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It is known that in a rank two free group any primitive element is conjugate either to a palindrome or to the product of two palindromes, but known iteration schemes for all primitive words give only a representative for the conjugacy class. Here we derive a new iteration scheme that gives either the unique palindrome in the conjugacy class or expresse"},"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":"0802.2731","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2008-02-19T23:02:26Z","cross_cats_sorted":["math.CV","math.GT","math.NT","math.RT"],"title_canon_sha256":"7937794b2440a45fe5e3f84769a78d88a8dd6bce6003bbf35f9ff050b2152b45","abstract_canon_sha256":"32cafc844c9648a336dda9c2c1eea9f9be213dc0e9030e62670d565274cab74a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:55.908302Z","signature_b64":"NmresqaxwErU1tMo05lHexEA5p+1q2Ya6zfPwz0uOyTHtmzOfemx9fqgFLkgzS+LmCADs8JgVvvm+7KLJ/nnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea615d5a60302c46b3c3d4b2332d537c4371cc819ea0f5af8e4fb5b3de27bafc","last_reissued_at":"2026-05-18T04:28:55.907858Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:55.907858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enumerating Palindromes and Primitives in Rank Two Free Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.GT","math.NT","math.RT"],"primary_cat":"math.GR","authors_text":"Jane Gilman, Linda Keen","submitted_at":"2008-02-19T23:02:26Z","abstract_excerpt":"Let $F= < a,b>$ be a rank two free group. 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