{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:C5EJHKIOE64ANYHYURU4YVIRR4","short_pith_number":"pith:C5EJHKIO","canonical_record":{"source":{"id":"1606.01188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-03T17:07:50Z","cross_cats_sorted":[],"title_canon_sha256":"e9b8294309486cc31bd0f9c2925b2d8e2415b3d0c40df498bf34b15e7711beb0","abstract_canon_sha256":"df0f03526c8bb14fc8b7ad00214a40a8bbf519f16c456dff8307f7adfa1e56da"},"schema_version":"1.0"},"canonical_sha256":"174893a90e27b806e0f8a469cc55118f04b6ffb57a9a1d1a33fa5fd69eb89868","source":{"kind":"arxiv","id":"1606.01188","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01188","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01188v1","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01188","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"pith_short_12","alias_value":"C5EJHKIOE64A","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C5EJHKIOE64ANYHY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C5EJHKIO","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:C5EJHKIOE64ANYHYURU4YVIRR4","target":"record","payload":{"canonical_record":{"source":{"id":"1606.01188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-03T17:07:50Z","cross_cats_sorted":[],"title_canon_sha256":"e9b8294309486cc31bd0f9c2925b2d8e2415b3d0c40df498bf34b15e7711beb0","abstract_canon_sha256":"df0f03526c8bb14fc8b7ad00214a40a8bbf519f16c456dff8307f7adfa1e56da"},"schema_version":"1.0"},"canonical_sha256":"174893a90e27b806e0f8a469cc55118f04b6ffb57a9a1d1a33fa5fd69eb89868","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:59.107875Z","signature_b64":"zZrNhZFHVoPnPGSCuy80gsQze6j8Q9W7QNZ6sEDwl9hFRXhGbukHvusUjT+u4no5vK2Zyns5aAxRvFknkM3ECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"174893a90e27b806e0f8a469cc55118f04b6ffb57a9a1d1a33fa5fd69eb89868","last_reissued_at":"2026-05-18T01:12:59.107532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:59.107532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.01188","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":"2026-05-18T01:12:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"po3nVaFWKe6QmNya/57Fhk2UQqDOCmHp490VJth7sKGtjReJ81eN0WlIPzZr84VblTap1wlUrcLrmyMvg0uRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:47:54.224309Z"},"content_sha256":"5ac42ec8a21d85c9619bcca46a3781b1bc3835174519b1a440cf853d5c7b4b93","schema_version":"1.0","event_id":"sha256:5ac42ec8a21d85c9619bcca46a3781b1bc3835174519b1a440cf853d5c7b4b93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:C5EJHKIOE64ANYHYURU4YVIRR4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A parabolic Triebel-Lizorkin space estimate for the fractional Laplacian operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Minsuk Yang","submitted_at":"2016-06-03T17:07:50Z","abstract_excerpt":"In this paper we prove a parabolic Triebel-Lizorkin space estimate for the operator given by \\[T^{\\alpha}f(t,x) = \\int_0^t \\int_{{\\mathbb R}^d} P^{\\alpha}(t-s,x-y)f(s,y) dyds,\\] where the kernel is \\[P^{\\alpha}(t,x) = \\int_{{\\mathbb R}^d} e^{2\\pi ix\\cdot\\xi} e^{-t|\\xi|^\\alpha} d\\xi.\\] The operator $T^{\\alpha}$ maps from $L^{p}F_{s}^{p,q}$ to $L^{p}F_{s+\\alpha/p}^{p,q}$ continuously. It has an application to a class of stochastic integro-differential equations of the type $du = -(-\\Delta)^{\\alpha/2} u dt + f dX_t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01188","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":"2026-05-18T01:12:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e4JhVQPmrRlRoS0e5xe3e2rWuqGKUVZE6HlQhiC0qOezBGQaRrRNHG6X71AFT15GebtdQWmmQF4k0mOiwzNMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:47:54.225081Z"},"content_sha256":"a7d7de71081be5ac9529b0b4eaa018ce175c8833c6830c5d593fab59b17d63ec","schema_version":"1.0","event_id":"sha256:a7d7de71081be5ac9529b0b4eaa018ce175c8833c6830c5d593fab59b17d63ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C5EJHKIOE64ANYHYURU4YVIRR4/bundle.json","state_url":"https://pith.science/pith/C5EJHKIOE64ANYHYURU4YVIRR4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C5EJHKIOE64ANYHYURU4YVIRR4/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":"2026-05-31T08:47:54Z","links":{"resolver":"https://pith.science/pith/C5EJHKIOE64ANYHYURU4YVIRR4","bundle":"https://pith.science/pith/C5EJHKIOE64ANYHYURU4YVIRR4/bundle.json","state":"https://pith.science/pith/C5EJHKIOE64ANYHYURU4YVIRR4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C5EJHKIOE64ANYHYURU4YVIRR4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C5EJHKIOE64ANYHYURU4YVIRR4","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":"df0f03526c8bb14fc8b7ad00214a40a8bbf519f16c456dff8307f7adfa1e56da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-03T17:07:50Z","title_canon_sha256":"e9b8294309486cc31bd0f9c2925b2d8e2415b3d0c40df498bf34b15e7711beb0"},"schema_version":"1.0","source":{"id":"1606.01188","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01188","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01188v1","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01188","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"pith_short_12","alias_value":"C5EJHKIOE64A","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C5EJHKIOE64ANYHY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C5EJHKIO","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:a7d7de71081be5ac9529b0b4eaa018ce175c8833c6830c5d593fab59b17d63ec","target":"graph","created_at":"2026-05-18T01:12:59Z","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 Triebel-Lizorkin space estimate for the operator given by \\[T^{\\alpha}f(t,x) = \\int_0^t \\int_{{\\mathbb R}^d} P^{\\alpha}(t-s,x-y)f(s,y) dyds,\\] where the kernel is \\[P^{\\alpha}(t,x) = \\int_{{\\mathbb R}^d} e^{2\\pi ix\\cdot\\xi} e^{-t|\\xi|^\\alpha} d\\xi.\\] The operator $T^{\\alpha}$ maps from $L^{p}F_{s}^{p,q}$ to $L^{p}F_{s+\\alpha/p}^{p,q}$ continuously. It has an application to a class of stochastic integro-differential equations of the type $du = -(-\\Delta)^{\\alpha/2} u dt + f dX_t$.","authors_text":"Minsuk Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-03T17:07:50Z","title":"A parabolic Triebel-Lizorkin space estimate for the fractional Laplacian operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01188","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":"sha256:5ac42ec8a21d85c9619bcca46a3781b1bc3835174519b1a440cf853d5c7b4b93","target":"record","created_at":"2026-05-18T01:12:59Z","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":"df0f03526c8bb14fc8b7ad00214a40a8bbf519f16c456dff8307f7adfa1e56da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-03T17:07:50Z","title_canon_sha256":"e9b8294309486cc31bd0f9c2925b2d8e2415b3d0c40df498bf34b15e7711beb0"},"schema_version":"1.0","source":{"id":"1606.01188","kind":"arxiv","version":1}},"canonical_sha256":"174893a90e27b806e0f8a469cc55118f04b6ffb57a9a1d1a33fa5fd69eb89868","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"174893a90e27b806e0f8a469cc55118f04b6ffb57a9a1d1a33fa5fd69eb89868","first_computed_at":"2026-05-18T01:12:59.107532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:59.107532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zZrNhZFHVoPnPGSCuy80gsQze6j8Q9W7QNZ6sEDwl9hFRXhGbukHvusUjT+u4no5vK2Zyns5aAxRvFknkM3ECw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:59.107875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.01188","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ac42ec8a21d85c9619bcca46a3781b1bc3835174519b1a440cf853d5c7b4b93","sha256:a7d7de71081be5ac9529b0b4eaa018ce175c8833c6830c5d593fab59b17d63ec"],"state_sha256":"9a590a1e3888e949489be8265b77aed13a4f2c8be07e45737a078ac58c2c46b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xvKoYQR1A9wgaLpYlAaR0mWSclabu/CAWNKZXBXdaSX0K580MvyOJlpjFQAXNoyF0wLOBbtJQSmnmW5ivv6fCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:47:54.228874Z","bundle_sha256":"156555409b30c7b240c3f4059dafcf62d767a18510940fbf8686615aee9ba5a8"}}