{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:4VQS6ATKEZNOWY43XOG3ROML74","short_pith_number":"pith:4VQS6ATK","canonical_record":{"source":{"id":"2405.13813","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-22T16:43:23Z","cross_cats_sorted":[],"title_canon_sha256":"89ee31ba8ecb597c6c963c0a9d97469b8042bbf5306ac9291d4dec15e422b3e0","abstract_canon_sha256":"cb87b0096a399c70068668fc0e19bc8d543eaeb5d735ebb3ea2b1d3cc0dee825"},"schema_version":"1.0"},"canonical_sha256":"e5612f026a265aeb639bbb8db8b98bff2bec4ccccb28b3b79d62732dd0f6a9e4","source":{"kind":"arxiv","id":"2405.13813","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.13813","created_at":"2026-07-05T08:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"2405.13813v1","created_at":"2026-07-05T08:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.13813","created_at":"2026-07-05T08:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"4VQS6ATKEZNO","created_at":"2026-07-05T08:22:07Z"},{"alias_kind":"pith_short_16","alias_value":"4VQS6ATKEZNOWY43","created_at":"2026-07-05T08:22:07Z"},{"alias_kind":"pith_short_8","alias_value":"4VQS6ATK","created_at":"2026-07-05T08:22:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:4VQS6ATKEZNOWY43XOG3ROML74","target":"record","payload":{"canonical_record":{"source":{"id":"2405.13813","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-22T16:43:23Z","cross_cats_sorted":[],"title_canon_sha256":"89ee31ba8ecb597c6c963c0a9d97469b8042bbf5306ac9291d4dec15e422b3e0","abstract_canon_sha256":"cb87b0096a399c70068668fc0e19bc8d543eaeb5d735ebb3ea2b1d3cc0dee825"},"schema_version":"1.0"},"canonical_sha256":"e5612f026a265aeb639bbb8db8b98bff2bec4ccccb28b3b79d62732dd0f6a9e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:22:07.266567Z","signature_b64":"vffsn8bJ+ZW6EyTRKnRLfU19Uy5lNAEPDQJeeYi57YU8B89l7gxJbVgkV+YVwFS59Isd2avo1YIyNgD1RTGlAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5612f026a265aeb639bbb8db8b98bff2bec4ccccb28b3b79d62732dd0f6a9e4","last_reissued_at":"2026-07-05T08:22:07.266027Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:22:07.266027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.13813","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":"2026-07-05T08:22:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ydpnb1yjoG/FQoetjHZkEBxTuYCuwigMY+TXN1basG9iRnVogDO7vEHoDcKjJKys+DdQP1hNftIMT48PuFZqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:17:57.290827Z"},"content_sha256":"6330af9345a03388f57700240be8f662eec35bfd58b0a71cd4d9f8ff151ac0e3","schema_version":"1.0","event_id":"sha256:6330af9345a03388f57700240be8f662eec35bfd58b0a71cd4d9f8ff151ac0e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:4VQS6ATKEZNOWY43XOG3ROML74","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate Tempered Space-Fractional Negative Binomial Process and Risk Models with Shocks","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":"2024-05-22T16:43:23Z","abstract_excerpt":"In this paper, we first define the multivariate tempered space-fractional Poisson process (MTSFPP) by time-changing the multivariate Poisson process with an independent tempered {\\alpha}-stable subordinator. Its distributional properties, the mixture tempered time and space variants and their PDEs connections are studied. Then we define the multivariate tempered space-fractional negative binomial process (MTSFNBP) and explore its key features. The L\\'evy measure density for the MTSFNBP is also derived. We present a bivariate risk model with a common shock driven by the tempered space-fractiona"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.13813","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/2405.13813/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":"2026-07-05T08:22:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Keax3bqw9UsC2xg5H1nxgg3w77KrdbVZMryI8a4BNyHDrqEm7aN4JBH7W9UDMuPSO1LmbHYM7sf4LvMvq1LcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:17:57.291382Z"},"content_sha256":"c4cac09509d14411305fd2bfc42c24d9c08cdeed37e7832da0b7687327b58bf8","schema_version":"1.0","event_id":"sha256:c4cac09509d14411305fd2bfc42c24d9c08cdeed37e7832da0b7687327b58bf8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VQS6ATKEZNOWY43XOG3ROML74/bundle.json","state_url":"https://pith.science/pith/4VQS6ATKEZNOWY43XOG3ROML74/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VQS6ATKEZNOWY43XOG3ROML74/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":"2026-08-22T11:17:57Z","links":{"resolver":"https://pith.science/pith/4VQS6ATKEZNOWY43XOG3ROML74","bundle":"https://pith.science/pith/4VQS6ATKEZNOWY43XOG3ROML74/bundle.json","state":"https://pith.science/pith/4VQS6ATKEZNOWY43XOG3ROML74/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VQS6ATKEZNOWY43XOG3ROML74/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4VQS6ATKEZNOWY43XOG3ROML74","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":"cb87b0096a399c70068668fc0e19bc8d543eaeb5d735ebb3ea2b1d3cc0dee825","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-22T16:43:23Z","title_canon_sha256":"89ee31ba8ecb597c6c963c0a9d97469b8042bbf5306ac9291d4dec15e422b3e0"},"schema_version":"1.0","source":{"id":"2405.13813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.13813","created_at":"2026-07-05T08:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"2405.13813v1","created_at":"2026-07-05T08:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.13813","created_at":"2026-07-05T08:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"4VQS6ATKEZNO","created_at":"2026-07-05T08:22:07Z"},{"alias_kind":"pith_short_16","alias_value":"4VQS6ATKEZNOWY43","created_at":"2026-07-05T08:22:07Z"},{"alias_kind":"pith_short_8","alias_value":"4VQS6ATK","created_at":"2026-07-05T08:22:07Z"}],"graph_snapshots":[{"event_id":"sha256:c4cac09509d14411305fd2bfc42c24d9c08cdeed37e7832da0b7687327b58bf8","target":"graph","created_at":"2026-07-05T08:22:07Z","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/2405.13813/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we first define the multivariate tempered space-fractional Poisson process (MTSFPP) by time-changing the multivariate Poisson process with an independent tempered {\\alpha}-stable subordinator. Its distributional properties, the mixture tempered time and space variants and their PDEs connections are studied. Then we define the multivariate tempered space-fractional negative binomial process (MTSFNBP) and explore its key features. The L\\'evy measure density for the MTSFNBP is also derived. We present a bivariate risk model with a common shock driven by the tempered space-fractiona","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":"2024-05-22T16:43:23Z","title":"Multivariate Tempered Space-Fractional Negative Binomial Process and Risk Models with Shocks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.13813","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":"sha256:6330af9345a03388f57700240be8f662eec35bfd58b0a71cd4d9f8ff151ac0e3","target":"record","created_at":"2026-07-05T08:22:07Z","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":"cb87b0096a399c70068668fc0e19bc8d543eaeb5d735ebb3ea2b1d3cc0dee825","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-05-22T16:43:23Z","title_canon_sha256":"89ee31ba8ecb597c6c963c0a9d97469b8042bbf5306ac9291d4dec15e422b3e0"},"schema_version":"1.0","source":{"id":"2405.13813","kind":"arxiv","version":1}},"canonical_sha256":"e5612f026a265aeb639bbb8db8b98bff2bec4ccccb28b3b79d62732dd0f6a9e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5612f026a265aeb639bbb8db8b98bff2bec4ccccb28b3b79d62732dd0f6a9e4","first_computed_at":"2026-07-05T08:22:07.266027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:22:07.266027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vffsn8bJ+ZW6EyTRKnRLfU19Uy5lNAEPDQJeeYi57YU8B89l7gxJbVgkV+YVwFS59Isd2avo1YIyNgD1RTGlAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:22:07.266567Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.13813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6330af9345a03388f57700240be8f662eec35bfd58b0a71cd4d9f8ff151ac0e3","sha256:c4cac09509d14411305fd2bfc42c24d9c08cdeed37e7832da0b7687327b58bf8"],"state_sha256":"802b870c354693b11b4f341982e8d62afe8f00de555f2e5fee32f71d72272552"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R1n9uGye83Unl5xRpN/RqEQlu4BAML3ceaoAsTa1SMcY8eH8JoF9X9SRlhxs/GBfCyAgg2l3z3kkes5QXiZnCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T11:17:57.294834Z","bundle_sha256":"506e07c51c7dd0088f22a1624dac69d682edf2d16a47351478750c0442d8f05f"}}