{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BFCYLCXOYRG4FHM43J2O2ST4C5","short_pith_number":"pith:BFCYLCXO","canonical_record":{"source":{"id":"1704.03705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-12T11:15:26Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"cce9b506aabc1b0e6538378381e8839a90835ca97c313c7d68a91a1a156d574a","abstract_canon_sha256":"671c1c2a9ebe293e00878f33dbc90b7ca2a053a8ecf8ea58c1340f90b2fff211"},"schema_version":"1.0"},"canonical_sha256":"0945858aeec44dc29d9cda74ed4a7c1766dabffc52e3f29fa588e9feccf4e143","source":{"kind":"arxiv","id":"1704.03705","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03705","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03705v1","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03705","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"pith_short_12","alias_value":"BFCYLCXOYRG4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BFCYLCXOYRG4FHM4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BFCYLCXO","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BFCYLCXOYRG4FHM43J2O2ST4C5","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-12T11:15:26Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"cce9b506aabc1b0e6538378381e8839a90835ca97c313c7d68a91a1a156d574a","abstract_canon_sha256":"671c1c2a9ebe293e00878f33dbc90b7ca2a053a8ecf8ea58c1340f90b2fff211"},"schema_version":"1.0"},"canonical_sha256":"0945858aeec44dc29d9cda74ed4a7c1766dabffc52e3f29fa588e9feccf4e143","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:27.079301Z","signature_b64":"t8qi7vwK8nmKAFOw4WTXkGXDcF09xuGeMpRW1Se5rXdBmBVFFC+kDGsIpmPpR/8G3ka9Msj6s3kBoZfkeaO7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0945858aeec44dc29d9cda74ed4a7c1766dabffc52e3f29fa588e9feccf4e143","last_reissued_at":"2026-05-18T00:46:27.078723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:27.078723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03705","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":"2026-05-18T00:46:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kCkKarXSRNvfif4myoTvkXirJjmjVz/sDoTPDuadQyLKxOAoXWMF68VvxVKuCJKA1lNjd3PThEODUV4FyTtHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:35:32.957532Z"},"content_sha256":"f0be00012d33714a0c007a7139740996b9b78376f8e6b51d8b5162568057bcb0","schema_version":"1.0","event_id":"sha256:f0be00012d33714a0c007a7139740996b9b78376f8e6b51d8b5162568057bcb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BFCYLCXOYRG4FHM43J2O2ST4C5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heat kernel of anisotropic nonlocal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Krzysztof Bogdan, Pawe{\\l} Sztonyk, Victoria Knopova","submitted_at":"2017-04-12T11:15:26Z","abstract_excerpt":"We construct and estimate the fundamental solution of highly anisotropic space-inhomogeneous integro-differential operators. We use the Levi method. We give applications to the Cauchy problem for such operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03705","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":"2026-05-18T00:46:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YeCinWdO4sfiKUCRrBRjZvyFFm5zPnWxVbwfBzwnWElChDZtvTf4lO2s+6c1vU4PSSiN+TneSw1Mtc9MNQkUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:35:32.957981Z"},"content_sha256":"f899e4806f485bf1b39807c3fd2c97d04f9080aa0ef562eafb45b04676342340","schema_version":"1.0","event_id":"sha256:f899e4806f485bf1b39807c3fd2c97d04f9080aa0ef562eafb45b04676342340"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFCYLCXOYRG4FHM43J2O2ST4C5/bundle.json","state_url":"https://pith.science/pith/BFCYLCXOYRG4FHM43J2O2ST4C5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFCYLCXOYRG4FHM43J2O2ST4C5/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":"2026-08-16T11:35:32Z","links":{"resolver":"https://pith.science/pith/BFCYLCXOYRG4FHM43J2O2ST4C5","bundle":"https://pith.science/pith/BFCYLCXOYRG4FHM43J2O2ST4C5/bundle.json","state":"https://pith.science/pith/BFCYLCXOYRG4FHM43J2O2ST4C5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFCYLCXOYRG4FHM43J2O2ST4C5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BFCYLCXOYRG4FHM43J2O2ST4C5","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":"671c1c2a9ebe293e00878f33dbc90b7ca2a053a8ecf8ea58c1340f90b2fff211","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-12T11:15:26Z","title_canon_sha256":"cce9b506aabc1b0e6538378381e8839a90835ca97c313c7d68a91a1a156d574a"},"schema_version":"1.0","source":{"id":"1704.03705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03705","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03705v1","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03705","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"pith_short_12","alias_value":"BFCYLCXOYRG4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BFCYLCXOYRG4FHM4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BFCYLCXO","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:f899e4806f485bf1b39807c3fd2c97d04f9080aa0ef562eafb45b04676342340","target":"graph","created_at":"2026-05-18T00:46:27Z","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 construct and estimate the fundamental solution of highly anisotropic space-inhomogeneous integro-differential operators. We use the Levi method. We give applications to the Cauchy problem for such operators.","authors_text":"Krzysztof Bogdan, Pawe{\\l} Sztonyk, Victoria Knopova","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-12T11:15:26Z","title":"Heat kernel of anisotropic nonlocal operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03705","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:f0be00012d33714a0c007a7139740996b9b78376f8e6b51d8b5162568057bcb0","target":"record","created_at":"2026-05-18T00:46:27Z","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":"671c1c2a9ebe293e00878f33dbc90b7ca2a053a8ecf8ea58c1340f90b2fff211","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-12T11:15:26Z","title_canon_sha256":"cce9b506aabc1b0e6538378381e8839a90835ca97c313c7d68a91a1a156d574a"},"schema_version":"1.0","source":{"id":"1704.03705","kind":"arxiv","version":1}},"canonical_sha256":"0945858aeec44dc29d9cda74ed4a7c1766dabffc52e3f29fa588e9feccf4e143","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0945858aeec44dc29d9cda74ed4a7c1766dabffc52e3f29fa588e9feccf4e143","first_computed_at":"2026-05-18T00:46:27.078723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:27.078723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t8qi7vwK8nmKAFOw4WTXkGXDcF09xuGeMpRW1Se5rXdBmBVFFC+kDGsIpmPpR/8G3ka9Msj6s3kBoZfkeaO7CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:27.079301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0be00012d33714a0c007a7139740996b9b78376f8e6b51d8b5162568057bcb0","sha256:f899e4806f485bf1b39807c3fd2c97d04f9080aa0ef562eafb45b04676342340"],"state_sha256":"856ffee81370b92e02ff8b9e16d4ede26344dac6b8f3f17bb03c931a1c0c3d64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N2YL2svH5gTYlYJpBp7QNqdmlxrz0VgIKtAt3X5nSJPXzdS51EI9GxoB1iRwtpyZVtJKSutU9ZOAuP/V0ps/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T11:35:32.962661Z","bundle_sha256":"5eff53f59f35fdaa2c73dbbe5d3d0e1f514049c937fc30c2abd9273520c811bf"}}