{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:RYROP2WBV57MWG2Z63AUQASIX3","short_pith_number":"pith:RYROP2WB","schema_version":"1.0","canonical_sha256":"8e22e7eac1af7ecb1b59f6c1480248bed2fa957d8b2c3738470a43a29036f00f","source":{"kind":"arxiv","id":"1401.5259","version":1},"attestation_state":"computed","paper":{"title":"Characterization algorithms for shift radix systems with finiteness property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mario Weitzer","submitted_at":"2014-01-21T10:55:15Z","abstract_excerpt":"For a natural number d and a d-dimensional real vector r let Tau(r) denote the (d-dimensional) shift radix system associated with r. Tau(r) is said to have the finiteness property iff all orbits of Tau(r) end up in the zero vector; the set of all corresponding parameters r is denoted by DN(d), whereas D(d) consists of those parameters r for which all orbits are eventually periodic. DN(d) has a very complicated structure even for d=2. In the present paper two algorithms are presented which allow the characterization of the intersection of DN(d) and any closed convex hull of finitely many interi"},"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":"1401.5259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-21T10:55:15Z","cross_cats_sorted":[],"title_canon_sha256":"10f3f181f9752a775e339ed1021d43ae2748e1a88c03bf85930a24bcc0c4c66d","abstract_canon_sha256":"905e311de99cf73a0e441126d4c5e584402bea821906677ecc52b01a66be93dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:34.361460Z","signature_b64":"1v5nGrC5d8JIXuObiewIwUTT6vfzt+h4l7MJRcCMAibuEKYntYGU7NKLuIR3k6rgJw43p/HBdvCi1hmW/nMQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e22e7eac1af7ecb1b59f6c1480248bed2fa957d8b2c3738470a43a29036f00f","last_reissued_at":"2026-05-18T03:01:34.360779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:34.360779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterization algorithms for shift radix systems with finiteness property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mario Weitzer","submitted_at":"2014-01-21T10:55:15Z","abstract_excerpt":"For a natural number d and a d-dimensional real vector r let Tau(r) denote the (d-dimensional) shift radix system associated with r. Tau(r) is said to have the finiteness property iff all orbits of Tau(r) end up in the zero vector; the set of all corresponding parameters r is denoted by DN(d), whereas D(d) consists of those parameters r for which all orbits are eventually periodic. DN(d) has a very complicated structure even for d=2. In the present paper two algorithms are presented which allow the characterization of the intersection of DN(d) and any closed convex hull of finitely many interi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5259","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":"1401.5259","created_at":"2026-05-18T03:01:34.360870+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.5259v1","created_at":"2026-05-18T03:01:34.360870+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5259","created_at":"2026-05-18T03:01:34.360870+00:00"},{"alias_kind":"pith_short_12","alias_value":"RYROP2WBV57M","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RYROP2WBV57MWG2Z","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RYROP2WB","created_at":"2026-05-18T12:28:46.137349+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/RYROP2WBV57MWG2Z63AUQASIX3","json":"https://pith.science/pith/RYROP2WBV57MWG2Z63AUQASIX3.json","graph_json":"https://pith.science/api/pith-number/RYROP2WBV57MWG2Z63AUQASIX3/graph.json","events_json":"https://pith.science/api/pith-number/RYROP2WBV57MWG2Z63AUQASIX3/events.json","paper":"https://pith.science/paper/RYROP2WB"},"agent_actions":{"view_html":"https://pith.science/pith/RYROP2WBV57MWG2Z63AUQASIX3","download_json":"https://pith.science/pith/RYROP2WBV57MWG2Z63AUQASIX3.json","view_paper":"https://pith.science/paper/RYROP2WB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.5259&json=true","fetch_graph":"https://pith.science/api/pith-number/RYROP2WBV57MWG2Z63AUQASIX3/graph.json","fetch_events":"https://pith.science/api/pith-number/RYROP2WBV57MWG2Z63AUQASIX3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RYROP2WBV57MWG2Z63AUQASIX3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RYROP2WBV57MWG2Z63AUQASIX3/action/storage_attestation","attest_author":"https://pith.science/pith/RYROP2WBV57MWG2Z63AUQASIX3/action/author_attestation","sign_citation":"https://pith.science/pith/RYROP2WBV57MWG2Z63AUQASIX3/action/citation_signature","submit_replication":"https://pith.science/pith/RYROP2WBV57MWG2Z63AUQASIX3/action/replication_record"}},"created_at":"2026-05-18T03:01:34.360870+00:00","updated_at":"2026-05-18T03:01:34.360870+00:00"}