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These averages take the form \\[ \\frac{1}{N^k}\\sum_{1\\leq n_1,\\ldots, n_k\\leq N} T_m^{n_{\\alpha(m)}}A_{m-1}T^{n_{\\alpha(m-1)}}_{m-1}\\ldots A_2T_2^{n_{\\alpha(2)}}A_1T_1^{n_{\\alpha(1)}} f, \\] where $f\\in L^p(X,\\mu)$ for some $1\\leq p<\\infty$, and $\\alpha:\\left\\{1,\\ldots,m\\right\\}\\to\\left\\{1,\\ldots,k\\right\\}$ encodes the entanglement. We prove that under some joint boundedness and twisted compactness conditions on the pairs $(A_i,T_i)$, almost everywh"},"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":"1705.07693","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-22T12:27:28Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"79bc578188e94b8f1318e02185cb47cf289f425087d6b10c58178c997b315b85","abstract_canon_sha256":"92fb38385187c2e7f0453bfad721ddb4b383cb364ae56680e067c885f001a50f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:32.359617Z","signature_b64":"vKrHOQCj/VoWu+ZRY6QY5deWBlVzGnql4nnAvZzBjZlInmpH1FUpLZbn+gzr1P9G1O7W0fH5PfXR+2NW3+kFCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a226b5113e812cf6f8ef0add0f285fce02ed5622e508c956d438e1003cabf651","last_reissued_at":"2026-05-18T00:10:32.358968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:32.358968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pointwise entangled ergodic theorems for Dunford-Schwartz operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"D\\'avid Kunszenti-Kov\\'acs","submitted_at":"2017-05-22T12:27:28Z","abstract_excerpt":"We investigate pointwise convergence of entangled ergodic averages of Dunford-Schwartz operators $T_0,T_1,\\ldots, T_m$ on a Borel probability space. These averages take the form \\[ \\frac{1}{N^k}\\sum_{1\\leq n_1,\\ldots, n_k\\leq N} T_m^{n_{\\alpha(m)}}A_{m-1}T^{n_{\\alpha(m-1)}}_{m-1}\\ldots A_2T_2^{n_{\\alpha(2)}}A_1T_1^{n_{\\alpha(1)}} f, \\] where $f\\in L^p(X,\\mu)$ for some $1\\leq p<\\infty$, and $\\alpha:\\left\\{1,\\ldots,m\\right\\}\\to\\left\\{1,\\ldots,k\\right\\}$ encodes the entanglement. 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