{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ELNEKVOKCAHRD5KCBF5WLD7YGH","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":"f66ff5ca74ca0b2669ddc2af117777eb1201bf98cd6a252affee5cccfe3397a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-08T16:49:02Z","title_canon_sha256":"10f56ec095eb6755e45435a6de85fef0165a2147b562b9ec0ea81b2b1a136f4a"},"schema_version":"1.0","source":{"id":"1509.02440","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02440","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02440v1","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02440","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"pith_short_12","alias_value":"ELNEKVOKCAHR","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ELNEKVOKCAHRD5KC","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ELNEKVOK","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:27afb58178a792fecf043307efbc9c5224af5d6267e1fd707bff34490102ed65","target":"graph","created_at":"2026-05-18T01:33:40Z","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":"We prove a genuine analogue of Wiener Tauberian theorem for hypergeometric transforms. As an application we prove analogue of Furstenberg theorem on Harmonic functions.","authors_text":"Amit Samanta, Sanjoy Pusti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-08T16:49:02Z","title":"Wiener Tauberian theorem for hypergeometric transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02440","kind":"arxiv","version":1},"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":"sha256:44bd66a870c75964f47381200fa3c289ec8672be9404527bf64687a50eaa4c30","target":"record","created_at":"2026-05-18T01:33:40Z","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":"f66ff5ca74ca0b2669ddc2af117777eb1201bf98cd6a252affee5cccfe3397a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-08T16:49:02Z","title_canon_sha256":"10f56ec095eb6755e45435a6de85fef0165a2147b562b9ec0ea81b2b1a136f4a"},"schema_version":"1.0","source":{"id":"1509.02440","kind":"arxiv","version":1}},"canonical_sha256":"22da4555ca100f11f542097b658ff831e45d9ebea83f6788e4498aaddaf1b18c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22da4555ca100f11f542097b658ff831e45d9ebea83f6788e4498aaddaf1b18c","first_computed_at":"2026-05-18T01:33:40.884299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:40.884299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"784Kceo36IHVId1BAI4YKBjNgDJlGModDxQVrmiFC94alxdFxy3iIloXTOlLyIM32tg4vCrOlxn8HfTNOYMqDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:40.884767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02440","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44bd66a870c75964f47381200fa3c289ec8672be9404527bf64687a50eaa4c30","sha256:27afb58178a792fecf043307efbc9c5224af5d6267e1fd707bff34490102ed65"],"state_sha256":"d5f15cd484575185ba4da99f4f235ab0a58c4ce50636fb00da4990117dd59aa6"}