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We show that O(n/log(n))-copy sv-OWSGs (n represents the input length) are equivalent to poly(n)-copy sv-OWSGs and to quantum commitments. Since known results show that o(n/log(n))-copy OWSGs cannot imply commitments, this shows that O(n/log(n))-copy sv-OWSGs are the weakest OWSGs from which we can get commitments (and hence much of quantum cryptography).\n  Our construction follows along the lines of 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":"2404.03220","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-04-04T06:06:38Z","cross_cats_sorted":["cs.CR"],"title_canon_sha256":"8801516a098489e0e8764e02fab06440b7b48bbf09fb982d58ae0c3aaef263af","abstract_canon_sha256":"56e05614e1b2edaebe125fc4dfb816df873f9078d637344d1f3cfc9a6200ac0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:59:14.763165Z","signature_b64":"R8+OGbJvq5xfvnAaCowktCX/fytQ4h/2zN4fan3H2aV8kySAoJitUyDf0hf7Vi00RsRkh2DtRRs1PW/voy5dAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d69fd29cb2441301f854f9d0afca315df96b64c500bccb423fdab701723462c","last_reissued_at":"2026-07-05T09:59:14.762749Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:59:14.762749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Commitments are equivalent to statistically-verifiable one-way state generators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"quant-ph","authors_text":"Rahul Jain, Rishabh Batra","submitted_at":"2024-04-04T06:06:38Z","abstract_excerpt":"One-way state generators (OWSG) are natural quantum analogs to classical one-way functions. 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