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It follows that the assignment $P \\to \\Gamma(P)$ is a $p$-biset functor. We give an explicit formula for the action of bisets on $\\Gamma$, in terms of generalized transfers associated to left free bisets. Finally, we show that $\\Gamma$ is a rational $p$-biset functor, i.e. that $\\Gamma$ factors through the Roquette cate"},"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":"1604.07703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-04-26T14:57:34Z","cross_cats_sorted":["math.AT","math.CT","math.KT"],"title_canon_sha256":"e2fca4ec2821f34d4241747cda7f2a4065c3e7bb0946d71ff4740903af11ba80","abstract_canon_sha256":"89e7556a6b0ab71014dc2ad9ba51b6bc9252cb0abea82fe33c868210e1c25174"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:28.639347Z","signature_b64":"C1UUOa3n+06HOqRuwhHUWXMr9OAHbAgumx5qdjHhX6/7KvCzcQws99OZmiOd8sZwTAGpoPp0yfU0iJya4PkrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9217836701408214bb59a8275d05114bb1e27a3cb3329d0136f2b9908d9e4539","last_reissued_at":"2026-05-18T01:08:28.638712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:28.638712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"K-theory, genotypes, and biset functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT","math.KT"],"primary_cat":"math.GR","authors_text":"Serge Bouc (LAMFA)","submitted_at":"2016-04-26T14:57:34Z","abstract_excerpt":"Let p be an odd prime number. 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