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Non-closure under powering: There is a sequence of polynomials $(f_n(x_1,\\ldots, x_n))_n$ with $\\mathsf{poly}(n)$-sized roABPs such that any super-constant power of $f_n$ does not h"},"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":"2509.10725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2025-09-12T22:30:24Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"1c4e2272067ca8ba60515f66f54969cce19658a6243f72aaa020db46dca48e24","abstract_canon_sha256":"53ae22b8ead0fd68df45bb2472a5eaee6d050fd07054ce876266902407090683"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:11:26.906784Z","signature_b64":"NGErXVpb3hH3Akz+4gGVOFk0dZLzPogFm40DC9ofYnX+0Zej1wkXG8f+ksx5WA7Sle5c+J1NCW8kgIlxr11SCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffe99f817dc24962e72429dcd66aad86d6931db9d8b91a3aedca0a854664c198","last_reissued_at":"2026-07-05T12:11:26.906219Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:11:26.906219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Closure Properties of Read-Once Oblivious Algebraic Branching Programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CC","authors_text":"Jules Armand, Magnus Rahbek Dalgaard Hansen, Nutan Limaye, Prateek Dwivedi, S\\'ebastien Tavenas, Srikanth Srinivasan","submitted_at":"2025-09-12T22:30:24Z","abstract_excerpt":"We investigate the closure properties of read-once oblivious Algebraic Branching Programs (roABPs) under various natural algebraic operations and prove the following.\n  - 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