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The density of periodic configurations implies in particular that every injective endomorphism of $X$ is surjective and that the group of automorphisms of $X$ is residually finite. We also introduce a class of subshifts $X \\subset A^\\Z$, including all strongly irreducible subshifts and all irreducible sofic subshifts, in which periodic configurations are dense."},"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":"1110.4921","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-21T22:42:25Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b5d3924db2283ec6a7c731ff8c9b5fe621a4dd595178ce86c8749f3b4b60fdca","abstract_canon_sha256":"2f1fc086e284e44d074620c7824d851937009e208937fecab61db10810ed78b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:06.984283Z","signature_b64":"dyb4Swdgh5IOUITBMGPX+yL0VsK+YEnPxpmdM939XGEFc9ciUbJEYlO0v8puDASZoumz0nrEwlXg7a3aMgA5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0eb2e5a1020841dea7e853c45547fb4773ac5564f6282839c6510a3984c84a75","last_reissued_at":"2026-05-18T02:00:06.983793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:06.983793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the density of periodic configurations in strongly irreducible subshifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Michel Coornaert, Tullio Ceccherini-Silberstein","submitted_at":"2011-10-21T22:42:25Z","abstract_excerpt":"Let $G$ be a residually finite group and let $A$ be a finite set. 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