{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IQXRUONWPIBLDMIQ6KVKJPVNC3","short_pith_number":"pith:IQXRUONW","canonical_record":{"source":{"id":"1601.05177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-20T05:54:02Z","cross_cats_sorted":[],"title_canon_sha256":"cb48fa3680d0ba61109048fc251ec7fd68548d233c12604bce56fc9f0c599717","abstract_canon_sha256":"858dd430971e31779a5998a64ede635b859329af599cdb746e25340ceb0c5247"},"schema_version":"1.0"},"canonical_sha256":"442f1a39b67a02b1b110f2aaa4bead16c34c1d5a2a08194780b90fca43253a85","source":{"kind":"arxiv","id":"1601.05177","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05177","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05177v1","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05177","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"IQXRUONWPIBL","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IQXRUONWPIBLDMIQ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IQXRUONW","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IQXRUONWPIBLDMIQ6KVKJPVNC3","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-20T05:54:02Z","cross_cats_sorted":[],"title_canon_sha256":"cb48fa3680d0ba61109048fc251ec7fd68548d233c12604bce56fc9f0c599717","abstract_canon_sha256":"858dd430971e31779a5998a64ede635b859329af599cdb746e25340ceb0c5247"},"schema_version":"1.0"},"canonical_sha256":"442f1a39b67a02b1b110f2aaa4bead16c34c1d5a2a08194780b90fca43253a85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:15.932035Z","signature_b64":"m7p5YO+Kzm+zLVaP572fpwXppBsaQPT3Xuo9bUzYK1uCetiCm1kARXDM4SOEVe5kZmPElkhIb7WAP1Y7KtoTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"442f1a39b67a02b1b110f2aaa4bead16c34c1d5a2a08194780b90fca43253a85","last_reissued_at":"2026-05-18T01:22:15.931274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:15.931274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05177","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":"2026-05-18T01:22:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w2YdQACO5JQvyhPEFoJ+Rj0RF8PzeYX2uF4VVRptnJK2l5q87HFHH8X3vlAux0m9BmdLH2If/x0WPtY07QgTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:18:04.824793Z"},"content_sha256":"1d5baabbe077a232812817460230faddac61463138e6f36a67cbe76362d97860","schema_version":"1.0","event_id":"sha256:1d5baabbe077a232812817460230faddac61463138e6f36a67cbe76362d97860"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IQXRUONWPIBLDMIQ6KVKJPVNC3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Long-range Dependence of Fractional Poisson and Negative Binomial Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Maheshwari, P. Vellaisamy","submitted_at":"2016-01-20T05:54:02Z","abstract_excerpt":"We study the long-range dependence (LRD) of the increments of the fractional Poisson process (FPP), the fractional negative binomial process (FNBP) and the increments of the FNBP. We first point out an error in the proof of Theorem 1 of Biard and Saussereau (2014) and prove that the increments of the FPP has indeed the short-range dependence (SRD) property, when the fractional index $\\beta$ satisfies $0<\\beta<\\frac{1}{3}$. We also establish that the FNBP has the LRD property, while the increments of the FNBP possesses the SRD property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05177","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":""},"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":"2026-05-18T01:22:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z0OMzfAVk0nVH3iyMrldP/kI1WEH/ZRNaSMecThbY5Ol0yiTAh6z4ZJDKy2raUl0IUw6a9Q4BO7uVQndqqClBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:18:04.825129Z"},"content_sha256":"a4a19c635330dd8ceaab1c59cfea9b5c9b5740341fa927a215b9c63e1e6bb021","schema_version":"1.0","event_id":"sha256:a4a19c635330dd8ceaab1c59cfea9b5c9b5740341fa927a215b9c63e1e6bb021"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IQXRUONWPIBLDMIQ6KVKJPVNC3/bundle.json","state_url":"https://pith.science/pith/IQXRUONWPIBLDMIQ6KVKJPVNC3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IQXRUONWPIBLDMIQ6KVKJPVNC3/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":"2026-06-01T21:18:04Z","links":{"resolver":"https://pith.science/pith/IQXRUONWPIBLDMIQ6KVKJPVNC3","bundle":"https://pith.science/pith/IQXRUONWPIBLDMIQ6KVKJPVNC3/bundle.json","state":"https://pith.science/pith/IQXRUONWPIBLDMIQ6KVKJPVNC3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IQXRUONWPIBLDMIQ6KVKJPVNC3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IQXRUONWPIBLDMIQ6KVKJPVNC3","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":"858dd430971e31779a5998a64ede635b859329af599cdb746e25340ceb0c5247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-20T05:54:02Z","title_canon_sha256":"cb48fa3680d0ba61109048fc251ec7fd68548d233c12604bce56fc9f0c599717"},"schema_version":"1.0","source":{"id":"1601.05177","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05177","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05177v1","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05177","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"IQXRUONWPIBL","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IQXRUONWPIBLDMIQ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IQXRUONW","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:a4a19c635330dd8ceaab1c59cfea9b5c9b5740341fa927a215b9c63e1e6bb021","target":"graph","created_at":"2026-05-18T01:22:15Z","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":"We study the long-range dependence (LRD) of the increments of the fractional Poisson process (FPP), the fractional negative binomial process (FNBP) and the increments of the FNBP. We first point out an error in the proof of Theorem 1 of Biard and Saussereau (2014) and prove that the increments of the FPP has indeed the short-range dependence (SRD) property, when the fractional index $\\beta$ satisfies $0<\\beta<\\frac{1}{3}$. We also establish that the FNBP has the LRD property, while the increments of the FNBP possesses the SRD property.","authors_text":"A. Maheshwari, P. Vellaisamy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-20T05:54:02Z","title":"On the Long-range Dependence of Fractional Poisson and Negative Binomial Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05177","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":"sha256:1d5baabbe077a232812817460230faddac61463138e6f36a67cbe76362d97860","target":"record","created_at":"2026-05-18T01:22:15Z","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":"858dd430971e31779a5998a64ede635b859329af599cdb746e25340ceb0c5247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-20T05:54:02Z","title_canon_sha256":"cb48fa3680d0ba61109048fc251ec7fd68548d233c12604bce56fc9f0c599717"},"schema_version":"1.0","source":{"id":"1601.05177","kind":"arxiv","version":1}},"canonical_sha256":"442f1a39b67a02b1b110f2aaa4bead16c34c1d5a2a08194780b90fca43253a85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"442f1a39b67a02b1b110f2aaa4bead16c34c1d5a2a08194780b90fca43253a85","first_computed_at":"2026-05-18T01:22:15.931274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:15.931274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m7p5YO+Kzm+zLVaP572fpwXppBsaQPT3Xuo9bUzYK1uCetiCm1kARXDM4SOEVe5kZmPElkhIb7WAP1Y7KtoTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:15.932035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05177","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d5baabbe077a232812817460230faddac61463138e6f36a67cbe76362d97860","sha256:a4a19c635330dd8ceaab1c59cfea9b5c9b5740341fa927a215b9c63e1e6bb021"],"state_sha256":"805af322b734fa9ffe35348f0756d0689056442b083c5b5ddf8bf665ba9b9093"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Ohi7CME0QyjnVgn1T+QBjw7TKcM5HHcnV14tQg2rddzqBb5qswqeA1ClQ76xN8HsjcDC8amDLl6bJTFjZTsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:18:04.827137Z","bundle_sha256":"3dd0d654b24a1bbe79da7ef63611b4e0fd2b003bdc86521a0714a52ad3687789"}}