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As a result of an $f$-adaptive renaming algorithm each participating process gets a distinct name in the range $\\{1,\\dots,f(k)\\}$ provided $k$ processes participate.\n  Let $f: \\{1,\\dots,n\\} \\rightarrow \\mathbb{N}$ be a non-decreasing function satisfying $f(1) \\leq n-1$ and let $d = \\max\\{x ~|~ f(x) \\leq n-1\\}$. We show that any non-deterministic solo-terminating long-lived $f$-adaptive renaming object require"},"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":"1603.04067","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-03-13T19:28:20Z","cross_cats_sorted":[],"title_canon_sha256":"fb6157765616713e38e41f17950d8aea61b6a783a7ed74684881833019ff1eac","abstract_canon_sha256":"25bd37b2a37186aba8c099cc25fab17338a195b62eb7272063aa46e6101a3d33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:52.362583Z","signature_b64":"qXRZxbrcyyMlDUGfp0N9464glQl1aR0MhB5WedEOQcFlFV9uSZh+BqUOJHHkr7hSsbLD5v9KSXZpdKIkQRWKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6158d2acbca13f15bf65f1b9250d5df14c0ddcf0b9b82cc728e98a522bd8db18","last_reissued_at":"2026-05-18T01:14:52.361947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:52.361947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Space Bounds for Adaptive Renaming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Lisa Higham, Maryam Helmi, Philipp Woelfel","submitted_at":"2016-03-13T19:28:20Z","abstract_excerpt":"We study the space complexity of implementing long-lived and one-shot adaptive renaming from multi-reader multi-writer registers, in an asynchronous distributed system with $n$ processes. 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