{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SURDFAGVNJR3WTFKUHXOFMSIM2","short_pith_number":"pith:SURDFAGV","schema_version":"1.0","canonical_sha256":"95223280d56a63bb4caaa1eee2b248669b24c9986c5b11c9d2f876b04b4e3d7b","source":{"kind":"arxiv","id":"1703.09015","version":3},"attestation_state":"computed","paper":{"title":"Quantitative results using variants of Schmidt's game: Dimension bounds, arithmetic progressions, and more","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.MG","authors_text":"David Simmons, Lior Fishman, Ryan Broderick","submitted_at":"2017-03-27T11:20:57Z","abstract_excerpt":"Schmidt's game is generally used to deduce qualitative information about the Hausdorff dimensions of fractal sets and their intersections. However, one can also ask about quantitative versions of the properties of winning sets. In this paper we show that such quantitative information has applications to various questions including:\n  * What is the maximal length of an arithmetic progression on the \"middle $\\epsilon$\" Cantor set?\n  * What is the smallest $n$ such that there is some element of the ternary Cantor set whose continued fraction partial quotients are all $\\leq n$?\n  * What is the Hau"},"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":"1703.09015","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-03-27T11:20:57Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"6b19973a127e26f8142131abc98bcd201bb1af8e1750291dd7e4d9272c5ea3d9","abstract_canon_sha256":"bc7c4180184e2d116459f0f6ebd4986810c88aef18c085cb4094735b12a1b31b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:09.197010Z","signature_b64":"qJBA0sL1EstVp2H022tbeW3bSRlPf3o7/JwxVJvdVfCrW4rokpSUXP/j3xROVlvKEvZccK+vVEHsN1Xv1x9pBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95223280d56a63bb4caaa1eee2b248669b24c9986c5b11c9d2f876b04b4e3d7b","last_reissued_at":"2026-05-18T00:35:09.196438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:09.196438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantitative results using variants of Schmidt's game: Dimension bounds, arithmetic progressions, and more","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.MG","authors_text":"David Simmons, Lior Fishman, Ryan Broderick","submitted_at":"2017-03-27T11:20:57Z","abstract_excerpt":"Schmidt's game is generally used to deduce qualitative information about the Hausdorff dimensions of fractal sets and their intersections. However, one can also ask about quantitative versions of the properties of winning sets. In this paper we show that such quantitative information has applications to various questions including:\n  * What is the maximal length of an arithmetic progression on the \"middle $\\epsilon$\" Cantor set?\n  * What is the smallest $n$ such that there is some element of the ternary Cantor set whose continued fraction partial quotients are all $\\leq n$?\n  * What is the Hau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09015","kind":"arxiv","version":3},"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":"1703.09015","created_at":"2026-05-18T00:35:09.196519+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.09015v3","created_at":"2026-05-18T00:35:09.196519+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09015","created_at":"2026-05-18T00:35:09.196519+00:00"},{"alias_kind":"pith_short_12","alias_value":"SURDFAGVNJR3","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SURDFAGVNJR3WTFK","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SURDFAGV","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/SURDFAGVNJR3WTFKUHXOFMSIM2","json":"https://pith.science/pith/SURDFAGVNJR3WTFKUHXOFMSIM2.json","graph_json":"https://pith.science/api/pith-number/SURDFAGVNJR3WTFKUHXOFMSIM2/graph.json","events_json":"https://pith.science/api/pith-number/SURDFAGVNJR3WTFKUHXOFMSIM2/events.json","paper":"https://pith.science/paper/SURDFAGV"},"agent_actions":{"view_html":"https://pith.science/pith/SURDFAGVNJR3WTFKUHXOFMSIM2","download_json":"https://pith.science/pith/SURDFAGVNJR3WTFKUHXOFMSIM2.json","view_paper":"https://pith.science/paper/SURDFAGV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.09015&json=true","fetch_graph":"https://pith.science/api/pith-number/SURDFAGVNJR3WTFKUHXOFMSIM2/graph.json","fetch_events":"https://pith.science/api/pith-number/SURDFAGVNJR3WTFKUHXOFMSIM2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SURDFAGVNJR3WTFKUHXOFMSIM2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SURDFAGVNJR3WTFKUHXOFMSIM2/action/storage_attestation","attest_author":"https://pith.science/pith/SURDFAGVNJR3WTFKUHXOFMSIM2/action/author_attestation","sign_citation":"https://pith.science/pith/SURDFAGVNJR3WTFKUHXOFMSIM2/action/citation_signature","submit_replication":"https://pith.science/pith/SURDFAGVNJR3WTFKUHXOFMSIM2/action/replication_record"}},"created_at":"2026-05-18T00:35:09.196519+00:00","updated_at":"2026-05-18T00:35:09.196519+00:00"}