{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UGLB347UXMNVF7BNZVVZAWWW5S","short_pith_number":"pith:UGLB347U","schema_version":"1.0","canonical_sha256":"a1961df3f4bb1b52fc2dcd6b905ad6ecb2a9ed652ed9b88c0af97bd6e1668d4c","source":{"kind":"arxiv","id":"1510.01068","version":4},"attestation_state":"computed","paper":{"title":"Permutations of $\\mathbb{Z}^d$ with restricted movement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gabriel Strasser, Klaus Schmidt","submitted_at":"2015-10-05T09:01:44Z","abstract_excerpt":"We investigate dynamical properties of the set of permutations of $\\mathbb{Z}^d$ with restricted movement, i.e., permutations $\\pi $ of $\\mathbb{Z}^d$ such that $\\pi (\\mathbf{n})-\\mathbf{n}$ lies, for every $\\mathbf{n}\\in \\mathbb{Z}^d$, in a prescribed finite set $A\\subset \\mathbb{Z}^d$. For $d=1$, such permutations occur, for example, in restricted orbit equivalence, or in the calculation of determinants of certain bi-infinite multi-diagonal matrices. For $d\\ge2$ these sets of permutations provide natural classes of examples of multidimensional shifts of finite type."},"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":"1510.01068","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-05T09:01:44Z","cross_cats_sorted":[],"title_canon_sha256":"62f1873d6fdec9a91901b78f712291051687112ec2f2892ff3c7b0e56afcc7f3","abstract_canon_sha256":"4988ab33e32e1f4903fce76e91d7eb3b17b87807052cdae4a9eba2e8a8875271"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:51.559402Z","signature_b64":"gnlLOJpme/QyMZWAQN2g3rituBs6zaaV/hTSLNDj5qddcBgM6BydisGsn3OuRhsHitIbGZDIjxd5I+Zbd+lXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1961df3f4bb1b52fc2dcd6b905ad6ecb2a9ed652ed9b88c0af97bd6e1668d4c","last_reissued_at":"2026-05-18T00:41:51.558797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:51.558797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Permutations of $\\mathbb{Z}^d$ with restricted movement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gabriel Strasser, Klaus Schmidt","submitted_at":"2015-10-05T09:01:44Z","abstract_excerpt":"We investigate dynamical properties of the set of permutations of $\\mathbb{Z}^d$ with restricted movement, i.e., permutations $\\pi $ of $\\mathbb{Z}^d$ such that $\\pi (\\mathbf{n})-\\mathbf{n}$ lies, for every $\\mathbf{n}\\in \\mathbb{Z}^d$, in a prescribed finite set $A\\subset \\mathbb{Z}^d$. For $d=1$, such permutations occur, for example, in restricted orbit equivalence, or in the calculation of determinants of certain bi-infinite multi-diagonal matrices. For $d\\ge2$ these sets of permutations provide natural classes of examples of multidimensional shifts of finite type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01068","kind":"arxiv","version":4},"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":"1510.01068","created_at":"2026-05-18T00:41:51.558886+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.01068v4","created_at":"2026-05-18T00:41:51.558886+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01068","created_at":"2026-05-18T00:41:51.558886+00:00"},{"alias_kind":"pith_short_12","alias_value":"UGLB347UXMNV","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UGLB347UXMNVF7BN","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UGLB347U","created_at":"2026-05-18T12:29:44.643036+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/UGLB347UXMNVF7BNZVVZAWWW5S","json":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S.json","graph_json":"https://pith.science/api/pith-number/UGLB347UXMNVF7BNZVVZAWWW5S/graph.json","events_json":"https://pith.science/api/pith-number/UGLB347UXMNVF7BNZVVZAWWW5S/events.json","paper":"https://pith.science/paper/UGLB347U"},"agent_actions":{"view_html":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S","download_json":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S.json","view_paper":"https://pith.science/paper/UGLB347U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.01068&json=true","fetch_graph":"https://pith.science/api/pith-number/UGLB347UXMNVF7BNZVVZAWWW5S/graph.json","fetch_events":"https://pith.science/api/pith-number/UGLB347UXMNVF7BNZVVZAWWW5S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S/action/storage_attestation","attest_author":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S/action/author_attestation","sign_citation":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S/action/citation_signature","submit_replication":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S/action/replication_record"}},"created_at":"2026-05-18T00:41:51.558886+00:00","updated_at":"2026-05-18T00:41:51.558886+00:00"}