{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:24SS37EYUWHK3CVGQIMERKUVEB","short_pith_number":"pith:24SS37EY","schema_version":"1.0","canonical_sha256":"d7252dfc98a58ead8aa6821848aa95206431ebaaadda3d18b080086a5d0b3d84","source":{"kind":"arxiv","id":"1209.4791","version":2},"attestation_state":"computed","paper":{"title":"The lower algebraic $K$-theory of virtually cyclic subgroups of the braid groups of the sphere and of $\\mathbb{Z}[B\\_4(\\mathbb{S}^2)]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.KT","authors_text":"CNRS), Daniel Juan-Pineda (CCM), John Guaschi (LMNO, NU, Silvia Mill\\'an-L\\'opez, UNICAEN","submitted_at":"2012-09-21T11:46:07Z","abstract_excerpt":"We study $K$-theoretical aspects of the braid groups $B\\_n(\\mathbb{S}^{2})$ on $n$ strings of the $2$-sphere, which by results of the second two authors, are known to satisfy the Farrell-Jones fibred isomorphism conjecture~\\cite{JM}. In light of this, in order to determine the algebraic $K$-theory of the group ring $\\mathbb{Z}[B\\_n(\\mathbb{S}^{2})]$, one should first compute that of its virtually cyclic subgroups, which were classified by D.~L.~Gon{\\c c}alves and the first author. We calculate the Whitehead and $K\\_{-1}$-groups of the group rings of the finite subgroups (dicyclic and binary po"},"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":"1209.4791","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-09-21T11:46:07Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"5f743e953deb95407166fe1f9a5c8a4b3ee0dc065001aa6547926cdfe40a231e","abstract_canon_sha256":"1f56547633e4bdfac4a6393968a245c6b795d5780262185428c259f4de723e31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:01.386248Z","signature_b64":"yc68Ik+w9TWLFIYqcLrGVvf2YuHt5YuObo5jWCzb/z0fxRNVDPeo+nePHAebB8aywO3LZIelD4qjlHM0dXAGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7252dfc98a58ead8aa6821848aa95206431ebaaadda3d18b080086a5d0b3d84","last_reissued_at":"2026-05-18T00:12:01.385753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:01.385753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The lower algebraic $K$-theory of virtually cyclic subgroups of the braid groups of the sphere and of $\\mathbb{Z}[B\\_4(\\mathbb{S}^2)]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.KT","authors_text":"CNRS), Daniel Juan-Pineda (CCM), John Guaschi (LMNO, NU, Silvia Mill\\'an-L\\'opez, UNICAEN","submitted_at":"2012-09-21T11:46:07Z","abstract_excerpt":"We study $K$-theoretical aspects of the braid groups $B\\_n(\\mathbb{S}^{2})$ on $n$ strings of the $2$-sphere, which by results of the second two authors, are known to satisfy the Farrell-Jones fibred isomorphism conjecture~\\cite{JM}. In light of this, in order to determine the algebraic $K$-theory of the group ring $\\mathbb{Z}[B\\_n(\\mathbb{S}^{2})]$, one should first compute that of its virtually cyclic subgroups, which were classified by D.~L.~Gon{\\c c}alves and the first author. We calculate the Whitehead and $K\\_{-1}$-groups of the group rings of the finite subgroups (dicyclic and binary po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4791","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.4791","created_at":"2026-05-18T00:12:01.385818+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.4791v2","created_at":"2026-05-18T00:12:01.385818+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4791","created_at":"2026-05-18T00:12:01.385818+00:00"},{"alias_kind":"pith_short_12","alias_value":"24SS37EYUWHK","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"24SS37EYUWHK3CVG","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"24SS37EY","created_at":"2026-05-18T12:26:50.516681+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/24SS37EYUWHK3CVGQIMERKUVEB","json":"https://pith.science/pith/24SS37EYUWHK3CVGQIMERKUVEB.json","graph_json":"https://pith.science/api/pith-number/24SS37EYUWHK3CVGQIMERKUVEB/graph.json","events_json":"https://pith.science/api/pith-number/24SS37EYUWHK3CVGQIMERKUVEB/events.json","paper":"https://pith.science/paper/24SS37EY"},"agent_actions":{"view_html":"https://pith.science/pith/24SS37EYUWHK3CVGQIMERKUVEB","download_json":"https://pith.science/pith/24SS37EYUWHK3CVGQIMERKUVEB.json","view_paper":"https://pith.science/paper/24SS37EY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.4791&json=true","fetch_graph":"https://pith.science/api/pith-number/24SS37EYUWHK3CVGQIMERKUVEB/graph.json","fetch_events":"https://pith.science/api/pith-number/24SS37EYUWHK3CVGQIMERKUVEB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/24SS37EYUWHK3CVGQIMERKUVEB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/24SS37EYUWHK3CVGQIMERKUVEB/action/storage_attestation","attest_author":"https://pith.science/pith/24SS37EYUWHK3CVGQIMERKUVEB/action/author_attestation","sign_citation":"https://pith.science/pith/24SS37EYUWHK3CVGQIMERKUVEB/action/citation_signature","submit_replication":"https://pith.science/pith/24SS37EYUWHK3CVGQIMERKUVEB/action/replication_record"}},"created_at":"2026-05-18T00:12:01.385818+00:00","updated_at":"2026-05-18T00:12:01.385818+00:00"}