{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CFFA6XZ3G6SF2KPJJBYGUZFD3E","short_pith_number":"pith:CFFA6XZ3","canonical_record":{"source":{"id":"1705.01243","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-03T03:13:17Z","cross_cats_sorted":[],"title_canon_sha256":"37f17dff04c491d4c75fd35ba280cd6c1a47655c7ec7a5ec52eb68485ed7c2c3","abstract_canon_sha256":"cdc6af7df1ded28f62e9c645f34311da65577abf2f16ce3182126bc5b4c260b9"},"schema_version":"1.0"},"canonical_sha256":"114a0f5f3b37a45d29e948706a64a3d91c9daf261e17021b6c944ab534450a0f","source":{"kind":"arxiv","id":"1705.01243","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01243","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01243v2","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01243","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"CFFA6XZ3G6SF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CFFA6XZ3G6SF2KPJ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CFFA6XZ3","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CFFA6XZ3G6SF2KPJJBYGUZFD3E","target":"record","payload":{"canonical_record":{"source":{"id":"1705.01243","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-03T03:13:17Z","cross_cats_sorted":[],"title_canon_sha256":"37f17dff04c491d4c75fd35ba280cd6c1a47655c7ec7a5ec52eb68485ed7c2c3","abstract_canon_sha256":"cdc6af7df1ded28f62e9c645f34311da65577abf2f16ce3182126bc5b4c260b9"},"schema_version":"1.0"},"canonical_sha256":"114a0f5f3b37a45d29e948706a64a3d91c9daf261e17021b6c944ab534450a0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:55.891854Z","signature_b64":"uxO/eOPuVJBQyx+hJafihphln+rl+nqNKGWIwpnD/tJWnfD27W9U+4SZQiNJNREwuebtO5KldK+m6I7NwvfOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"114a0f5f3b37a45d29e948706a64a3d91c9daf261e17021b6c944ab534450a0f","last_reissued_at":"2026-05-18T00:31:55.891356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:55.891356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.01243","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":"2026-05-18T00:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hu57W1MADuGpjUBbIi0Z7zugi5REnppLeLYZsW5b2Y3tcAcMJytuVUiOpsDlc0Go55ENcK+M75k+caawiI5kCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:16:10.849159Z"},"content_sha256":"52a2a324a9cfaac5bfd940f95dbd2211b88032e2d98bff1ce81f5c86d96bbec5","schema_version":"1.0","event_id":"sha256:52a2a324a9cfaac5bfd940f95dbd2211b88032e2d98bff1ce81f5c86d96bbec5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CFFA6XZ3G6SF2KPJJBYGUZFD3E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An $L_p$-theory for diffusion equations related to stochastic processes with non-stationary independent increment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ildoo Kim, Kyeong-Hun Kim, Panki Kim","submitted_at":"2017-05-03T03:13:17Z","abstract_excerpt":"Let $X=(X_t)_{t \\ge 0}$ be a stochastic process which has an (not necessarily stationary) independent increment on a probability space $(\\Omega, \\mathbb{P})$. In this paper, we study the following Cauchy problem related to the stochastic process $X$:\n  $\\label{main eqn} \\frac{\\partial u}{\\partial t}(t,x) = \\cA(t)u(t,x) +f(t,x), \\quad u(0,\\cdot)=0, \\quad (t,x) \\in (0,T) \\times \\mathbf{R}^d, \\end{align} where $f \\in L_p( (0,T) ; L_p(\\mathbf{R}^d))=L_p( (0,T) ; L_p)$ and \\begin{align*} \\cA(t)u(t,x) = \\lim_{h \\downarrow 0}\\frac{\\mathbb{E}\\left[u(t,x+X_{t+h}-X_t)-u(t,x)\\right]}{h}$. We provide a su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01243","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":"2026-05-18T00:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zXHxU1wwdESYtBiBauep2drAggtDMI0E1ymw32pA4hy0BBAqojgH9y2RHZNW/2RiVJNsN0mXC9WQQF1xFl2tBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:16:10.849748Z"},"content_sha256":"7e9046e3d390d6d76ee611969e84246582b936dce2f2bad73c64a6ecc11b2fbd","schema_version":"1.0","event_id":"sha256:7e9046e3d390d6d76ee611969e84246582b936dce2f2bad73c64a6ecc11b2fbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFFA6XZ3G6SF2KPJJBYGUZFD3E/bundle.json","state_url":"https://pith.science/pith/CFFA6XZ3G6SF2KPJJBYGUZFD3E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFFA6XZ3G6SF2KPJJBYGUZFD3E/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":"2026-05-27T14:16:10Z","links":{"resolver":"https://pith.science/pith/CFFA6XZ3G6SF2KPJJBYGUZFD3E","bundle":"https://pith.science/pith/CFFA6XZ3G6SF2KPJJBYGUZFD3E/bundle.json","state":"https://pith.science/pith/CFFA6XZ3G6SF2KPJJBYGUZFD3E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFFA6XZ3G6SF2KPJJBYGUZFD3E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CFFA6XZ3G6SF2KPJJBYGUZFD3E","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":"cdc6af7df1ded28f62e9c645f34311da65577abf2f16ce3182126bc5b4c260b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-03T03:13:17Z","title_canon_sha256":"37f17dff04c491d4c75fd35ba280cd6c1a47655c7ec7a5ec52eb68485ed7c2c3"},"schema_version":"1.0","source":{"id":"1705.01243","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01243","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01243v2","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01243","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"CFFA6XZ3G6SF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CFFA6XZ3G6SF2KPJ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CFFA6XZ3","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:7e9046e3d390d6d76ee611969e84246582b936dce2f2bad73c64a6ecc11b2fbd","target":"graph","created_at":"2026-05-18T00:31:55Z","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":"Let $X=(X_t)_{t \\ge 0}$ be a stochastic process which has an (not necessarily stationary) independent increment on a probability space $(\\Omega, \\mathbb{P})$. In this paper, we study the following Cauchy problem related to the stochastic process $X$:\n  $\\label{main eqn} \\frac{\\partial u}{\\partial t}(t,x) = \\cA(t)u(t,x) +f(t,x), \\quad u(0,\\cdot)=0, \\quad (t,x) \\in (0,T) \\times \\mathbf{R}^d, \\end{align} where $f \\in L_p( (0,T) ; L_p(\\mathbf{R}^d))=L_p( (0,T) ; L_p)$ and \\begin{align*} \\cA(t)u(t,x) = \\lim_{h \\downarrow 0}\\frac{\\mathbb{E}\\left[u(t,x+X_{t+h}-X_t)-u(t,x)\\right]}{h}$. We provide a su","authors_text":"Ildoo Kim, Kyeong-Hun Kim, Panki Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-03T03:13:17Z","title":"An $L_p$-theory for diffusion equations related to stochastic processes with non-stationary independent increment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01243","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":"sha256:52a2a324a9cfaac5bfd940f95dbd2211b88032e2d98bff1ce81f5c86d96bbec5","target":"record","created_at":"2026-05-18T00:31:55Z","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":"cdc6af7df1ded28f62e9c645f34311da65577abf2f16ce3182126bc5b4c260b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-03T03:13:17Z","title_canon_sha256":"37f17dff04c491d4c75fd35ba280cd6c1a47655c7ec7a5ec52eb68485ed7c2c3"},"schema_version":"1.0","source":{"id":"1705.01243","kind":"arxiv","version":2}},"canonical_sha256":"114a0f5f3b37a45d29e948706a64a3d91c9daf261e17021b6c944ab534450a0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"114a0f5f3b37a45d29e948706a64a3d91c9daf261e17021b6c944ab534450a0f","first_computed_at":"2026-05-18T00:31:55.891356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:55.891356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uxO/eOPuVJBQyx+hJafihphln+rl+nqNKGWIwpnD/tJWnfD27W9U+4SZQiNJNREwuebtO5KldK+m6I7NwvfOBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:55.891854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01243","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52a2a324a9cfaac5bfd940f95dbd2211b88032e2d98bff1ce81f5c86d96bbec5","sha256:7e9046e3d390d6d76ee611969e84246582b936dce2f2bad73c64a6ecc11b2fbd"],"state_sha256":"5ea6e109053f3ea9590c00385dd448240deeb77b57ced9083bcff99d671074f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HhRxdNbPUhT+Ow8shmCMAnvQbGrG4/Nyux2THutBkOeRQQG34aTnn13Hw8EX7nJgxPN0FGbKgk5SYw9Hx4FVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:16:10.852447Z","bundle_sha256":"96f1a5bb89cbc5d5bac889f77ee043078630986eebcb78dd1062bbc22a4e9189"}}