{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LQTJH3O47GFLQAMDATCWS7Z52O","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":"ed702d1bd634937b9ff735f27aa548d6b2c701f2123cf4089bbd3952cc41419c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-05T16:49:02Z","title_canon_sha256":"ccad277f52db2ce7ea427b2ba28d5b8c95e382a7f8566d1ea5ac78d12365e1d0"},"schema_version":"1.0","source":{"id":"2412.04334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.04334","created_at":"2026-07-05T09:45:02Z"},{"alias_kind":"arxiv_version","alias_value":"2412.04334v1","created_at":"2026-07-05T09:45:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.04334","created_at":"2026-07-05T09:45:02Z"},{"alias_kind":"pith_short_12","alias_value":"LQTJH3O47GFL","created_at":"2026-07-05T09:45:02Z"},{"alias_kind":"pith_short_16","alias_value":"LQTJH3O47GFLQAMD","created_at":"2026-07-05T09:45:02Z"},{"alias_kind":"pith_short_8","alias_value":"LQTJH3O4","created_at":"2026-07-05T09:45:02Z"}],"graph_snapshots":[{"event_id":"sha256:a5e4cf44345824cedb142f9a846f8980828fce5f6133cf876e1f173d0122ebe6","target":"graph","created_at":"2026-07-05T09:45:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.04334/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Traditionally, fractional counting processes, such as the fractional Poisson process, etc. have been defined using fractional differential and integral operators. Recently, Laskin (2024) introduced a generalized fractional counting process (FCP) by changing the probability mass function (pmf) of the time fractional Poisson process using the generalized three-parameter Mittag-Leffler function. Here, we study some additional properties for the FCP and introduce a time-changed fractional counting process (TCFCP), defined by time-changing the FCP with an independent L\\'evy subordinator. We derive ","authors_text":"Aditya Maheshwari, Ashok Kumar Pathak, Shilpa Garg","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-05T16:49:02Z","title":"Fractional counting process at L\\'evy times and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.04334","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":"sha256:33e7ee0bc2c12e3b0a2c4ee39463229b768378968726b93e58d857cff59051bd","target":"record","created_at":"2026-07-05T09:45:02Z","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":"ed702d1bd634937b9ff735f27aa548d6b2c701f2123cf4089bbd3952cc41419c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-12-05T16:49:02Z","title_canon_sha256":"ccad277f52db2ce7ea427b2ba28d5b8c95e382a7f8566d1ea5ac78d12365e1d0"},"schema_version":"1.0","source":{"id":"2412.04334","kind":"arxiv","version":1}},"canonical_sha256":"5c2693eddcf98ab8018304c5697f3dd3b68a34cecdd535c1e44fd7c650689044","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c2693eddcf98ab8018304c5697f3dd3b68a34cecdd535c1e44fd7c650689044","first_computed_at":"2026-07-05T09:45:02.538013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:45:02.538013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A2rQbicjfwSzDCXgVZic4d0gzPglmUuUbf14SspZJ9W+sw4g14D2VOKkbJwB8+q1xwUWmoav6hTzSp4PZY3EDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:45:02.538470Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.04334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33e7ee0bc2c12e3b0a2c4ee39463229b768378968726b93e58d857cff59051bd","sha256:a5e4cf44345824cedb142f9a846f8980828fce5f6133cf876e1f173d0122ebe6"],"state_sha256":"a3febb4704b258081657056bcbd462b0ff4f7ea540d9f2215bb4493ae513096d"}