{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:EMFY6TOKPDNQ57QYF5N63UGCUB","short_pith_number":"pith:EMFY6TOK","schema_version":"1.0","canonical_sha256":"230b8f4dca78db0efe182f5bedd0c2a04954c682e86d4d42a3cb4560b7c8849b","source":{"kind":"arxiv","id":"1906.05124","version":1},"attestation_state":"computed","paper":{"title":"Amenability and harmonic $L^p$-functions on hypergroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jila Sohaei, Mehdi Nemati","submitted_at":"2019-06-12T13:14:22Z","abstract_excerpt":"Let $K$ be a locally compact hypergroup with a left invariant Haar measure. We show that the Liouville property and amenability are equivalent for $K$ when it is second countable. Suppose that $\\sigma$ is a non-degenerate probability measure on $K$, we show that there is no non-trivial $\\sigma$-harmonic function which is continuous and vanishing at infinity. Using this, we prove that the space $H_\\sigma^p(K)$ of all $\\sigma$-harmonic $L^p$-functions, is trivial for all $1\\leq p<\\infty$. Further, it is shown that $H_\\sigma^\\infty(K)$ contains only constant functions if and only if it is a subal"},"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":"1906.05124","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-06-12T13:14:22Z","cross_cats_sorted":[],"title_canon_sha256":"170d753fd7b63e04a62db1d6b6d67d04c4d65881010f206f715b7b0fe51677f7","abstract_canon_sha256":"b8fe4b2dca2a8832ed9e8b70ebd4a3df7871589a932c11a690440182212e1fc0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:29.408513Z","signature_b64":"G2klAPpqGXRioAHfSKyApFsABSs4OXpQxxZO/As7Ee6QwZqRg/MT9pjejKO9SBXVgskz4S6EsdopQXMRPSidCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"230b8f4dca78db0efe182f5bedd0c2a04954c682e86d4d42a3cb4560b7c8849b","last_reissued_at":"2026-05-17T23:43:29.408019Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:29.408019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Amenability and harmonic $L^p$-functions on hypergroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jila Sohaei, Mehdi Nemati","submitted_at":"2019-06-12T13:14:22Z","abstract_excerpt":"Let $K$ be a locally compact hypergroup with a left invariant Haar measure. We show that the Liouville property and amenability are equivalent for $K$ when it is second countable. Suppose that $\\sigma$ is a non-degenerate probability measure on $K$, we show that there is no non-trivial $\\sigma$-harmonic function which is continuous and vanishing at infinity. Using this, we prove that the space $H_\\sigma^p(K)$ of all $\\sigma$-harmonic $L^p$-functions, is trivial for all $1\\leq p<\\infty$. Further, it is shown that $H_\\sigma^\\infty(K)$ contains only constant functions if and only if it is a subal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05124","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":"1906.05124","created_at":"2026-05-17T23:43:29.408092+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.05124v1","created_at":"2026-05-17T23:43:29.408092+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.05124","created_at":"2026-05-17T23:43:29.408092+00:00"},{"alias_kind":"pith_short_12","alias_value":"EMFY6TOKPDNQ","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"EMFY6TOKPDNQ57QY","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"EMFY6TOK","created_at":"2026-05-18T12:33:15.570797+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/EMFY6TOKPDNQ57QYF5N63UGCUB","json":"https://pith.science/pith/EMFY6TOKPDNQ57QYF5N63UGCUB.json","graph_json":"https://pith.science/api/pith-number/EMFY6TOKPDNQ57QYF5N63UGCUB/graph.json","events_json":"https://pith.science/api/pith-number/EMFY6TOKPDNQ57QYF5N63UGCUB/events.json","paper":"https://pith.science/paper/EMFY6TOK"},"agent_actions":{"view_html":"https://pith.science/pith/EMFY6TOKPDNQ57QYF5N63UGCUB","download_json":"https://pith.science/pith/EMFY6TOKPDNQ57QYF5N63UGCUB.json","view_paper":"https://pith.science/paper/EMFY6TOK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.05124&json=true","fetch_graph":"https://pith.science/api/pith-number/EMFY6TOKPDNQ57QYF5N63UGCUB/graph.json","fetch_events":"https://pith.science/api/pith-number/EMFY6TOKPDNQ57QYF5N63UGCUB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EMFY6TOKPDNQ57QYF5N63UGCUB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EMFY6TOKPDNQ57QYF5N63UGCUB/action/storage_attestation","attest_author":"https://pith.science/pith/EMFY6TOKPDNQ57QYF5N63UGCUB/action/author_attestation","sign_citation":"https://pith.science/pith/EMFY6TOKPDNQ57QYF5N63UGCUB/action/citation_signature","submit_replication":"https://pith.science/pith/EMFY6TOKPDNQ57QYF5N63UGCUB/action/replication_record"}},"created_at":"2026-05-17T23:43:29.408092+00:00","updated_at":"2026-05-17T23:43:29.408092+00:00"}