{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UGLB347UXMNVF7BNZVVZAWWW5S","short_pith_number":"pith:UGLB347U","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"},"canonical_sha256":"a1961df3f4bb1b52fc2dcd6b905ad6ecb2a9ed652ed9b88c0af97bd6e1668d4c","source":{"kind":"arxiv","id":"1510.01068","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01068","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01068v4","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01068","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"UGLB347UXMNV","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UGLB347UXMNVF7BN","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UGLB347U","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UGLB347UXMNVF7BNZVVZAWWW5S","target":"record","payload":{"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"},"canonical_sha256":"a1961df3f4bb1b52fc2dcd6b905ad6ecb2a9ed652ed9b88c0af97bd6e1668d4c","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"},"source_kind":"arxiv","source_id":"1510.01068","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/BPkBBtRm+soQy3kf7lmNbOXOLQGoCfdEgjW3QWszkbURkaebc6YrY1gSvZt4cyfpNiiZJVetXeMYdOiTb8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:31:24.603069Z"},"content_sha256":"37514c9fad0c8c643f29ad41119a54858549787b9c71a9f0e1c57795bfde0d3b","schema_version":"1.0","event_id":"sha256:37514c9fad0c8c643f29ad41119a54858549787b9c71a9f0e1c57795bfde0d3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UGLB347UXMNVF7BNZVVZAWWW5S","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m3ue1p48rYYjFUtBvya4/z09WBDpqPCR6icTxCb3nBG4Yi/E9CsFRm4LUuqNd4TvhH86UaALU+xWXEGsn73iDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:31:24.603774Z"},"content_sha256":"95d803f02275345d699fe7525ea563f4e2cd9753a00b6b1b8f89f7c3d750624e","schema_version":"1.0","event_id":"sha256:95d803f02275345d699fe7525ea563f4e2cd9753a00b6b1b8f89f7c3d750624e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S/bundle.json","state_url":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UGLB347UXMNVF7BNZVVZAWWW5S/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T14:31:24Z","links":{"resolver":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S","bundle":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S/bundle.json","state":"https://pith.science/pith/UGLB347UXMNVF7BNZVVZAWWW5S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UGLB347UXMNVF7BNZVVZAWWW5S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UGLB347UXMNVF7BNZVVZAWWW5S","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4988ab33e32e1f4903fce76e91d7eb3b17b87807052cdae4a9eba2e8a8875271","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-05T09:01:44Z","title_canon_sha256":"62f1873d6fdec9a91901b78f712291051687112ec2f2892ff3c7b0e56afcc7f3"},"schema_version":"1.0","source":{"id":"1510.01068","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01068","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01068v4","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01068","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"UGLB347UXMNV","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UGLB347UXMNVF7BN","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UGLB347U","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:95d803f02275345d699fe7525ea563f4e2cd9753a00b6b1b8f89f7c3d750624e","target":"graph","created_at":"2026-05-18T00:41:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Gabriel Strasser, Klaus Schmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-05T09:01:44Z","title":"Permutations of $\\mathbb{Z}^d$ with restricted movement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01068","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:37514c9fad0c8c643f29ad41119a54858549787b9c71a9f0e1c57795bfde0d3b","target":"record","created_at":"2026-05-18T00:41:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4988ab33e32e1f4903fce76e91d7eb3b17b87807052cdae4a9eba2e8a8875271","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-05T09:01:44Z","title_canon_sha256":"62f1873d6fdec9a91901b78f712291051687112ec2f2892ff3c7b0e56afcc7f3"},"schema_version":"1.0","source":{"id":"1510.01068","kind":"arxiv","version":4}},"canonical_sha256":"a1961df3f4bb1b52fc2dcd6b905ad6ecb2a9ed652ed9b88c0af97bd6e1668d4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1961df3f4bb1b52fc2dcd6b905ad6ecb2a9ed652ed9b88c0af97bd6e1668d4c","first_computed_at":"2026-05-18T00:41:51.558797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:51.558797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gnlLOJpme/QyMZWAQN2g3rituBs6zaaV/hTSLNDj5qddcBgM6BydisGsn3OuRhsHitIbGZDIjxd5I+Zbd+lXAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:51.559402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01068","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37514c9fad0c8c643f29ad41119a54858549787b9c71a9f0e1c57795bfde0d3b","sha256:95d803f02275345d699fe7525ea563f4e2cd9753a00b6b1b8f89f7c3d750624e"],"state_sha256":"c194ff9bd9433791a91fc822ff28d4adc0f4743a5c8d12261f59ba13d5266749"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"31CrtPRbMzVyvGwS2CVkDB2MyfMsOMEIm8NtJjvFK4SVSHuXhhwnHKcTTU5cSgKFsTNY8FNkHIVSuo7di5RmAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:31:24.606506Z","bundle_sha256":"9c3db628dfd68e5afead59de29abbbf12e3439cddfc80129f41aefb758244826"}}