{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:K2R6K3K6FUYWH6D24PCVJY2ZRK","short_pith_number":"pith:K2R6K3K6","schema_version":"1.0","canonical_sha256":"56a3e56d5e2d3163f87ae3c554e3598a806b34d2a7e825742f5ede5fe2825a8e","source":{"kind":"arxiv","id":"1710.08353","version":1},"attestation_state":"computed","paper":{"title":"When is an automatic set an additive basis?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.FL","math.CO"],"primary_cat":"math.NT","authors_text":"Jason Bell, Jeffrey Shallit, Kathryn Hare","submitted_at":"2017-10-23T15:54:31Z","abstract_excerpt":"We characterize those $k$-automatic sets $S$ of natural numbers that form an additive basis for the natural numbers, and we show that this characterization is effective. In addition, we give an algorithm to determine the smallest $j$ such that $S$ forms an additive basis of order $j$, if it exists."},"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":"1710.08353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-23T15:54:31Z","cross_cats_sorted":["cs.DM","cs.FL","math.CO"],"title_canon_sha256":"b334c51e49551aef527def0d4a27142813f5be12306f705362532e054ab653cb","abstract_canon_sha256":"cd782c92e64d59e437cd3b5ff4dfc023cd85f54fffb01025ed0dbe281df80a18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:16.625177Z","signature_b64":"BrpaS4ZllZgDW5+E5skrpfYHXEodTgDCX0M6nop2/WRz0rNXkkf7c1Wj+ROAYXocHkItVKeL/lTlE5MGjKgmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56a3e56d5e2d3163f87ae3c554e3598a806b34d2a7e825742f5ede5fe2825a8e","last_reissued_at":"2026-05-18T00:32:16.624690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:16.624690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When is an automatic set an additive basis?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.FL","math.CO"],"primary_cat":"math.NT","authors_text":"Jason Bell, Jeffrey Shallit, Kathryn Hare","submitted_at":"2017-10-23T15:54:31Z","abstract_excerpt":"We characterize those $k$-automatic sets $S$ of natural numbers that form an additive basis for the natural numbers, and we show that this characterization is effective. In addition, we give an algorithm to determine the smallest $j$ such that $S$ forms an additive basis of order $j$, if it exists."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08353","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":"1710.08353","created_at":"2026-05-18T00:32:16.624757+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.08353v1","created_at":"2026-05-18T00:32:16.624757+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08353","created_at":"2026-05-18T00:32:16.624757+00:00"},{"alias_kind":"pith_short_12","alias_value":"K2R6K3K6FUYW","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"K2R6K3K6FUYWH6D2","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"K2R6K3K6","created_at":"2026-05-18T12:31:24.725408+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/K2R6K3K6FUYWH6D24PCVJY2ZRK","json":"https://pith.science/pith/K2R6K3K6FUYWH6D24PCVJY2ZRK.json","graph_json":"https://pith.science/api/pith-number/K2R6K3K6FUYWH6D24PCVJY2ZRK/graph.json","events_json":"https://pith.science/api/pith-number/K2R6K3K6FUYWH6D24PCVJY2ZRK/events.json","paper":"https://pith.science/paper/K2R6K3K6"},"agent_actions":{"view_html":"https://pith.science/pith/K2R6K3K6FUYWH6D24PCVJY2ZRK","download_json":"https://pith.science/pith/K2R6K3K6FUYWH6D24PCVJY2ZRK.json","view_paper":"https://pith.science/paper/K2R6K3K6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.08353&json=true","fetch_graph":"https://pith.science/api/pith-number/K2R6K3K6FUYWH6D24PCVJY2ZRK/graph.json","fetch_events":"https://pith.science/api/pith-number/K2R6K3K6FUYWH6D24PCVJY2ZRK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K2R6K3K6FUYWH6D24PCVJY2ZRK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K2R6K3K6FUYWH6D24PCVJY2ZRK/action/storage_attestation","attest_author":"https://pith.science/pith/K2R6K3K6FUYWH6D24PCVJY2ZRK/action/author_attestation","sign_citation":"https://pith.science/pith/K2R6K3K6FUYWH6D24PCVJY2ZRK/action/citation_signature","submit_replication":"https://pith.science/pith/K2R6K3K6FUYWH6D24PCVJY2ZRK/action/replication_record"}},"created_at":"2026-05-18T00:32:16.624757+00:00","updated_at":"2026-05-18T00:32:16.624757+00:00"}