{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:RYYKTGW7AITLXVG7DJAEEWD3VV","short_pith_number":"pith:RYYKTGW7","schema_version":"1.0","canonical_sha256":"8e30a99adf0226bbd4df1a4042587bad6e0bf19d435e9fed07b8cd97b13a1e48","source":{"kind":"arxiv","id":"1707.06059","version":2},"attestation_state":"computed","paper":{"title":"Multifractal analysis of the Birkhoff sums of Saint-Petersburg potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Baowei Wang, Dong Han Kim, Lingmin Liao (LAMA), Michal Rams (PAN)","submitted_at":"2017-07-19T13:00:40Z","abstract_excerpt":"Let $((0,1], T)$ be the doubling map in the unit interval and $\\varphi$ be the Saint-Petersburg potential, defined by $\\varphi(x)=2^n$ if $x\\in (2^{-n-1}, 2^{-n}]$ for all $n\\geq 0$. We consider the asymptotic properties of the Birkhoff sum $S\\_n(x)=\\varphi(x)+\\cdots+\\varphi(T^{n-1}(x))$. With respect to the Lebesgue measure, the Saint-Petersburg potential is not integrable and it is known that $\\frac{1}{n\\log n}S\\_n(x)$ converges to $\\frac{1}{\\log 2}$ in probability. We determine the Hausdorff dimension of the level set $\\{x: \\lim\\_{n\\to\\infty}S\\_n(x)/n=\\alpha\\} \\ (\\alpha>0)$, as well as that"},"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":"1707.06059","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-19T13:00:40Z","cross_cats_sorted":[],"title_canon_sha256":"ba9160248e36a86ce9e155360be5c7be4daf9d36262d5f4ceecfcefa8f926cff","abstract_canon_sha256":"ba02f4b418f5e927ab85e950d938f7e447cd717364e78d0ea994ce13965c1582"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:31.044477Z","signature_b64":"KYJDA6pUUEZ6fmRw9ZJbMZ/QXeQlQgB39Jz8IHx+Qke0sDVdsgu1QNuUtdBebZ21fZe8cvKW91RMvZLUfzK+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e30a99adf0226bbd4df1a4042587bad6e0bf19d435e9fed07b8cd97b13a1e48","last_reissued_at":"2026-05-18T00:09:31.043660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:31.043660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multifractal analysis of the Birkhoff sums of Saint-Petersburg potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Baowei Wang, Dong Han Kim, Lingmin Liao (LAMA), Michal Rams (PAN)","submitted_at":"2017-07-19T13:00:40Z","abstract_excerpt":"Let $((0,1], T)$ be the doubling map in the unit interval and $\\varphi$ be the Saint-Petersburg potential, defined by $\\varphi(x)=2^n$ if $x\\in (2^{-n-1}, 2^{-n}]$ for all $n\\geq 0$. We consider the asymptotic properties of the Birkhoff sum $S\\_n(x)=\\varphi(x)+\\cdots+\\varphi(T^{n-1}(x))$. With respect to the Lebesgue measure, the Saint-Petersburg potential is not integrable and it is known that $\\frac{1}{n\\log n}S\\_n(x)$ converges to $\\frac{1}{\\log 2}$ in probability. We determine the Hausdorff dimension of the level set $\\{x: \\lim\\_{n\\to\\infty}S\\_n(x)/n=\\alpha\\} \\ (\\alpha>0)$, as well as that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06059","kind":"arxiv","version":2},"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":"1707.06059","created_at":"2026-05-18T00:09:31.043785+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06059v2","created_at":"2026-05-18T00:09:31.043785+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06059","created_at":"2026-05-18T00:09:31.043785+00:00"},{"alias_kind":"pith_short_12","alias_value":"RYYKTGW7AITL","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"RYYKTGW7AITLXVG7","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"RYYKTGW7","created_at":"2026-05-18T12:31:43.269735+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/RYYKTGW7AITLXVG7DJAEEWD3VV","json":"https://pith.science/pith/RYYKTGW7AITLXVG7DJAEEWD3VV.json","graph_json":"https://pith.science/api/pith-number/RYYKTGW7AITLXVG7DJAEEWD3VV/graph.json","events_json":"https://pith.science/api/pith-number/RYYKTGW7AITLXVG7DJAEEWD3VV/events.json","paper":"https://pith.science/paper/RYYKTGW7"},"agent_actions":{"view_html":"https://pith.science/pith/RYYKTGW7AITLXVG7DJAEEWD3VV","download_json":"https://pith.science/pith/RYYKTGW7AITLXVG7DJAEEWD3VV.json","view_paper":"https://pith.science/paper/RYYKTGW7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06059&json=true","fetch_graph":"https://pith.science/api/pith-number/RYYKTGW7AITLXVG7DJAEEWD3VV/graph.json","fetch_events":"https://pith.science/api/pith-number/RYYKTGW7AITLXVG7DJAEEWD3VV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RYYKTGW7AITLXVG7DJAEEWD3VV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RYYKTGW7AITLXVG7DJAEEWD3VV/action/storage_attestation","attest_author":"https://pith.science/pith/RYYKTGW7AITLXVG7DJAEEWD3VV/action/author_attestation","sign_citation":"https://pith.science/pith/RYYKTGW7AITLXVG7DJAEEWD3VV/action/citation_signature","submit_replication":"https://pith.science/pith/RYYKTGW7AITLXVG7DJAEEWD3VV/action/replication_record"}},"created_at":"2026-05-18T00:09:31.043785+00:00","updated_at":"2026-05-18T00:09:31.043785+00:00"}