{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DWHLF2Y43FDJCMXSIEYDW5FIQG","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":"a645bb08cad599b3f576e8ed511fb268986971b1697710e13b2a536e6c187222","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-26T23:01:53Z","title_canon_sha256":"a2c3e546070efdf1e29a1fdcd09a55d5fd5fcdd06b6fa18144756c2d7b7b4c60"},"schema_version":"1.0","source":{"id":"1303.6699","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6699","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6699v2","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6699","created_at":"2026-05-18T01:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"DWHLF2Y43FDJ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DWHLF2Y43FDJCMXS","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DWHLF2Y4","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:bb95bf0b39173a48e311fc231e94328a5780f0d777e53839fc456b248d1fede6","target":"graph","created_at":"2026-05-18T01:32:43Z","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":"The aim of this paper is the analysis of the fractional Poisson process where the state probabilities $p_k^{\\nu_k}(t)$, $t\\ge 0$, are governed by time-fractional equations of order $0<\\nu_k\\leq 1$ depending on the number $k$ of events occurred up to time $t$. We are able to obtain explicitely the Laplace transform of $p_k^{\\nu_k}(t)$ and various representations of state probabilities. We show that the Poisson process with intermediate waiting times depending on $\\nu_k$ differs from that constructed from the fractional state equations (in the case $\\nu_k = \\nu$, for all $k$, they coincide with ","authors_text":"Enzo Orsingher, Federico Polito, Roberto Garra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-26T23:01:53Z","title":"State-dependent Fractional Point Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6699","kind":"arxiv","version":2},"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":"sha256:01ade822f13da69442212120080c229c52aace04c7f95b7092203f6091c7c9ce","target":"record","created_at":"2026-05-18T01:32:43Z","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":"a645bb08cad599b3f576e8ed511fb268986971b1697710e13b2a536e6c187222","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-26T23:01:53Z","title_canon_sha256":"a2c3e546070efdf1e29a1fdcd09a55d5fd5fcdd06b6fa18144756c2d7b7b4c60"},"schema_version":"1.0","source":{"id":"1303.6699","kind":"arxiv","version":2}},"canonical_sha256":"1d8eb2eb1cd9469132f241303b74a881ac952ab71793225570eea058becd8ca9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d8eb2eb1cd9469132f241303b74a881ac952ab71793225570eea058becd8ca9","first_computed_at":"2026-05-18T01:32:43.973926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:43.973926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YvhiGRB5u+OqdlX8o5qAoN51IbYiFD+uy33WIElInmDuU4ay8HmUlmQgdf8+6p3LWhA5zLKWaoSE0wsJnvhoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:43.974356Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6699","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01ade822f13da69442212120080c229c52aace04c7f95b7092203f6091c7c9ce","sha256:bb95bf0b39173a48e311fc231e94328a5780f0d777e53839fc456b248d1fede6"],"state_sha256":"d63be26b22778029f8577616aa761ee7e2a10945b51fc001c4839db2ccdf8c58"}