{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QWTQ3I5K46HSWH2U5VFNV2HPET","short_pith_number":"pith:QWTQ3I5K","schema_version":"1.0","canonical_sha256":"85a70da3aae78f2b1f54ed4adae8ef24d3a290c4a387f80d0ac1b1061adf3ae4","source":{"kind":"arxiv","id":"1701.07690","version":1},"attestation_state":"computed","paper":{"title":"Harnack inequality for subordinate random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ante Mimica, Stjepan \\v{S}ebek","submitted_at":"2017-01-26T13:29:55Z","abstract_excerpt":"In this paper, we consider a large class of subordinate random walks $X$ on integer lattice $\\mathbb{Z}^d$ via subordinators with Laplace exponents which are complete Bernstein functions satisfying a certain lower scaling condition at zero. We establish estimates for one-step transition probabilities, the Green function and the Green function of a ball, and prove the Harnack inequality for non-negative harmonic functions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.07690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-26T13:29:55Z","cross_cats_sorted":[],"title_canon_sha256":"edafe58a082cb6601a643849625f688811f0cc51545e8cd72932fae02fbf6555","abstract_canon_sha256":"6d4279258cc89064ee5dbf4c59776c2f86f358c639e4872fea47ab1490d1b4fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:02.849216Z","signature_b64":"D1/czbwe4vJgSTAaEYdkh4kLpABwqHQxFy1BrVgxDCZB9M3+R6Ysvdoyj/DDi7eBz1t063Tkjh2nTYOG4vfMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85a70da3aae78f2b1f54ed4adae8ef24d3a290c4a387f80d0ac1b1061adf3ae4","last_reissued_at":"2026-05-18T00:52:02.848661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:02.848661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harnack inequality for subordinate random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ante Mimica, Stjepan \\v{S}ebek","submitted_at":"2017-01-26T13:29:55Z","abstract_excerpt":"In this paper, we consider a large class of subordinate random walks $X$ on integer lattice $\\mathbb{Z}^d$ via subordinators with Laplace exponents which are complete Bernstein functions satisfying a certain lower scaling condition at zero. We establish estimates for one-step transition probabilities, the Green function and the Green function of a ball, and prove the Harnack inequality for non-negative harmonic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07690","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.07690","created_at":"2026-05-18T00:52:02.848757+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.07690v1","created_at":"2026-05-18T00:52:02.848757+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07690","created_at":"2026-05-18T00:52:02.848757+00:00"},{"alias_kind":"pith_short_12","alias_value":"QWTQ3I5K46HS","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"QWTQ3I5K46HSWH2U","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"QWTQ3I5K","created_at":"2026-05-18T12:31:39.905425+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QWTQ3I5K46HSWH2U5VFNV2HPET","json":"https://pith.science/pith/QWTQ3I5K46HSWH2U5VFNV2HPET.json","graph_json":"https://pith.science/api/pith-number/QWTQ3I5K46HSWH2U5VFNV2HPET/graph.json","events_json":"https://pith.science/api/pith-number/QWTQ3I5K46HSWH2U5VFNV2HPET/events.json","paper":"https://pith.science/paper/QWTQ3I5K"},"agent_actions":{"view_html":"https://pith.science/pith/QWTQ3I5K46HSWH2U5VFNV2HPET","download_json":"https://pith.science/pith/QWTQ3I5K46HSWH2U5VFNV2HPET.json","view_paper":"https://pith.science/paper/QWTQ3I5K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.07690&json=true","fetch_graph":"https://pith.science/api/pith-number/QWTQ3I5K46HSWH2U5VFNV2HPET/graph.json","fetch_events":"https://pith.science/api/pith-number/QWTQ3I5K46HSWH2U5VFNV2HPET/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QWTQ3I5K46HSWH2U5VFNV2HPET/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QWTQ3I5K46HSWH2U5VFNV2HPET/action/storage_attestation","attest_author":"https://pith.science/pith/QWTQ3I5K46HSWH2U5VFNV2HPET/action/author_attestation","sign_citation":"https://pith.science/pith/QWTQ3I5K46HSWH2U5VFNV2HPET/action/citation_signature","submit_replication":"https://pith.science/pith/QWTQ3I5K46HSWH2U5VFNV2HPET/action/replication_record"}},"created_at":"2026-05-18T00:52:02.848757+00:00","updated_at":"2026-05-18T00:52:02.848757+00:00"}