{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BY543JCMB64Y6ITMBUBVOKK74Y","short_pith_number":"pith:BY543JCM","canonical_record":{"source":{"id":"1508.01264","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-08-06T02:24:27Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"8c5bf30b8f0624cfda6c010f5fc2a50fc95a38b7da8110b796cfb391888c1d0e","abstract_canon_sha256":"7819eaef19b21604efd15352d82096262827e8c30734e26ad5950126f17f129e"},"schema_version":"1.0"},"canonical_sha256":"0e3bcda44c0fb98f226c0d0357295fe609fa923bf9b784f7f2ac7c10171609c2","source":{"kind":"arxiv","id":"1508.01264","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01264","created_at":"2026-05-18T00:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01264v8","created_at":"2026-05-18T00:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01264","created_at":"2026-05-18T00:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"BY543JCMB64Y","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BY543JCMB64Y6ITM","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BY543JCM","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BY543JCMB64Y6ITMBUBVOKK74Y","target":"record","payload":{"canonical_record":{"source":{"id":"1508.01264","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-08-06T02:24:27Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"8c5bf30b8f0624cfda6c010f5fc2a50fc95a38b7da8110b796cfb391888c1d0e","abstract_canon_sha256":"7819eaef19b21604efd15352d82096262827e8c30734e26ad5950126f17f129e"},"schema_version":"1.0"},"canonical_sha256":"0e3bcda44c0fb98f226c0d0357295fe609fa923bf9b784f7f2ac7c10171609c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:17.377738Z","signature_b64":"wJe+DsWvSonlMvR4vHVGrSP70HDLbEM11LBQhejI5VnoUsUpH/PA5qzktscg72TEor3S98Uh/nzH2MPCFT1QAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e3bcda44c0fb98f226c0d0357295fe609fa923bf9b784f7f2ac7c10171609c2","last_reissued_at":"2026-05-18T00:23:17.376952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:17.376952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.01264","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wKwsoMc5uIxmWgbNPrOUvG6V6cJto+blgQWvkWMVNP5TWz+lJZ+2MygNw6NAx3O5pji5DOKeOJhoVAHYmRYBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:28:56.417286Z"},"content_sha256":"d229bf2462a080c006cafeea3f12e7db2703fd0919c0f3a4882584dbf8e072ca","schema_version":"1.0","event_id":"sha256:d229bf2462a080c006cafeea3f12e7db2703fd0919c0f3a4882584dbf8e072ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BY543JCMB64Y6ITMBUBVOKK74Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Stopped Negative Binomial Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Daniel Zelterman, Michael J. Kane, Michelle DeVeaux","submitted_at":"2015-08-06T02:24:27Z","abstract_excerpt":"This paper introduces a new discrete distribution suggested by curtailed sampling rules common in early-stage clinical trials. We derive the distribution of the smallest number of independent Bernoulli(p) trials needed in order to observe either s successes or t failures. The closed form expression for the distribution as well as the compound distribution are derived. Properties of the distribution are shown and discussed. A case study is presented showing how the distribution can be used to monitor sequential enrollment of clinical trials with binary outcomes as well as providing post-hoc ana"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01264","kind":"arxiv","version":8},"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":"2026-05-18T00:23:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tIw3ztaZPa0wC+XiVv8WGQ92E6d8y2HdAPH9r4r2pz/CdcV+yNP0CzLPPn+YCco7Bb0G3UXAiYEk9kCoOePZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:28:56.417683Z"},"content_sha256":"2858c66e378897a1666567d60a30a8c763a16f3997c901ed1da5fcfa68b954ba","schema_version":"1.0","event_id":"sha256:2858c66e378897a1666567d60a30a8c763a16f3997c901ed1da5fcfa68b954ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BY543JCMB64Y6ITMBUBVOKK74Y/bundle.json","state_url":"https://pith.science/pith/BY543JCMB64Y6ITMBUBVOKK74Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BY543JCMB64Y6ITMBUBVOKK74Y/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":"2026-07-01T23:28:56Z","links":{"resolver":"https://pith.science/pith/BY543JCMB64Y6ITMBUBVOKK74Y","bundle":"https://pith.science/pith/BY543JCMB64Y6ITMBUBVOKK74Y/bundle.json","state":"https://pith.science/pith/BY543JCMB64Y6ITMBUBVOKK74Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BY543JCMB64Y6ITMBUBVOKK74Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BY543JCMB64Y6ITMBUBVOKK74Y","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":"7819eaef19b21604efd15352d82096262827e8c30734e26ad5950126f17f129e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-08-06T02:24:27Z","title_canon_sha256":"8c5bf30b8f0624cfda6c010f5fc2a50fc95a38b7da8110b796cfb391888c1d0e"},"schema_version":"1.0","source":{"id":"1508.01264","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01264","created_at":"2026-05-18T00:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01264v8","created_at":"2026-05-18T00:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01264","created_at":"2026-05-18T00:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"BY543JCMB64Y","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BY543JCMB64Y6ITM","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BY543JCM","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:2858c66e378897a1666567d60a30a8c763a16f3997c901ed1da5fcfa68b954ba","target":"graph","created_at":"2026-05-18T00:23:17Z","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":"This paper introduces a new discrete distribution suggested by curtailed sampling rules common in early-stage clinical trials. We derive the distribution of the smallest number of independent Bernoulli(p) trials needed in order to observe either s successes or t failures. The closed form expression for the distribution as well as the compound distribution are derived. Properties of the distribution are shown and discussed. A case study is presented showing how the distribution can be used to monitor sequential enrollment of clinical trials with binary outcomes as well as providing post-hoc ana","authors_text":"Daniel Zelterman, Michael J. Kane, Michelle DeVeaux","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-08-06T02:24:27Z","title":"A Stopped Negative Binomial Distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01264","kind":"arxiv","version":8},"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:d229bf2462a080c006cafeea3f12e7db2703fd0919c0f3a4882584dbf8e072ca","target":"record","created_at":"2026-05-18T00:23:17Z","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":"7819eaef19b21604efd15352d82096262827e8c30734e26ad5950126f17f129e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-08-06T02:24:27Z","title_canon_sha256":"8c5bf30b8f0624cfda6c010f5fc2a50fc95a38b7da8110b796cfb391888c1d0e"},"schema_version":"1.0","source":{"id":"1508.01264","kind":"arxiv","version":8}},"canonical_sha256":"0e3bcda44c0fb98f226c0d0357295fe609fa923bf9b784f7f2ac7c10171609c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e3bcda44c0fb98f226c0d0357295fe609fa923bf9b784f7f2ac7c10171609c2","first_computed_at":"2026-05-18T00:23:17.376952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:17.376952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wJe+DsWvSonlMvR4vHVGrSP70HDLbEM11LBQhejI5VnoUsUpH/PA5qzktscg72TEor3S98Uh/nzH2MPCFT1QAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:17.377738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01264","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d229bf2462a080c006cafeea3f12e7db2703fd0919c0f3a4882584dbf8e072ca","sha256:2858c66e378897a1666567d60a30a8c763a16f3997c901ed1da5fcfa68b954ba"],"state_sha256":"b62e240d5693425a6e72ac5d2efca7bdae9baebd6b9be3a52e3525d0b52e3507"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7hha7BuaZ6fCTAqD3/qlNcorsfYLFML3WCB5W19XnfvHmNsu24hdXRusBdqTL7R4+8Du1eIx7TjZNcuTbCKHBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T23:28:56.419962Z","bundle_sha256":"ca87c1529e2544a5cd52868c075105c89abe8cf70c21204701ddb4a7a099292d"}}