},"schema_version":"1.0"},"canonical_sha256":"4788ea8df086ddb25315f9dcd4a06ffd632c4b98d0c35cedd23456ec47899092","source":{"kind":"arxiv","id":"1905.07545","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07545","created_at":"2026-05-17T23:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07545v1","created_at":"2026-05-17T23:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07545","created_at":"2026-05-17T23:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"I6EOVDPQQ3O3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I6EOVDPQQ3O3EUYV","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I6EOVDPQ","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:I6EOVDPQQ3O3EUYV7HONJIDP7V","target":"record","payload":{"canonical_record":{"source":{"id":"1905.07545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-18T07:29:14Z","cross_cats_sorted":[],"title_canon_sha256":"cc1b31d603e49c301f3269173773e2e0041cafaa26f956fdb7014e094d5e31d8","abstract_canon_sha256":"00aa6cee36472a6fe9bb6be2cb8db5b5d655cd37697fb7e6649a5e0b98854e84"},"schema_version":"1.0"},"canonical_sha256":"4788ea8df086ddb25315f9dcd4a06ffd632c4b98d0c35cedd23456ec47899092","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:49.387419Z","signature_b64":"ipZRPITvYMTwQT6K9s5gKHiynApJeAAE8Zx3DY1hJ6A4wPN0cqI4/Y+Tc034e2vhNM9Lokumjv1BrYMy9ZZIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4788ea8df086ddb25315f9dcd4a06ffd632c4b98d0c35cedd23456ec47899092","last_reissued_at":"2026-05-17T23:45:49.386578Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:49.386578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.07545","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":"2026-05-17T23:45:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RzTqDMFYTiK9gwBIYPyz8OFxNRsjeuf3xneaJijDylAWHLZYTurKVfT2aWxAtmUwFSkwoMpGGQu83xfzQFB5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:34:18.662632Z"},"content_sha256":"d1aa62f0885dc2ad3bdfea68a1d4b526a5300ca883910da43fbf790061c647b2","schema_version":"1.0","event_id":"sha256:d1aa62f0885dc2ad3bdfea68a1d4b526a5300ca883910da43fbf790061c647b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:I6EOVDPQQ3O3EUYV7HONJIDP7V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A sharp $L_p$-regularity result for second-order stochastic partial differential equations with unbounded and fully degenerate leading coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ildoo Kim, Kyeong-Hun Kim","submitted_at":"2019-05-18T07:29:14Z","abstract_excerpt":"We present existence, uniqueness, and sharp regularity results of solution\n  to the stochastic partial differential equation (SPDE)\n  \\begin{align}\n  \\label{abs eqn}\n  du=(a^{ij}(\\omega,t)u_{x^ix^j}+f)dt + (\\sigma^{ik}(\\omega,t)u_{x^i}+g^k)dw^k_t, \\quad u(0,x)=u_0,\n  \\end{align}\n  where $\\{w^k_t:k=1,2,\\cdots\\}$ is a sequence of independent Brownian motions. The coefficients are merely measurable in $(\\omega,t)$ and can be unbounded and fully degenerate, that is, coefficients $a^{ij}$, $\\sigma^{ik}$ merely satisfy\n  \\begin{align}\n  \\label{abs only} \\left(\\alpha^{ij}(\\omega,t)\\right)_{d\\times d}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07545","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":"2026-05-17T23:45:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sqIdJ5eCmAlhxQ3jAUU89G3ydnX0Bigwq8+Y5fFbW83z3M8pYVTXLQtd0PTljDwU8JydzWe3tiNS28z3Fb+ADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:34:18.663002Z"},"content_sha256":"0f98dcb4ade8e158ad8f954a7b71ae0576490dd87ddbd6fd51df1811371ed30c","schema_version":"1.0","event_id":"sha256:0f98dcb4ade8e158ad8f954a7b71ae0576490dd87ddbd6fd51df1811371ed30c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I6EOVDPQQ3O3EUYV7HONJIDP7V/bundle.json","state_url":"https://pith.science/pith/I6EOVDPQQ3O3EUYV7HONJIDP7V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I6EOVDPQQ3O3EUYV7HONJIDP7V/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":"2026-05-27T05:34:18Z","links":{"resolver":"https://pith.science/pith/I6EOVDPQQ3O3EUYV7HONJIDP7V","bundle":"https://pith.science/pith/I6EOVDPQQ3O3EUYV7HONJIDP7V/bundle.json","state":"https://pith.science/pith/I6EOVDPQQ3O3EUYV7HONJIDP7V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I6EOVDPQQ3O3EUYV7HONJIDP7V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:I6EOVDPQQ3O3EUYV7HONJIDP7V","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":"00aa6cee36472a6fe9bb6be2cb8db5b5d655cd37697fb7e6649a5e0b98854e84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-18T07:29:14Z","title_canon_sha256":"cc1b31d603e49c301f3269173773e2e0041cafaa26f956fdb7014e094d5e31d8"},"schema_version":"1.0","source":{"id":"1905.07545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07545","created_at":"2026-05-17T23:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07545v1","created_at":"2026-05-17T23:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07545","created_at":"2026-05-17T23:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"I6EOVDPQQ3O3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I6EOVDPQQ3O3EUYV","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I6EOVDPQ","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:0f98dcb4ade8e158ad8f954a7b71ae0576490dd87ddbd6fd51df1811371ed30c","target":"graph","created_at":"2026-05-17T23:45:49Z","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 present existence, uniqueness, and sharp regularity results of solution\n  to the stochastic partial differential equation (SPDE)\n  \\begin{align}\n  \\label{abs eqn}\n  du=(a^{ij}(\\omega,t)u_{x^ix^j}+f)dt + (\\sigma^{ik}(\\omega,t)u_{x^i}+g^k)dw^k_t, \\quad u(0,x)=u_0,\n  \\end{align}\n  where $\\{w^k_t:k=1,2,\\cdots\\}$ is a sequence of independent Brownian motions. The coefficients are merely measurable in $(\\omega,t)$ and can be unbounded and fully degenerate, that is, coefficients $a^{ij}$, $\\sigma^{ik}$ merely satisfy\n  \\begin{align}\n  \\label{abs only} \\left(\\alpha^{ij}(\\omega,t)\\right)_{d\\times d}","authors_text":"Ildoo Kim, Kyeong-Hun Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-18T07:29:14Z","title":"A sharp $L_p$-regularity result for second-order stochastic partial differential equations with unbounded and fully degenerate leading coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07545","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:d1aa62f0885dc2ad3bdfea68a1d4b526a5300ca883910da43fbf790061c647b2","target":"record","created_at":"2026-05-17T23:45:49Z","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":"00aa6cee36472a6fe9bb6be2cb8db5b5d655cd37697fb7e6649a5e0b98854e84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-18T07:29:14Z","title_canon_sha256":"cc1b31d603e49c301f3269173773e2e0041cafaa26f956fdb7014e094d5e31d8"},"schema_version":"1.0","source":{"id":"1905.07545","kind":"arxiv","version":1}},"canonical_sha256":"4788ea8df086ddb25315f9dcd4a06ffd632c4b98d0c35cedd23456ec47899092","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4788ea8df086ddb25315f9dcd4a06ffd632c4b98d0c35cedd23456ec47899092","first_computed_at":"2026-05-17T23:45:49.386578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:49.386578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ipZRPITvYMTwQT6K9s5gKHiynApJeAAE8Zx3DY1hJ6A4wPN0cqI4/Y+Tc034e2vhNM9Lokumjv1BrYMy9ZZIAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:49.387419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1aa62f0885dc2ad3bdfea68a1d4b526a5300ca883910da43fbf790061c647b2","sha256:0f98dcb4ade8e158ad8f954a7b71ae0576490dd87ddbd6fd51df1811371ed30c"],"state_sha256":"8aa2645aab4764025cddcb71d5b898b0e1da81264f94d5508014288d31959d40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W0oynrLoZ/G1m4KrjeTYxkyRQX2C2zlbxZUEfAwBJKGRpCT0CL+NtjCQwc1qZLDbOs7yn1VcptoRZjPlFNXZCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:34:18.666139Z","bundle_sha256":"298b7066708393bb1db77f0dab797efaf5771bc401e8a30ef70709d7052c993f"}}