{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HFZAWACMDRQWXXDADO3VZISICQ","short_pith_number":"pith:HFZAWACM","schema_version":"1.0","canonical_sha256":"39720b004c1c616bdc601bb75ca2481417377d753fe964cfa4b7fd69d18ff380","source":{"kind":"arxiv","id":"1301.5115","version":1},"attestation_state":"computed","paper":{"title":"Central sets generated by uniformly recurrent words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GN"],"primary_cat":"math.CO","authors_text":"Luca Q. Zamboni, Michelangelo Bucci, Svetlana Puzynina","submitted_at":"2013-01-22T09:11:13Z","abstract_excerpt":"A subset $A$ of $\\nats$ is called an IP-set if $A$ contains all finite sums of distinct terms of some infinite sequence $(x_n)_{n\\in \\nats} $ of natural numbers. Central sets, first introduced by Furstenberg using notions from topological dynamics, constitute a special class of IP-sets possessing rich combinatorial properties: Each central set contains arbitrarily long arithmetic progressions, and solutions to all partition regular systems of homogeneous linear equations. In this paper we investigate central sets in the framework of combinatorics on words. Using various families of uniformly r"},"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":"1301.5115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T09:11:13Z","cross_cats_sorted":["math.DS","math.GN"],"title_canon_sha256":"149811fb95b2905a51eac37bc1f6c3108af62e3b0e20dc306af9085967cbcaf1","abstract_canon_sha256":"c0f69a713ecc5a20884c79ae7213bf0b8f2a35d08011f8aa75ad32e8b7e10c7e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:52.996452Z","signature_b64":"8cU1jVzlyEp7PAsfOdJl5XNRpwy0J9IwoamGRkootV2x/L7mZ5DXUS5AwzDMjpnZcYpOJaJ3wElxY5NSNLLNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39720b004c1c616bdc601bb75ca2481417377d753fe964cfa4b7fd69d18ff380","last_reissued_at":"2026-05-18T03:35:52.995703Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:52.995703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Central sets generated by uniformly recurrent words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GN"],"primary_cat":"math.CO","authors_text":"Luca Q. Zamboni, Michelangelo Bucci, Svetlana Puzynina","submitted_at":"2013-01-22T09:11:13Z","abstract_excerpt":"A subset $A$ of $\\nats$ is called an IP-set if $A$ contains all finite sums of distinct terms of some infinite sequence $(x_n)_{n\\in \\nats} $ of natural numbers. Central sets, first introduced by Furstenberg using notions from topological dynamics, constitute a special class of IP-sets possessing rich combinatorial properties: Each central set contains arbitrarily long arithmetic progressions, and solutions to all partition regular systems of homogeneous linear equations. In this paper we investigate central sets in the framework of combinatorics on words. Using various families of uniformly r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5115","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":"1301.5115","created_at":"2026-05-18T03:35:52.995841+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.5115v1","created_at":"2026-05-18T03:35:52.995841+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5115","created_at":"2026-05-18T03:35:52.995841+00:00"},{"alias_kind":"pith_short_12","alias_value":"HFZAWACMDRQW","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HFZAWACMDRQWXXDA","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HFZAWACM","created_at":"2026-05-18T12:27:46.883200+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/HFZAWACMDRQWXXDADO3VZISICQ","json":"https://pith.science/pith/HFZAWACMDRQWXXDADO3VZISICQ.json","graph_json":"https://pith.science/api/pith-number/HFZAWACMDRQWXXDADO3VZISICQ/graph.json","events_json":"https://pith.science/api/pith-number/HFZAWACMDRQWXXDADO3VZISICQ/events.json","paper":"https://pith.science/paper/HFZAWACM"},"agent_actions":{"view_html":"https://pith.science/pith/HFZAWACMDRQWXXDADO3VZISICQ","download_json":"https://pith.science/pith/HFZAWACMDRQWXXDADO3VZISICQ.json","view_paper":"https://pith.science/paper/HFZAWACM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.5115&json=true","fetch_graph":"https://pith.science/api/pith-number/HFZAWACMDRQWXXDADO3VZISICQ/graph.json","fetch_events":"https://pith.science/api/pith-number/HFZAWACMDRQWXXDADO3VZISICQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HFZAWACMDRQWXXDADO3VZISICQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HFZAWACMDRQWXXDADO3VZISICQ/action/storage_attestation","attest_author":"https://pith.science/pith/HFZAWACMDRQWXXDADO3VZISICQ/action/author_attestation","sign_citation":"https://pith.science/pith/HFZAWACMDRQWXXDADO3VZISICQ/action/citation_signature","submit_replication":"https://pith.science/pith/HFZAWACMDRQWXXDADO3VZISICQ/action/replication_record"}},"created_at":"2026-05-18T03:35:52.995841+00:00","updated_at":"2026-05-18T03:35:52.995841+00:00"}