{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XFR4C6RMXLZN6BVB6EG5JHXKSU","short_pith_number":"pith:XFR4C6RM","canonical_record":{"source":{"id":"1610.06157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-19T19:10:15Z","cross_cats_sorted":[],"title_canon_sha256":"42ab77f6162479e7e4dddb7cf33d6a1f64b25fd0e9135c27bdcd3d257d4b98e9","abstract_canon_sha256":"188d2bb73e3ed170e1ec5a8c71e80262e97004cc7900b7d5bcd84a006991e7c5"},"schema_version":"1.0"},"canonical_sha256":"b963c17a2cbaf2df06a1f10dd49eea952c0f65317668a8dda2e17a0dc01911fd","source":{"kind":"arxiv","id":"1610.06157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06157","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06157v1","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06157","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"pith_short_12","alias_value":"XFR4C6RMXLZN","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XFR4C6RMXLZN6BVB","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XFR4C6RM","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XFR4C6RMXLZN6BVB6EG5JHXKSU","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-19T19:10:15Z","cross_cats_sorted":[],"title_canon_sha256":"42ab77f6162479e7e4dddb7cf33d6a1f64b25fd0e9135c27bdcd3d257d4b98e9","abstract_canon_sha256":"188d2bb73e3ed170e1ec5a8c71e80262e97004cc7900b7d5bcd84a006991e7c5"},"schema_version":"1.0"},"canonical_sha256":"b963c17a2cbaf2df06a1f10dd49eea952c0f65317668a8dda2e17a0dc01911fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:49.845730Z","signature_b64":"ga4Jdnm3Mw8qmGX8ti3Y+2nB682z6WJp3UKtqVTAC3DulVyW8Vcuftbo9se3zE07WCOduoyH2jm9Z8+MZBIUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b963c17a2cbaf2df06a1f10dd49eea952c0f65317668a8dda2e17a0dc01911fd","last_reissued_at":"2026-05-18T01:01:49.845255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:49.845255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06157","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":"2026-05-18T01:01:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2lC8i3IOLWG8mw7bKLfolPCgSqO+hq5bcFJz1KQHYun0duXQAMo3lrVXlOJreJyFXG33hM5RfEgVLEQRulagAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:08:08.386389Z"},"content_sha256":"c1e512149687c465d0ff1a84a7cef191788fe1e64ac0d572e95338ecb30311ab","schema_version":"1.0","event_id":"sha256:c1e512149687c465d0ff1a84a7cef191788fe1e64ac0d572e95338ecb30311ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XFR4C6RMXLZN6BVB6EG5JHXKSU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Event count distributions from renewal processes: fast computation of probabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Rose Baker, Tarak Kharrat","submitted_at":"2016-10-19T19:10:15Z","abstract_excerpt":"Discrete distributions derived from renewal processes, ie distributions of the number of events by some time t are beginning to be used in econometrics and health sciences. A new fast method is presented for computation of the probabilities for these distributions. We calculate the count probabilities by repeatedly convolving the discretized distribution, and then correct them using Richardson extrapolation. When just one probability is required, a second algorithm is described, an adaptation of De Pril's method, in which the computation time does not depend on the ordinality, so that even hig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06157","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":"2026-05-18T01:01:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PovtA/G5QBkJsVWJL2fyNPSAF0ARyM+7aexagcd6D7jilb/q/Yc1SpIIrL1+6Qo+Um7Sc7ve4EGs02QFbU1IBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:08:08.386738Z"},"content_sha256":"78e6ea044837cbabfa48c149f20ac7fa215ba7db15e7ab38a5845e86220513bf","schema_version":"1.0","event_id":"sha256:78e6ea044837cbabfa48c149f20ac7fa215ba7db15e7ab38a5845e86220513bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XFR4C6RMXLZN6BVB6EG5JHXKSU/bundle.json","state_url":"https://pith.science/pith/XFR4C6RMXLZN6BVB6EG5JHXKSU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XFR4C6RMXLZN6BVB6EG5JHXKSU/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":"2026-06-02T00:08:08Z","links":{"resolver":"https://pith.science/pith/XFR4C6RMXLZN6BVB6EG5JHXKSU","bundle":"https://pith.science/pith/XFR4C6RMXLZN6BVB6EG5JHXKSU/bundle.json","state":"https://pith.science/pith/XFR4C6RMXLZN6BVB6EG5JHXKSU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XFR4C6RMXLZN6BVB6EG5JHXKSU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XFR4C6RMXLZN6BVB6EG5JHXKSU","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":"188d2bb73e3ed170e1ec5a8c71e80262e97004cc7900b7d5bcd84a006991e7c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-19T19:10:15Z","title_canon_sha256":"42ab77f6162479e7e4dddb7cf33d6a1f64b25fd0e9135c27bdcd3d257d4b98e9"},"schema_version":"1.0","source":{"id":"1610.06157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06157","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06157v1","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06157","created_at":"2026-05-18T01:01:49Z"},{"alias_kind":"pith_short_12","alias_value":"XFR4C6RMXLZN","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XFR4C6RMXLZN6BVB","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XFR4C6RM","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:78e6ea044837cbabfa48c149f20ac7fa215ba7db15e7ab38a5845e86220513bf","target":"graph","created_at":"2026-05-18T01:01:49Z","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":"Discrete distributions derived from renewal processes, ie distributions of the number of events by some time t are beginning to be used in econometrics and health sciences. A new fast method is presented for computation of the probabilities for these distributions. We calculate the count probabilities by repeatedly convolving the discretized distribution, and then correct them using Richardson extrapolation. When just one probability is required, a second algorithm is described, an adaptation of De Pril's method, in which the computation time does not depend on the ordinality, so that even hig","authors_text":"Rose Baker, Tarak Kharrat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-19T19:10:15Z","title":"Event count distributions from renewal processes: fast computation of probabilities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06157","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:c1e512149687c465d0ff1a84a7cef191788fe1e64ac0d572e95338ecb30311ab","target":"record","created_at":"2026-05-18T01:01:49Z","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":"188d2bb73e3ed170e1ec5a8c71e80262e97004cc7900b7d5bcd84a006991e7c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-19T19:10:15Z","title_canon_sha256":"42ab77f6162479e7e4dddb7cf33d6a1f64b25fd0e9135c27bdcd3d257d4b98e9"},"schema_version":"1.0","source":{"id":"1610.06157","kind":"arxiv","version":1}},"canonical_sha256":"b963c17a2cbaf2df06a1f10dd49eea952c0f65317668a8dda2e17a0dc01911fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b963c17a2cbaf2df06a1f10dd49eea952c0f65317668a8dda2e17a0dc01911fd","first_computed_at":"2026-05-18T01:01:49.845255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:49.845255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ga4Jdnm3Mw8qmGX8ti3Y+2nB682z6WJp3UKtqVTAC3DulVyW8Vcuftbo9se3zE07WCOduoyH2jm9Z8+MZBIUAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:49.845730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1e512149687c465d0ff1a84a7cef191788fe1e64ac0d572e95338ecb30311ab","sha256:78e6ea044837cbabfa48c149f20ac7fa215ba7db15e7ab38a5845e86220513bf"],"state_sha256":"52d91368f580d090bafc91edf2b4164d36c40a13a64cb933ff1b190ab697ebd5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8WEkiNY60Zs286SOeUtVMJAmvkcsQOnB+sH4vHsTnEY98M9ft+1qDoXrZL9sYjEDsTdG2YEGloxhAIChAWKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:08:08.388586Z","bundle_sha256":"43d87dd5127737695d421e3791cd6f6efd1f6120bc10880822c00dbe49d163fe"}}