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We denote by l_g(d) the length of a shortest addition chain for d. Many results have been established in the case g=2. Our aim is to establish the same sort of results for arbitrary fixed g. In particular, we adapt methods for constructing g-addition chains when g=2 to the case g>2 and we s"},"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":"1607.07011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-07-24T08:28:54Z","cross_cats_sorted":["cs.CC","cs.DM"],"title_canon_sha256":"e24dd85ea47aa6df99c8a52a40960e3828a6e375112b104198a33b35506fa71b","abstract_canon_sha256":"67f4f48539343d59b67cb74cd6fdb8d1db0ca6a53bb18b5f69a2892ba5086d7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:35.139866Z","signature_b64":"CmNKbyO6+P4JDaR9cO9qgQ0rQgvWzo+FV56+rSn6PHVkxHskHfAkuAmdSlDZJyxPcdg4XpUfK7eNeQSTAnU4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a4d28abf4f6cc05b5110f48d57182338fb13ed0a166131495951f574c7da559","last_reissued_at":"2026-05-18T01:10:35.139310Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:35.139310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Generalized Addition Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"math.NT","authors_text":"Pierre McKenzie, Yara Elias","submitted_at":"2016-07-24T08:28:54Z","abstract_excerpt":"Given integers d >= 1, and g >= 2, a g-addition chain for d is a sequence of integers a_0=1, a_1, a_2,..., a_{r-1}, a_r=d where a_i=a_{j_1}+a_{j_2}+...+a_{j_k}, with 2 =< k =< g, and 0 =< j_1 =< j_2 =< ... =< j_k =< i-1. The length of a g-addition chain is r, the number of terms following 1 in the sequence. We denote by l_g(d) the length of a shortest addition chain for d. Many results have been established in the case g=2. Our aim is to establish the same sort of results for arbitrary fixed g. 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