{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CF3KQGB2OV5CGGA7H7BB6GSX7I","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":"0b19a9ccdc6bc96b70ec9c31c1a8f91ad8105090a62cba3a80c58021ffe4d5c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-14T17:31:13Z","title_canon_sha256":"e12650289dd1ff36b67bc02b3ffe206ab8d0b3224d6f3cfd4cb7fbd6d6835502"},"schema_version":"1.0","source":{"id":"1107.2874","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2874","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2874v1","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2874","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"pith_short_12","alias_value":"CF3KQGB2OV5C","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CF3KQGB2OV5CGGA7","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CF3KQGB2","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:1bc574e59682aeaa57eb83a1ba0a267626851a48ed734f1ee7b4de9b308c7d8c","target":"graph","created_at":"2026-05-18T03:29:40Z","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":"In this paper we introduce the space-fractional Poisson process whose state probabilities $p_k^\\alpha(t)$, $t>0$, $\\alpha \\in (0,1]$, are governed by the equations $(\\mathrm d/\\mathrm dt)p_k(t) = -\\lambda^\\alpha (1-B)p_k^\\alpha(t)$, where $(1-B)^\\alpha$ is the fractional difference operator found in the study of time series analysis. We explicitly obtain the distributions $p_k^\\alpha(t)$, the probability generating functions $G_\\alpha(u,t)$, which are also expressed as distributions of the minimum of i.i.d.\\ uniform random variables. The comparison with the time-fractional Poisson process is i","authors_text":"Enzo Orsingher, Federico Polito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-14T17:31:13Z","title":"The Space-Fractional Poisson Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2874","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:b3be447c4e1a4220790e6dbdb1c5b2495eb26deef05bb808651ba04c519a8ec1","target":"record","created_at":"2026-05-18T03:29:40Z","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":"0b19a9ccdc6bc96b70ec9c31c1a8f91ad8105090a62cba3a80c58021ffe4d5c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-14T17:31:13Z","title_canon_sha256":"e12650289dd1ff36b67bc02b3ffe206ab8d0b3224d6f3cfd4cb7fbd6d6835502"},"schema_version":"1.0","source":{"id":"1107.2874","kind":"arxiv","version":1}},"canonical_sha256":"1176a8183a757a23181f3fc21f1a57fa28b196ad53d460e954b6a027680823c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1176a8183a757a23181f3fc21f1a57fa28b196ad53d460e954b6a027680823c4","first_computed_at":"2026-05-18T03:29:40.893553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:40.893553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l5lrL9HaBriI2V8ou/e+ucZo4FbDWTWONbtMtLfJv4nSicqwi8NWDoEnxzoLD3VjgYE9XNHdc+7vuSJ7m1xTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:40.894170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2874","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3be447c4e1a4220790e6dbdb1c5b2495eb26deef05bb808651ba04c519a8ec1","sha256:1bc574e59682aeaa57eb83a1ba0a267626851a48ed734f1ee7b4de9b308c7d8c"],"state_sha256":"33763ee53dadf10622812dc9540c851f0b116cb8c3c1e31b988e4972bb4926a7"}