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The {\\em shift radix system} $\\tau_\\mathbf{r}: \\mathbb{Z}^d \\to \\mathbb{Z}^d$ is defined by $$ \\tau_{{\\bf r}}({\\bf z})=(z_1,\\dots,z_{d-1},-\\lfloor {\\bf r} {\\bf z}\\rfloor)^t \\qquad ({\\bf z}=(z_0,\\dots,z_{d-1})^t). $$ $\\tau_\\mathbf{r}$ has the {\\em finiteness property} if each ${\\bf z} \\in \\mathbb{Z}^d$ is eventually mapped to ${\\bf 0}$ under iterations of $\\tau_\\mathbf{r}$. In the present survey we summarize results on these nearly linear mappings. We discuss how these mappings are related to well-known numeration sy"},"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":"1312.0386","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-02T09:31:20Z","cross_cats_sorted":[],"title_canon_sha256":"4f8ca262c68081b1d509c0d11684f186f77784493c68c4d2efa335dac37ada3a","abstract_canon_sha256":"1caf23dd06e9348f94ea5aabe05fbeab6504bb36756d69cd4ac877c857924e95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:55.260460Z","signature_b64":"b8/Fy37TkXAC94PIsNXWFnWR8R6tTFEVrvqDLTjUmwlTUc4Ba7+UKvW6/+V928dYvpF/AJyAn6VNsm+z8iFbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b469a7ced0f126f80cf7fca17fe9b4d225b9b9385b00596d54dd49e177a7dde9","last_reissued_at":"2026-05-18T02:28:55.260075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:55.260075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shift Radix Systems - A Survey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J\\\"org M. 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