{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:SZFLWNEQH2DHJXHMIQ2MXRYLAA","short_pith_number":"pith:SZFLWNEQ","schema_version":"1.0","canonical_sha256":"964abb34903e8674dcec4434cbc70b002c18185539b14150d65be12a819da468","source":{"kind":"arxiv","id":"1810.06092","version":1},"attestation_state":"computed","paper":{"title":"A Feyman-Kac approach to a paper of Chung and Feller on fluctuations in the coin-tossing game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. Alberto Gr\\\"unbaum","submitted_at":"2018-10-14T19:53:54Z","abstract_excerpt":"A classical result of K. L. Chung and W. Feller deals with the partial sums $S_k$ arising in a fair coin-tossing game. If $N_n$ is the number of \"positive\" terms among $S_1, S_2,\\dots,S_n$ then the quantity $P(N_{2n}=2r)$ takes an elegant form. We lift the restriction on an even number of tosses and give a simple expression for $P(N_{2n+1}=r)$, $r=0,1,2,\\dots,2n+1$. We get to this result by adapting the Feynman-Kac methodology."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.06092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-14T19:53:54Z","cross_cats_sorted":[],"title_canon_sha256":"27c6d907024001059db8349274e645cff917b050b39f4e23b6b1921b43a1422e","abstract_canon_sha256":"7c1a014b6189b8b002d3bcc52bddfac010bd3b2ca633c928252ebc7ef7acbbca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:21.429531Z","signature_b64":"YUkn70g+p7D63oQMYECm9c/ITyMJ2D25YMrilGIg1zuL/EOjNC0XMspq9qKQL+F/vxRNHGh9uTTC/hKUHyO1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"964abb34903e8674dcec4434cbc70b002c18185539b14150d65be12a819da468","last_reissued_at":"2026-05-18T00:03:21.429010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:21.429010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Feyman-Kac approach to a paper of Chung and Feller on fluctuations in the coin-tossing game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. Alberto Gr\\\"unbaum","submitted_at":"2018-10-14T19:53:54Z","abstract_excerpt":"A classical result of K. L. Chung and W. Feller deals with the partial sums $S_k$ arising in a fair coin-tossing game. If $N_n$ is the number of \"positive\" terms among $S_1, S_2,\\dots,S_n$ then the quantity $P(N_{2n}=2r)$ takes an elegant form. We lift the restriction on an even number of tosses and give a simple expression for $P(N_{2n+1}=r)$, $r=0,1,2,\\dots,2n+1$. We get to this result by adapting the Feynman-Kac methodology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06092","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.06092","created_at":"2026-05-18T00:03:21.429083+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.06092v1","created_at":"2026-05-18T00:03:21.429083+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06092","created_at":"2026-05-18T00:03:21.429083+00:00"},{"alias_kind":"pith_short_12","alias_value":"SZFLWNEQH2DH","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"SZFLWNEQH2DHJXHM","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"SZFLWNEQ","created_at":"2026-05-18T12:32:53.628368+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SZFLWNEQH2DHJXHMIQ2MXRYLAA","json":"https://pith.science/pith/SZFLWNEQH2DHJXHMIQ2MXRYLAA.json","graph_json":"https://pith.science/api/pith-number/SZFLWNEQH2DHJXHMIQ2MXRYLAA/graph.json","events_json":"https://pith.science/api/pith-number/SZFLWNEQH2DHJXHMIQ2MXRYLAA/events.json","paper":"https://pith.science/paper/SZFLWNEQ"},"agent_actions":{"view_html":"https://pith.science/pith/SZFLWNEQH2DHJXHMIQ2MXRYLAA","download_json":"https://pith.science/pith/SZFLWNEQH2DHJXHMIQ2MXRYLAA.json","view_paper":"https://pith.science/paper/SZFLWNEQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.06092&json=true","fetch_graph":"https://pith.science/api/pith-number/SZFLWNEQH2DHJXHMIQ2MXRYLAA/graph.json","fetch_events":"https://pith.science/api/pith-number/SZFLWNEQH2DHJXHMIQ2MXRYLAA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SZFLWNEQH2DHJXHMIQ2MXRYLAA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SZFLWNEQH2DHJXHMIQ2MXRYLAA/action/storage_attestation","attest_author":"https://pith.science/pith/SZFLWNEQH2DHJXHMIQ2MXRYLAA/action/author_attestation","sign_citation":"https://pith.science/pith/SZFLWNEQH2DHJXHMIQ2MXRYLAA/action/citation_signature","submit_replication":"https://pith.science/pith/SZFLWNEQH2DHJXHMIQ2MXRYLAA/action/replication_record"}},"created_at":"2026-05-18T00:03:21.429083+00:00","updated_at":"2026-05-18T00:03:21.429083+00:00"}