{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QUEL6PMLH4L7XTVM5B24YCQQ6A","short_pith_number":"pith:QUEL6PML","schema_version":"1.0","canonical_sha256":"8508bf3d8b3f17fbceace875cc0a10f00a0f90975bed65d2a1cc8cd704a8fd23","source":{"kind":"arxiv","id":"1809.02430","version":1},"attestation_state":"computed","paper":{"title":"Arithmetic Progressions with Restricted Digits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Aled Walker, Alexander Walker","submitted_at":"2018-09-07T12:14:17Z","abstract_excerpt":"For an integer $b \\geqslant 2$ and a set $S\\subset \\{0,\\cdots,b-1\\}$, we define the Kempner set $\\mathcal{K}(S,b)$ to be the set of all non-negative integers whose base-$b$ digital expansions contain only digits from $S$. These well-studied sparse sets provide a rich setting for additive number theory, and in this paper we study various questions relating to the appearance of arithmetic progressions in these sets. In particular, for all $b$ we determine exactly the maximal length of an arithmetic progression that omits a base-$b$ digit."},"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":"1809.02430","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-07T12:14:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"491aeb9b25b0a93b8b13784da7310b2cc42f61a97fb26a1cd11fad25dc4b1933","abstract_canon_sha256":"5774c440dad2fc7941f90da70c6e6fcfe21e5f322c3f38ae93589e577684bcdd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:17.143915Z","signature_b64":"ZLXkF97EO+F7xUyApD6yms5zCzRW/JQ/f1/f+CmISkDHNF07mMCwR36SWeXBHEStGQZmitriaFqjshai0fBqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8508bf3d8b3f17fbceace875cc0a10f00a0f90975bed65d2a1cc8cd704a8fd23","last_reissued_at":"2026-05-18T00:06:17.143259Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:17.143259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arithmetic Progressions with Restricted Digits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Aled Walker, Alexander Walker","submitted_at":"2018-09-07T12:14:17Z","abstract_excerpt":"For an integer $b \\geqslant 2$ and a set $S\\subset \\{0,\\cdots,b-1\\}$, we define the Kempner set $\\mathcal{K}(S,b)$ to be the set of all non-negative integers whose base-$b$ digital expansions contain only digits from $S$. These well-studied sparse sets provide a rich setting for additive number theory, and in this paper we study various questions relating to the appearance of arithmetic progressions in these sets. In particular, for all $b$ we determine exactly the maximal length of an arithmetic progression that omits a base-$b$ digit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02430","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":"1809.02430","created_at":"2026-05-18T00:06:17.143377+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.02430v1","created_at":"2026-05-18T00:06:17.143377+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02430","created_at":"2026-05-18T00:06:17.143377+00:00"},{"alias_kind":"pith_short_12","alias_value":"QUEL6PMLH4L7","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QUEL6PMLH4L7XTVM","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QUEL6PML","created_at":"2026-05-18T12:32:46.962924+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/QUEL6PMLH4L7XTVM5B24YCQQ6A","json":"https://pith.science/pith/QUEL6PMLH4L7XTVM5B24YCQQ6A.json","graph_json":"https://pith.science/api/pith-number/QUEL6PMLH4L7XTVM5B24YCQQ6A/graph.json","events_json":"https://pith.science/api/pith-number/QUEL6PMLH4L7XTVM5B24YCQQ6A/events.json","paper":"https://pith.science/paper/QUEL6PML"},"agent_actions":{"view_html":"https://pith.science/pith/QUEL6PMLH4L7XTVM5B24YCQQ6A","download_json":"https://pith.science/pith/QUEL6PMLH4L7XTVM5B24YCQQ6A.json","view_paper":"https://pith.science/paper/QUEL6PML","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.02430&json=true","fetch_graph":"https://pith.science/api/pith-number/QUEL6PMLH4L7XTVM5B24YCQQ6A/graph.json","fetch_events":"https://pith.science/api/pith-number/QUEL6PMLH4L7XTVM5B24YCQQ6A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QUEL6PMLH4L7XTVM5B24YCQQ6A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QUEL6PMLH4L7XTVM5B24YCQQ6A/action/storage_attestation","attest_author":"https://pith.science/pith/QUEL6PMLH4L7XTVM5B24YCQQ6A/action/author_attestation","sign_citation":"https://pith.science/pith/QUEL6PMLH4L7XTVM5B24YCQQ6A/action/citation_signature","submit_replication":"https://pith.science/pith/QUEL6PMLH4L7XTVM5B24YCQQ6A/action/replication_record"}},"created_at":"2026-05-18T00:06:17.143377+00:00","updated_at":"2026-05-18T00:06:17.143377+00:00"}