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For a family $\\mathfrak{F}$ of subset of $X$ and $A\\in \\mathfrak{F}$, we denote $\\Delta_{\\mathfrak{F}}(A)=\\{g\\in G: gB\\subseteq A$ for some $B\\in \\mathfrak{F}, \\ B\\subseteq A\\}$, and say that a subset $R$ of $G$ is $\\mathfrak{F}$-recurrent if $R\\bigcap \\Delta_{\\mathfrak{F}} (A)\\neq\\emptyset$ for each $A\\in \\mathfrak{F}$."},"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":"1703.00695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-03-02T10:09:58Z","cross_cats_sorted":[],"title_canon_sha256":"e049160443a6be0607de7cec5d6b14c905b04a5007dcc64d208aace2a7776233","abstract_canon_sha256":"e2e6d82b21ab128e3ab7071f68f6c0156223005e8138c1cc7d23616894568a36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:41.008624Z","signature_b64":"apBPFUukaaBSrzQw504S8m/uN6048qDIAbZQpJAkG9Lm3uyK2DbwieWk6cZciAN8GMWJs5nr0NVW54x19TkUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7579bc4de3db1a50069bbcffce5749468b728c1c45c66bd7bd98df2c5f45b3e4","last_reissued_at":"2026-05-18T00:49:41.007875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:41.007875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On recurrence in G-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Igor Protasov, Ksenia Protasova","submitted_at":"2017-03-02T10:09:58Z","abstract_excerpt":"We introduce and analyze the following general concept of recurrence. 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