{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4GPRFAX5NQARSINXZGFP6V6TPM","short_pith_number":"pith:4GPRFAX5","schema_version":"1.0","canonical_sha256":"e19f1282fd6c011921b7c98aff57d37b344ae50cc3615a7faf8c2c5dda69d98c","source":{"kind":"arxiv","id":"1809.08611","version":3},"attestation_state":"computed","paper":{"title":"Nearly hyperharmonic functions are infima of excessive functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ivan Netuka, Wolfhard Hansen","submitted_at":"2018-09-23T15:04:04Z","abstract_excerpt":"Let $\\mathfrak X$ be a Hunt process on a locally compact space $X$ such that the set $\\mathcal E_{\\mathfrak X}$ of its Borel measurable excessive functions separates points, every function in $\\mathcal E_{\\mathfrak X}$ is the supremum of its continuous minorants in $\\mathcal E_{\\mathfrak X}$ and there are strictly positive continuous functions $v,w\\in\\mathcal E_{\\mathfrak X}$ such that $v/w$ vanishes at infinity.\n  A numerical function $u\\ge 0$ on $X$ is said to be nearly hyperharmonic, if $\\int^\\ast u\\circ X_{\\tau_V}\\,dP^x\\le u(x)$ for all $x\\in X$ and relatively compact open neighborhoods $V"},"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":"1809.08611","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-23T15:04:04Z","cross_cats_sorted":[],"title_canon_sha256":"a702f90f61fe9ee2918ec816bb9c9cbd82c2c333621b8f8925beb516d8ab7720","abstract_canon_sha256":"c5b08c52dff9b46327f7d9e3e3b0e9d3102f7efdcae3c53ed74d7db11cd14c42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:07.625942Z","signature_b64":"cmOnM9R7tS/pmDNw5MIhj96hibrGSgnJ77hYKcIw+x2NxpRFwnlDKkOXqD9xs0ngVUkcMDFJM1AN/Zz7hE7uBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e19f1282fd6c011921b7c98aff57d37b344ae50cc3615a7faf8c2c5dda69d98c","last_reissued_at":"2026-05-17T23:44:07.625256Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:07.625256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nearly hyperharmonic functions are infima of excessive functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ivan Netuka, Wolfhard Hansen","submitted_at":"2018-09-23T15:04:04Z","abstract_excerpt":"Let $\\mathfrak X$ be a Hunt process on a locally compact space $X$ such that the set $\\mathcal E_{\\mathfrak X}$ of its Borel measurable excessive functions separates points, every function in $\\mathcal E_{\\mathfrak X}$ is the supremum of its continuous minorants in $\\mathcal E_{\\mathfrak X}$ and there are strictly positive continuous functions $v,w\\in\\mathcal E_{\\mathfrak X}$ such that $v/w$ vanishes at infinity.\n  A numerical function $u\\ge 0$ on $X$ is said to be nearly hyperharmonic, if $\\int^\\ast u\\circ X_{\\tau_V}\\,dP^x\\le u(x)$ for all $x\\in X$ and relatively compact open neighborhoods $V"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08611","kind":"arxiv","version":3},"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":"1809.08611","created_at":"2026-05-17T23:44:07.625387+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.08611v3","created_at":"2026-05-17T23:44:07.625387+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08611","created_at":"2026-05-17T23:44:07.625387+00:00"},{"alias_kind":"pith_short_12","alias_value":"4GPRFAX5NQAR","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4GPRFAX5NQARSINX","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4GPRFAX5","created_at":"2026-05-18T12:32:05.422762+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/4GPRFAX5NQARSINXZGFP6V6TPM","json":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM.json","graph_json":"https://pith.science/api/pith-number/4GPRFAX5NQARSINXZGFP6V6TPM/graph.json","events_json":"https://pith.science/api/pith-number/4GPRFAX5NQARSINXZGFP6V6TPM/events.json","paper":"https://pith.science/paper/4GPRFAX5"},"agent_actions":{"view_html":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM","download_json":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM.json","view_paper":"https://pith.science/paper/4GPRFAX5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.08611&json=true","fetch_graph":"https://pith.science/api/pith-number/4GPRFAX5NQARSINXZGFP6V6TPM/graph.json","fetch_events":"https://pith.science/api/pith-number/4GPRFAX5NQARSINXZGFP6V6TPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM/action/storage_attestation","attest_author":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM/action/author_attestation","sign_citation":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM/action/citation_signature","submit_replication":"https://pith.science/pith/4GPRFAX5NQARSINXZGFP6V6TPM/action/replication_record"}},"created_at":"2026-05-17T23:44:07.625387+00:00","updated_at":"2026-05-17T23:44:07.625387+00:00"}