{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MMMRX2T2HA5JXVBCQUDAPPJOLL","short_pith_number":"pith:MMMRX2T2","schema_version":"1.0","canonical_sha256":"63191bea7a383a9bd422850607bd2e5ad764b5ffcaf09916381ff3cf3825e7d4","source":{"kind":"arxiv","id":"2607.16064","version":1},"attestation_state":"computed","paper":{"title":"Pointwise Convergence of Ergodic Averages Along Integer Cantor Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.DS","authors_text":"Alex Iosevich, Ben Krause, F\\'elix Brokering Pinilla","submitted_at":"2026-07-17T15:44:52Z","abstract_excerpt":"Let $d \\geq 3$,\n  \\[ D \\subsetneq \\{ 0,1,\\dots,d-1\\}, \\qquad |D| \\geq 2, \\ 0 \\in D \\]\n  be a finite alphabet, and define the integer Cantor set\n  \\begin{align} \\mathcal{C} := \\mathcal{C}_{D} := \\bigcup_{J \\geq 0} \\Big\\{ \\sum_{j =0}^J a_j d^j : a_j \\in D \\Big\\}.\n  \\end{align} We prove that for any $\\sigma$-finite measure-preserving system, $(X,\\mu,T)$, and any $f \\in L^p(X)$, $2\\leq p<\\infty$, the ergodic averages \\begin{align}\n  \\frac{1}{|\\mathcal{C}_N|} \\sum_{n \\in \\mathcal{C}_N } f(T^n x), \\qquad \\mathcal{C}_N := \\mathcal{C} \\cap \\{1,2,\\dots,N \\} \\end{align}\n  converge $\\mu$-almost everywher"},"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":"2607.16064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-17T15:44:52Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"3180fbf6c3902dd13616136c8f94245aa846267d6f6cc50b758a6cd34c6ff86f","abstract_canon_sha256":"9b22e99dec9fe48514ee548d1a3381ddfbd1694c1ab270a7b3defb2359dfe654"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-20T02:19:29.051180Z","signature_b64":"4NKgxJODZ78VEkuVErRz5EJ7Z8lSYB5gbYthK9wxg+wI9PH948VVMi2vWg8rHPxNVDF6n/k/8MV4w2XELjgpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63191bea7a383a9bd422850607bd2e5ad764b5ffcaf09916381ff3cf3825e7d4","last_reissued_at":"2026-07-20T02:19:29.050367Z","signature_status":"signed_v1","first_computed_at":"2026-07-20T02:19:29.050367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pointwise Convergence of Ergodic Averages Along Integer Cantor Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.DS","authors_text":"Alex Iosevich, Ben Krause, F\\'elix Brokering Pinilla","submitted_at":"2026-07-17T15:44:52Z","abstract_excerpt":"Let $d \\geq 3$,\n  \\[ D \\subsetneq \\{ 0,1,\\dots,d-1\\}, \\qquad |D| \\geq 2, \\ 0 \\in D \\]\n  be a finite alphabet, and define the integer Cantor set\n  \\begin{align} \\mathcal{C} := \\mathcal{C}_{D} := \\bigcup_{J \\geq 0} \\Big\\{ \\sum_{j =0}^J a_j d^j : a_j \\in D \\Big\\}.\n  \\end{align} We prove that for any $\\sigma$-finite measure-preserving system, $(X,\\mu,T)$, and any $f \\in L^p(X)$, $2\\leq p<\\infty$, the ergodic averages \\begin{align}\n  \\frac{1}{|\\mathcal{C}_N|} \\sum_{n \\in \\mathcal{C}_N } f(T^n x), \\qquad \\mathcal{C}_N := \\mathcal{C} \\cap \\{1,2,\\dots,N \\} \\end{align}\n  converge $\\mu$-almost 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