{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KJO5IGALYUYUQMJN2G53R6Z7HO","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":"c39230f824dae2f2335d45dec76361e06a17df018425abe3c6c64f07854181c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-06T22:16:06Z","title_canon_sha256":"d4bf7b0d7260cd1d97c377a42471b8594a42ab61ddb3a4e42ad487debc0467fb"},"schema_version":"1.0","source":{"id":"1506.02198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02198","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02198v1","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02198","created_at":"2026-05-18T01:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"KJO5IGALYUYU","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KJO5IGALYUYUQMJN","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KJO5IGAL","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:2c161d2023a60d8254b2f03538c512f523caabc2ddcd8556d8d2f264997e1c77","target":"graph","created_at":"2026-05-18T01:55:51Z","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":"A generalization of stable and casual stable probability distribution is proposed. The notion of $\\go G$-casual stability can be used to introduce discrete analogues of stable distributions on the sent $\\mathbb Z$ of integers. In contrary to limit definition of stable distributions on $\\mathbb Z$ our has algebraic character. Examples of corresponding limit theorems are given.\n  Keywords: stable distributions; casual stable distribution; discrete stable distributions; limit theorems","authors_text":"Lev B. Klebanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-06T22:16:06Z","title":"G-casual Stable Probability Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02198","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":"sha256:6d3b343f5b5029adf7057079fbb4c6651a0c7665337c5d05edd6aeb660d24d4a","target":"record","created_at":"2026-05-18T01:55:51Z","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":"c39230f824dae2f2335d45dec76361e06a17df018425abe3c6c64f07854181c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-06T22:16:06Z","title_canon_sha256":"d4bf7b0d7260cd1d97c377a42471b8594a42ab61ddb3a4e42ad487debc0467fb"},"schema_version":"1.0","source":{"id":"1506.02198","kind":"arxiv","version":1}},"canonical_sha256":"525dd4180bc53148312dd1bbb8fb3f3ba454a4cb73530c93a5426153e7c4474c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"525dd4180bc53148312dd1bbb8fb3f3ba454a4cb73530c93a5426153e7c4474c","first_computed_at":"2026-05-18T01:55:51.875238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:51.875238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8nr6UZjfS1hwZc2Uik5cEoTIR06G01cEOCJ7XAUeOd+Q7ZLy8Qd7yFWpd+SfZ6Cu6yShJny+o47a2LSijJuACg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:51.875894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d3b343f5b5029adf7057079fbb4c6651a0c7665337c5d05edd6aeb660d24d4a","sha256:2c161d2023a60d8254b2f03538c512f523caabc2ddcd8556d8d2f264997e1c77"],"state_sha256":"0d452e61e998b1c07b5d5aae81a85c757369f742f8e8e00da853a867f1aa2b03"}