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We show that (1) for all a,b, f(a,b) \\ge lg(lg(a+b)) + (2) for an infinite number of (a,b), f(a,b) \\le 1+lg(lg(a+b)."},"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":"1206.1553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2012-06-07T16:54:19Z","cross_cats_sorted":[],"title_canon_sha256":"222e12454208bfd6573a7a685e7e52ed1cb359e2df029df852bdbf9236ddec15","abstract_canon_sha256":"2b7165cc2e1db34a5422a581cba8580fe859326e27ba8a04b5350599bcf8fa3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:04.835667Z","signature_b64":"05sFqKL9DUPWdvE0oUQ3FbxUUJCtSknqlGjHKO+jvl0GP7G+AnNCUZPRwN0sAiNsPBopAlwiOED63tPCQth4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b713720f504283e3a37a2dc2ab21a7904231e5d9b340fb7c54b1329c2f9a3ae6","last_reissued_at":"2026-05-18T03:54:04.834730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:04.834730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tight Lower Bounds for Unequal Division","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Andrew Lohr","submitted_at":"2012-06-07T16:54:19Z","abstract_excerpt":"Alice and Bob want to cut a cake; however, in contrast to the usual problems of fair division, they want to cut it unfairly. 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