{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IPIGZHNP56S5QVGFY57X2OW4WW","short_pith_number":"pith:IPIGZHNP","schema_version":"1.0","canonical_sha256":"43d06c9dafefa5d854c5c77f7d3adcb5bc6711da6e61c0884d0f78a5a5548e6e","source":{"kind":"arxiv","id":"1305.5697","version":1},"attestation_state":"computed","paper":{"title":"The dimension of the St. Petersburg game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lina Wedrich, Peter Kern","submitted_at":"2013-05-24T11:49:25Z","abstract_excerpt":"Let $S_n$ be the total gain in $n$ repeated St.\\ Petersburg games. It is known that $n^{-1}(S_n-n\\log_2n)$ converges in distribution to a random element $Y(t)$ along subsequences of the form $k(n)=2^{p(n)}t(n)$ with $p(n)=\\lceil\\log_2k(n)\\rceil\\to\\infty$ and $t(n)\\to t\\in[\\frac12,1]$. We determine the Hausdorff and box-counting dimension of the range and the graph for almost all sample paths of the stochastic process $\\{Y(t)\\}_{t\\in[1/2,1]}$. The results are compared to the fractal dimension of the corresponding limiting objects when gains are given by a deterministic sequence initiated by Hug"},"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":"1305.5697","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-24T11:49:25Z","cross_cats_sorted":[],"title_canon_sha256":"39b1d0a7a1869b0ba678d23070a0f671de714fe5c091742e66a1eb37c2f9aa87","abstract_canon_sha256":"da9c40b37e5ed33addeeb066c0bf75ac68c37a9af50e4225976e5b624874626d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:09.434530Z","signature_b64":"qwiI7YSUKlF1TGXVBjbIVnH5kjziCMQr23XSq0lwDAvGCdCGRPXX3+I06LsUbmo5ZSTYfu1SsuG0JUFDuqR1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43d06c9dafefa5d854c5c77f7d3adcb5bc6711da6e61c0884d0f78a5a5548e6e","last_reissued_at":"2026-05-18T02:43:09.433881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:09.433881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The dimension of the St. Petersburg game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lina Wedrich, Peter Kern","submitted_at":"2013-05-24T11:49:25Z","abstract_excerpt":"Let $S_n$ be the total gain in $n$ repeated St.\\ Petersburg games. It is known that $n^{-1}(S_n-n\\log_2n)$ converges in distribution to a random element $Y(t)$ along subsequences of the form $k(n)=2^{p(n)}t(n)$ with $p(n)=\\lceil\\log_2k(n)\\rceil\\to\\infty$ and $t(n)\\to t\\in[\\frac12,1]$. We determine the Hausdorff and box-counting dimension of the range and the graph for almost all sample paths of the stochastic process $\\{Y(t)\\}_{t\\in[1/2,1]}$. The results are compared to the fractal dimension of the corresponding limiting objects when gains are given by a deterministic sequence initiated by Hug"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5697","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":"1305.5697","created_at":"2026-05-18T02:43:09.433973+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.5697v1","created_at":"2026-05-18T02:43:09.433973+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5697","created_at":"2026-05-18T02:43:09.433973+00:00"},{"alias_kind":"pith_short_12","alias_value":"IPIGZHNP56S5","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"IPIGZHNP56S5QVGF","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"IPIGZHNP","created_at":"2026-05-18T12:27:46.883200+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/IPIGZHNP56S5QVGFY57X2OW4WW","json":"https://pith.science/pith/IPIGZHNP56S5QVGFY57X2OW4WW.json","graph_json":"https://pith.science/api/pith-number/IPIGZHNP56S5QVGFY57X2OW4WW/graph.json","events_json":"https://pith.science/api/pith-number/IPIGZHNP56S5QVGFY57X2OW4WW/events.json","paper":"https://pith.science/paper/IPIGZHNP"},"agent_actions":{"view_html":"https://pith.science/pith/IPIGZHNP56S5QVGFY57X2OW4WW","download_json":"https://pith.science/pith/IPIGZHNP56S5QVGFY57X2OW4WW.json","view_paper":"https://pith.science/paper/IPIGZHNP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.5697&json=true","fetch_graph":"https://pith.science/api/pith-number/IPIGZHNP56S5QVGFY57X2OW4WW/graph.json","fetch_events":"https://pith.science/api/pith-number/IPIGZHNP56S5QVGFY57X2OW4WW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IPIGZHNP56S5QVGFY57X2OW4WW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IPIGZHNP56S5QVGFY57X2OW4WW/action/storage_attestation","attest_author":"https://pith.science/pith/IPIGZHNP56S5QVGFY57X2OW4WW/action/author_attestation","sign_citation":"https://pith.science/pith/IPIGZHNP56S5QVGFY57X2OW4WW/action/citation_signature","submit_replication":"https://pith.science/pith/IPIGZHNP56S5QVGFY57X2OW4WW/action/replication_record"}},"created_at":"2026-05-18T02:43:09.433973+00:00","updated_at":"2026-05-18T02:43:09.433973+00:00"}