{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ED67FUOUABX2JES4QASQF7OTSL","short_pith_number":"pith:ED67FUOU","canonical_record":{"source":{"id":"1604.02418","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-08T18:20:41Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"c7aeb9a70ebf470babb916058e9566e1097cfd8c33107bdea2a9e05121f4b25c","abstract_canon_sha256":"c077192472fa9c52619793e4efa3759eb8553ff48e00be8aa0421c43bb7cf73a"},"schema_version":"1.0"},"canonical_sha256":"20fdf2d1d4006fa4925c802502fdd392fa0365e3f17828267cafffe65f9c593d","source":{"kind":"arxiv","id":"1604.02418","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02418","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02418v2","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02418","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"ED67FUOUABX2","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"ED67FUOUABX2JES4","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"ED67FUOU","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ED67FUOUABX2JES4QASQF7OTSL","target":"record","payload":{"canonical_record":{"source":{"id":"1604.02418","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-08T18:20:41Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"c7aeb9a70ebf470babb916058e9566e1097cfd8c33107bdea2a9e05121f4b25c","abstract_canon_sha256":"c077192472fa9c52619793e4efa3759eb8553ff48e00be8aa0421c43bb7cf73a"},"schema_version":"1.0"},"canonical_sha256":"20fdf2d1d4006fa4925c802502fdd392fa0365e3f17828267cafffe65f9c593d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:33.941882Z","signature_b64":"ofnuG/t7I2wuauZOmQYBdNG/ZqH81xibt4Kg/kmpOSwD53XmIr6SAC/1er5byxXlyk232CLYWOAfYN2NoAwxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20fdf2d1d4006fa4925c802502fdd392fa0365e3f17828267cafffe65f9c593d","last_reissued_at":"2026-05-18T01:15:33.941247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:33.941247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.02418","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":"2026-05-18T01:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxGwxWLWx+FYR25I3GnwpWC31JtfJxDEBsXBG/fmhdgGn8od8ZIOjv3idGg6cWFEK+zTFwSDn2YOtjG5eAiDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:27:17.689948Z"},"content_sha256":"946169679b23ddac43fa7fdc823c4320c4062cdd7ff3562e8b954fb5c99155d6","schema_version":"1.0","event_id":"sha256:946169679b23ddac43fa7fdc823c4320c4062cdd7ff3562e8b954fb5c99155d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ED67FUOUABX2JES4QASQF7OTSL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient estimates of Dirichlet heat kernels for unimodal Levy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Michal Ryznar, Tadeusz Kulczycki","submitted_at":"2016-04-08T18:20:41Z","abstract_excerpt":"Under some mild assumptions on the Levy measure and the symbol we obtain gradient estimates of Dirichlet heat kernels for pure-jump isotropic unimodal Levy processes in $R^d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02418","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":"2026-05-18T01:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G9lhGblQimleajdamUnV0i7CmWUh1ffiAIVIhWGWLX8WtYMW6pHcR1e+1oQYQYlQYnX6Rrof1yGDrwvRm2WdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:27:17.690297Z"},"content_sha256":"43a6ff0cbb9f82bfd999f749f31fcc7039045dd3cc31291beea2c3b761d5996b","schema_version":"1.0","event_id":"sha256:43a6ff0cbb9f82bfd999f749f31fcc7039045dd3cc31291beea2c3b761d5996b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ED67FUOUABX2JES4QASQF7OTSL/bundle.json","state_url":"https://pith.science/pith/ED67FUOUABX2JES4QASQF7OTSL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ED67FUOUABX2JES4QASQF7OTSL/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":"2026-05-28T00:27:17Z","links":{"resolver":"https://pith.science/pith/ED67FUOUABX2JES4QASQF7OTSL","bundle":"https://pith.science/pith/ED67FUOUABX2JES4QASQF7OTSL/bundle.json","state":"https://pith.science/pith/ED67FUOUABX2JES4QASQF7OTSL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ED67FUOUABX2JES4QASQF7OTSL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ED67FUOUABX2JES4QASQF7OTSL","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":"c077192472fa9c52619793e4efa3759eb8553ff48e00be8aa0421c43bb7cf73a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-08T18:20:41Z","title_canon_sha256":"c7aeb9a70ebf470babb916058e9566e1097cfd8c33107bdea2a9e05121f4b25c"},"schema_version":"1.0","source":{"id":"1604.02418","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02418","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02418v2","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02418","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"ED67FUOUABX2","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"ED67FUOUABX2JES4","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"ED67FUOU","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:43a6ff0cbb9f82bfd999f749f31fcc7039045dd3cc31291beea2c3b761d5996b","target":"graph","created_at":"2026-05-18T01:15:33Z","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":"Under some mild assumptions on the Levy measure and the symbol we obtain gradient estimates of Dirichlet heat kernels for pure-jump isotropic unimodal Levy processes in $R^d$.","authors_text":"Michal Ryznar, Tadeusz Kulczycki","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-08T18:20:41Z","title":"Gradient estimates of Dirichlet heat kernels for unimodal Levy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02418","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":"sha256:946169679b23ddac43fa7fdc823c4320c4062cdd7ff3562e8b954fb5c99155d6","target":"record","created_at":"2026-05-18T01:15:33Z","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":"c077192472fa9c52619793e4efa3759eb8553ff48e00be8aa0421c43bb7cf73a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-08T18:20:41Z","title_canon_sha256":"c7aeb9a70ebf470babb916058e9566e1097cfd8c33107bdea2a9e05121f4b25c"},"schema_version":"1.0","source":{"id":"1604.02418","kind":"arxiv","version":2}},"canonical_sha256":"20fdf2d1d4006fa4925c802502fdd392fa0365e3f17828267cafffe65f9c593d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20fdf2d1d4006fa4925c802502fdd392fa0365e3f17828267cafffe65f9c593d","first_computed_at":"2026-05-18T01:15:33.941247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:33.941247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ofnuG/t7I2wuauZOmQYBdNG/ZqH81xibt4Kg/kmpOSwD53XmIr6SAC/1er5byxXlyk232CLYWOAfYN2NoAwxCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:33.941882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02418","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:946169679b23ddac43fa7fdc823c4320c4062cdd7ff3562e8b954fb5c99155d6","sha256:43a6ff0cbb9f82bfd999f749f31fcc7039045dd3cc31291beea2c3b761d5996b"],"state_sha256":"4ed4d9edd1eb2f75d0798c2fe51828c5f5dab84bb10fbcfda118ac0336b37133"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1YJ3eK3oLNo1j+wtZ3Udl7f0IFUSlNs/xKV7AWhcXVsfMU953eu5DFUEXaO4FReNHZ4+L7XksiPsMg9NHDq/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:27:17.692470Z","bundle_sha256":"8b5ed1e5211e33b1475a70cfbc799b79fb5dbc3c2693a42cf9e9c9cecd814ae2"}}