{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NRT3533H2KKVKPJNFFZSZJUF2D","short_pith_number":"pith:NRT3533H","schema_version":"1.0","canonical_sha256":"6c67beef67d295553d2d29732ca685d0f87099a8e710d0d8734efa64091073a4","source":{"kind":"arxiv","id":"1509.05677","version":1},"attestation_state":"computed","paper":{"title":"Martin kernels for Markov processes with jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mateusz Kwa\\'snicki, Tomasz Juszczyszyn","submitted_at":"2015-09-18T15:59:03Z","abstract_excerpt":"We prove existence of boundary limits of ratios of positive harmonic functions for a wide class of Markov processes with jumps and irregular domains, in the context of general metric measure spaces. As a corollary, we prove uniqueness of the Martin kernel at each boundary point, that is, we identify the Martin boundary with the topological boundary. We also prove a Martin representation theorem for harmonic functions. Examples covered by our results include: strictly stable L\\'evy processes in R^d with positive continuous density of the L\\'evy measure; stable-like processes in R^d and in domai"},"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":"1509.05677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-18T15:59:03Z","cross_cats_sorted":[],"title_canon_sha256":"270b1afecade26826d65e4747acc754f75ca50358b99f966e1cedc546ccbf72c","abstract_canon_sha256":"6eb7bfa51335e07c6e8ac9a05139c351a4197557b381fc21c73cb3ba01b18535"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:42.614093Z","signature_b64":"wkhFX7Bw6acIzleIJYFTthE8Ai/x9ybQRpicDT53oVOaOom+xsPNW4D1FglbwoZqKowqsqPZZOA1XNN68g68Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c67beef67d295553d2d29732ca685d0f87099a8e710d0d8734efa64091073a4","last_reissued_at":"2026-05-18T01:32:42.613669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:42.613669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Martin kernels for Markov processes with jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mateusz Kwa\\'snicki, Tomasz Juszczyszyn","submitted_at":"2015-09-18T15:59:03Z","abstract_excerpt":"We prove existence of boundary limits of ratios of positive harmonic functions for a wide class of Markov processes with jumps and irregular domains, in the context of general metric measure spaces. As a corollary, we prove uniqueness of the Martin kernel at each boundary point, that is, we identify the Martin boundary with the topological boundary. We also prove a Martin representation theorem for harmonic functions. Examples covered by our results include: strictly stable L\\'evy processes in R^d with positive continuous density of the L\\'evy measure; stable-like processes in R^d and in domai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05677","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":"1509.05677","created_at":"2026-05-18T01:32:42.613738+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.05677v1","created_at":"2026-05-18T01:32:42.613738+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05677","created_at":"2026-05-18T01:32:42.613738+00:00"},{"alias_kind":"pith_short_12","alias_value":"NRT3533H2KKV","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NRT3533H2KKVKPJN","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NRT3533H","created_at":"2026-05-18T12:29:34.919912+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/NRT3533H2KKVKPJNFFZSZJUF2D","json":"https://pith.science/pith/NRT3533H2KKVKPJNFFZSZJUF2D.json","graph_json":"https://pith.science/api/pith-number/NRT3533H2KKVKPJNFFZSZJUF2D/graph.json","events_json":"https://pith.science/api/pith-number/NRT3533H2KKVKPJNFFZSZJUF2D/events.json","paper":"https://pith.science/paper/NRT3533H"},"agent_actions":{"view_html":"https://pith.science/pith/NRT3533H2KKVKPJNFFZSZJUF2D","download_json":"https://pith.science/pith/NRT3533H2KKVKPJNFFZSZJUF2D.json","view_paper":"https://pith.science/paper/NRT3533H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.05677&json=true","fetch_graph":"https://pith.science/api/pith-number/NRT3533H2KKVKPJNFFZSZJUF2D/graph.json","fetch_events":"https://pith.science/api/pith-number/NRT3533H2KKVKPJNFFZSZJUF2D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NRT3533H2KKVKPJNFFZSZJUF2D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NRT3533H2KKVKPJNFFZSZJUF2D/action/storage_attestation","attest_author":"https://pith.science/pith/NRT3533H2KKVKPJNFFZSZJUF2D/action/author_attestation","sign_citation":"https://pith.science/pith/NRT3533H2KKVKPJNFFZSZJUF2D/action/citation_signature","submit_replication":"https://pith.science/pith/NRT3533H2KKVKPJNFFZSZJUF2D/action/replication_record"}},"created_at":"2026-05-18T01:32:42.613738+00:00","updated_at":"2026-05-18T01:32:42.613738+00:00"}