{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IL7BQ2FOKFAK2W5P6JGEGB35ZT","short_pith_number":"pith:IL7BQ2FO","canonical_record":{"source":{"id":"1007.5455","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-30T14:06:37Z","cross_cats_sorted":[],"title_canon_sha256":"4de6c8f633234f6c62b2f12d9036cb28b625fd2e2e962511b6859d8a4bfa638a","abstract_canon_sha256":"d54d3fd9b63c4e3163615cd3d24f6319b3886cf95570791d435b287d186efafb"},"schema_version":"1.0"},"canonical_sha256":"42fe1868ae5140ad5baff24c43077dccffb8107abc5bd19ba51d61e3e6747ac5","source":{"kind":"arxiv","id":"1007.5455","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5455","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5455v2","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5455","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"IL7BQ2FOKFAK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IL7BQ2FOKFAK2W5P","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IL7BQ2FO","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IL7BQ2FOKFAK2W5P6JGEGB35ZT","target":"record","payload":{"canonical_record":{"source":{"id":"1007.5455","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-30T14:06:37Z","cross_cats_sorted":[],"title_canon_sha256":"4de6c8f633234f6c62b2f12d9036cb28b625fd2e2e962511b6859d8a4bfa638a","abstract_canon_sha256":"d54d3fd9b63c4e3163615cd3d24f6319b3886cf95570791d435b287d186efafb"},"schema_version":"1.0"},"canonical_sha256":"42fe1868ae5140ad5baff24c43077dccffb8107abc5bd19ba51d61e3e6747ac5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:01.975338Z","signature_b64":"4LVhV3VvcLjncuN/ulIAA66ItlfboqVXE4bxIe/vpYjGfhVgvsrr4AKSIbywQbevsDavfgccg407qO62BAFtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42fe1868ae5140ad5baff24c43077dccffb8107abc5bd19ba51d61e3e6747ac5","last_reissued_at":"2026-05-18T02:58:01.974775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:01.974775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.5455","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":"2026-05-18T02:58:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3OufLVACWUXFWqpQkbmzdn72HN155uFrxKuysNxz5/H1Yn5JRGJHMku4VvlwmtIX+X9xhrEoomFPOmP49b2XBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:19:18.405949Z"},"content_sha256":"c8744726610d056ae099bf92bddfeec2a65004d47c3bc15c17d52dfdc93fa5fb","schema_version":"1.0","event_id":"sha256:c8744726610d056ae099bf92bddfeec2a65004d47c3bc15c17d52dfdc93fa5fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IL7BQ2FOKFAK2W5P6JGEGB35ZT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-sided Green function estimates for killed subordinate Brownian motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Panki Kim, Renming Song, Zoran Vondracek","submitted_at":"2010-07-30T14:06:37Z","abstract_excerpt":"A subordinate Brownian motion is a L\\'evy process which can be obtained by replacing the time of the Brownian motion by an independent subordinator. The infinitesimal generator of a subordinate Brownian motion is $-\\phi(-\\Delta)$, where $\\phi$ is the Laplace exponent of the subordinator. In this paper, we consider a large class of subordinate Brownian motions without diffusion component and with $\\phi$ comparable to a regularly varying function at infinity. This class of processes includes symmetric stable processes, relativistic stable processes, sums of independent symmetric stable processes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5455","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":"2026-05-18T02:58:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xokujlv9BoJVeMRdLdJANJhEK8JiZOZB9jJD3LHSBGmLdQz0Vg6BxDdjWxb3cY0Gsl2lLUWmJylY/bEdljjtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:19:18.406506Z"},"content_sha256":"ccca49d1f3d8bc29b7378b696a6dff35a6af5ad15138cc2835eb843d482dff83","schema_version":"1.0","event_id":"sha256:ccca49d1f3d8bc29b7378b696a6dff35a6af5ad15138cc2835eb843d482dff83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IL7BQ2FOKFAK2W5P6JGEGB35ZT/bundle.json","state_url":"https://pith.science/pith/IL7BQ2FOKFAK2W5P6JGEGB35ZT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IL7BQ2FOKFAK2W5P6JGEGB35ZT/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":"2026-06-25T08:19:18Z","links":{"resolver":"https://pith.science/pith/IL7BQ2FOKFAK2W5P6JGEGB35ZT","bundle":"https://pith.science/pith/IL7BQ2FOKFAK2W5P6JGEGB35ZT/bundle.json","state":"https://pith.science/pith/IL7BQ2FOKFAK2W5P6JGEGB35ZT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IL7BQ2FOKFAK2W5P6JGEGB35ZT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IL7BQ2FOKFAK2W5P6JGEGB35ZT","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":"d54d3fd9b63c4e3163615cd3d24f6319b3886cf95570791d435b287d186efafb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-30T14:06:37Z","title_canon_sha256":"4de6c8f633234f6c62b2f12d9036cb28b625fd2e2e962511b6859d8a4bfa638a"},"schema_version":"1.0","source":{"id":"1007.5455","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5455","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5455v2","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5455","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"IL7BQ2FOKFAK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IL7BQ2FOKFAK2W5P","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IL7BQ2FO","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:ccca49d1f3d8bc29b7378b696a6dff35a6af5ad15138cc2835eb843d482dff83","target":"graph","created_at":"2026-05-18T02:58:01Z","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":"A subordinate Brownian motion is a L\\'evy process which can be obtained by replacing the time of the Brownian motion by an independent subordinator. The infinitesimal generator of a subordinate Brownian motion is $-\\phi(-\\Delta)$, where $\\phi$ is the Laplace exponent of the subordinator. In this paper, we consider a large class of subordinate Brownian motions without diffusion component and with $\\phi$ comparable to a regularly varying function at infinity. This class of processes includes symmetric stable processes, relativistic stable processes, sums of independent symmetric stable processes","authors_text":"Panki Kim, Renming Song, Zoran Vondracek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-30T14:06:37Z","title":"Two-sided Green function estimates for killed subordinate Brownian motions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5455","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:c8744726610d056ae099bf92bddfeec2a65004d47c3bc15c17d52dfdc93fa5fb","target":"record","created_at":"2026-05-18T02:58:01Z","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":"d54d3fd9b63c4e3163615cd3d24f6319b3886cf95570791d435b287d186efafb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-30T14:06:37Z","title_canon_sha256":"4de6c8f633234f6c62b2f12d9036cb28b625fd2e2e962511b6859d8a4bfa638a"},"schema_version":"1.0","source":{"id":"1007.5455","kind":"arxiv","version":2}},"canonical_sha256":"42fe1868ae5140ad5baff24c43077dccffb8107abc5bd19ba51d61e3e6747ac5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42fe1868ae5140ad5baff24c43077dccffb8107abc5bd19ba51d61e3e6747ac5","first_computed_at":"2026-05-18T02:58:01.974775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:01.974775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4LVhV3VvcLjncuN/ulIAA66ItlfboqVXE4bxIe/vpYjGfhVgvsrr4AKSIbywQbevsDavfgccg407qO62BAFtBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:01.975338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.5455","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8744726610d056ae099bf92bddfeec2a65004d47c3bc15c17d52dfdc93fa5fb","sha256:ccca49d1f3d8bc29b7378b696a6dff35a6af5ad15138cc2835eb843d482dff83"],"state_sha256":"43da11d1b65055d47a414672bce1b390388554a9615063d1a11768dd89646847"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FgljxXRYAnGB7nOx5/4ezDjpn51GlbKesM7Z2rwjB3U/WqKxbwZ0+jdNLV+cDMWhz81vDF6Tf5GHQlXQnLuwDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:19:18.409041Z","bundle_sha256":"220a5e71d3906d6d7b8615512befbde69ade13679730132690c63f7660076d6f"}}