{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:YAXYBCTSBPHP3AX6XNFOSAXIMO","short_pith_number":"pith:YAXYBCTS","canonical_record":{"source":{"id":"2304.10487","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2023-04-20T17:31:10Z","cross_cats_sorted":[],"title_canon_sha256":"5abe32c0b5a1f57bce095f7a61eaa3737db4e60841259d9cf8f97f7f2367ff6f","abstract_canon_sha256":"cc111cde4971365f2767d56eaa6d79ae4ae6a4183d323f9c8f63e98fe014fe38"},"schema_version":"1.0"},"canonical_sha256":"c02f808a720bcefd82febb4ae902e863879c1b2a56d6948f0aa896892792ac76","source":{"kind":"arxiv","id":"2304.10487","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.10487","created_at":"2026-07-05T06:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"2304.10487v1","created_at":"2026-07-05T06:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.10487","created_at":"2026-07-05T06:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"YAXYBCTSBPHP","created_at":"2026-07-05T06:02:58Z"},{"alias_kind":"pith_short_16","alias_value":"YAXYBCTSBPHP3AX6","created_at":"2026-07-05T06:02:58Z"},{"alias_kind":"pith_short_8","alias_value":"YAXYBCTS","created_at":"2026-07-05T06:02:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:YAXYBCTSBPHP3AX6XNFOSAXIMO","target":"record","payload":{"canonical_record":{"source":{"id":"2304.10487","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2023-04-20T17:31:10Z","cross_cats_sorted":[],"title_canon_sha256":"5abe32c0b5a1f57bce095f7a61eaa3737db4e60841259d9cf8f97f7f2367ff6f","abstract_canon_sha256":"cc111cde4971365f2767d56eaa6d79ae4ae6a4183d323f9c8f63e98fe014fe38"},"schema_version":"1.0"},"canonical_sha256":"c02f808a720bcefd82febb4ae902e863879c1b2a56d6948f0aa896892792ac76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:02:58.814988Z","signature_b64":"H9LfY0uKxKqiflx1Sw0/mrPMxxgiWiDdPIimftj2i18NnlIUB1+UdD04ghuNUfJFc08czBndL9YBBoO4mV4GDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c02f808a720bcefd82febb4ae902e863879c1b2a56d6948f0aa896892792ac76","last_reissued_at":"2026-07-05T06:02:58.814473Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:02:58.814473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.10487","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:02:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kT3lB6+qqdVoF60+sJZqk57cZcYYb4AbdNSUvampTE/nMaRNiul6gbjzoOP9gVLFAQap5PHalU2IdSDKBh5MAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T06:34:32.453436Z"},"content_sha256":"e4021db072cd24a3a826cc932201742ee994c0c6b7d8cfe0796cd56ffba0fc9d","schema_version":"1.0","event_id":"sha256:e4021db072cd24a3a826cc932201742ee994c0c6b7d8cfe0796cd56ffba0fc9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:YAXYBCTSBPHP3AX6XNFOSAXIMO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Fractional Negative Binomial Process","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ashok Kumar Pathak, Ritik Soni","submitted_at":"2023-04-20T17:31:10Z","abstract_excerpt":"In this paper, we introduce a generalized fractional negative binomial process (GFNBP) by time changing the fractional Poisson process with an independent Mittag-Leffler (ML) Levy subordinator. We study its distributional properties and its connection to PDEs. We examine the long-range dependence (LRD) property of the GFNBP and show that it is not infinitely divisible. The space fractional and the non-homogeneous variants of the GFNBP are explored. Finally, simulated sample paths for the ML Levy subordinator and the GFNBP are also presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.10487","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.10487/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:02:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"94nQ14DeqNvunoFAaBaqNLOsKHqIGdeTf9WM3rlKvCkh02FjO570ZEVNAq5wGLp/WTUS41Wxbv5620exBsTOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T06:34:32.453931Z"},"content_sha256":"18e3f7f962b5f75b08d734f6d24091da311cf05ce226243754e646d8b06a55d8","schema_version":"1.0","event_id":"sha256:18e3f7f962b5f75b08d734f6d24091da311cf05ce226243754e646d8b06a55d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YAXYBCTSBPHP3AX6XNFOSAXIMO/bundle.json","state_url":"https://pith.science/pith/YAXYBCTSBPHP3AX6XNFOSAXIMO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YAXYBCTSBPHP3AX6XNFOSAXIMO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-22T06:34:32Z","links":{"resolver":"https://pith.science/pith/YAXYBCTSBPHP3AX6XNFOSAXIMO","bundle":"https://pith.science/pith/YAXYBCTSBPHP3AX6XNFOSAXIMO/bundle.json","state":"https://pith.science/pith/YAXYBCTSBPHP3AX6XNFOSAXIMO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YAXYBCTSBPHP3AX6XNFOSAXIMO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:YAXYBCTSBPHP3AX6XNFOSAXIMO","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":"cc111cde4971365f2767d56eaa6d79ae4ae6a4183d323f9c8f63e98fe014fe38","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2023-04-20T17:31:10Z","title_canon_sha256":"5abe32c0b5a1f57bce095f7a61eaa3737db4e60841259d9cf8f97f7f2367ff6f"},"schema_version":"1.0","source":{"id":"2304.10487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.10487","created_at":"2026-07-05T06:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"2304.10487v1","created_at":"2026-07-05T06:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.10487","created_at":"2026-07-05T06:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"YAXYBCTSBPHP","created_at":"2026-07-05T06:02:58Z"},{"alias_kind":"pith_short_16","alias_value":"YAXYBCTSBPHP3AX6","created_at":"2026-07-05T06:02:58Z"},{"alias_kind":"pith_short_8","alias_value":"YAXYBCTS","created_at":"2026-07-05T06:02:58Z"}],"graph_snapshots":[{"event_id":"sha256:18e3f7f962b5f75b08d734f6d24091da311cf05ce226243754e646d8b06a55d8","target":"graph","created_at":"2026-07-05T06:02:58Z","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/2304.10487/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce a generalized fractional negative binomial process (GFNBP) by time changing the fractional Poisson process with an independent Mittag-Leffler (ML) Levy subordinator. We study its distributional properties and its connection to PDEs. We examine the long-range dependence (LRD) property of the GFNBP and show that it is not infinitely divisible. The space fractional and the non-homogeneous variants of the GFNBP are explored. Finally, simulated sample paths for the ML Levy subordinator and the GFNBP are also presented.","authors_text":"Ashok Kumar Pathak, Ritik Soni","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2023-04-20T17:31:10Z","title":"Generalized Fractional Negative Binomial Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.10487","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:e4021db072cd24a3a826cc932201742ee994c0c6b7d8cfe0796cd56ffba0fc9d","target":"record","created_at":"2026-07-05T06:02:58Z","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":"cc111cde4971365f2767d56eaa6d79ae4ae6a4183d323f9c8f63e98fe014fe38","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2023-04-20T17:31:10Z","title_canon_sha256":"5abe32c0b5a1f57bce095f7a61eaa3737db4e60841259d9cf8f97f7f2367ff6f"},"schema_version":"1.0","source":{"id":"2304.10487","kind":"arxiv","version":1}},"canonical_sha256":"c02f808a720bcefd82febb4ae902e863879c1b2a56d6948f0aa896892792ac76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c02f808a720bcefd82febb4ae902e863879c1b2a56d6948f0aa896892792ac76","first_computed_at":"2026-07-05T06:02:58.814473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:02:58.814473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H9LfY0uKxKqiflx1Sw0/mrPMxxgiWiDdPIimftj2i18NnlIUB1+UdD04ghuNUfJFc08czBndL9YBBoO4mV4GDA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:02:58.814988Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.10487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4021db072cd24a3a826cc932201742ee994c0c6b7d8cfe0796cd56ffba0fc9d","sha256:18e3f7f962b5f75b08d734f6d24091da311cf05ce226243754e646d8b06a55d8"],"state_sha256":"2dbbed451ddbe45ac38fd8dff00419ee0ba241aac9bc1cd5be2f7e58c7140685"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"700tFUNn3Z9zPw4DNY9/AhRtx179oDBoSHzKPjjZake2Zvbd4L6NKUhCJiMTtECMg24VtAkH1pnS0PCPPRIBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T06:34:32.458192Z","bundle_sha256":"6363a25e655810c8747ab5be21cbc60c1799d33afcd52ce664f6676187506bbe"}}