{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IPIGZHNP56S5QVGFY57X2OW4WW","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":"da9c40b37e5ed33addeeb066c0bf75ac68c37a9af50e4225976e5b624874626d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-24T11:49:25Z","title_canon_sha256":"39b1d0a7a1869b0ba678d23070a0f671de714fe5c091742e66a1eb37c2f9aa87"},"schema_version":"1.0","source":{"id":"1305.5697","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5697","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5697v1","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5697","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"IPIGZHNP56S5","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IPIGZHNP56S5QVGF","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IPIGZHNP","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:94620cf1284a0ca4d3f3613cf5116d82fe37924f2f8157ffb27794386d52a845","target":"graph","created_at":"2026-05-18T02:43:09Z","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":"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","authors_text":"Lina Wedrich, Peter Kern","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-24T11:49:25Z","title":"The dimension of the St. Petersburg game"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5697","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:ea76a0809b705d8b5684e182d9dc24d978b9080c734c897ef530e27ecf11b801","target":"record","created_at":"2026-05-18T02:43:09Z","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":"da9c40b37e5ed33addeeb066c0bf75ac68c37a9af50e4225976e5b624874626d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-24T11:49:25Z","title_canon_sha256":"39b1d0a7a1869b0ba678d23070a0f671de714fe5c091742e66a1eb37c2f9aa87"},"schema_version":"1.0","source":{"id":"1305.5697","kind":"arxiv","version":1}},"canonical_sha256":"43d06c9dafefa5d854c5c77f7d3adcb5bc6711da6e61c0884d0f78a5a5548e6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43d06c9dafefa5d854c5c77f7d3adcb5bc6711da6e61c0884d0f78a5a5548e6e","first_computed_at":"2026-05-18T02:43:09.433881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:09.433881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qwiI7YSUKlF1TGXVBjbIVnH5kjziCMQr23XSq0lwDAvGCdCGRPXX3+I06LsUbmo5ZSTYfu1SsuG0JUFDuqR1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:09.434530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5697","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea76a0809b705d8b5684e182d9dc24d978b9080c734c897ef530e27ecf11b801","sha256:94620cf1284a0ca4d3f3613cf5116d82fe37924f2f8157ffb27794386d52a845"],"state_sha256":"8b6915565f47aa996cd6d7f4223dbd13095ffc08a52f23ba475c74ecf518bd61"}