{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:T73JOSDXGESQHTA6JPBKVUFDHI","short_pith_number":"pith:T73JOSDX","schema_version":"1.0","canonical_sha256":"9ff6974877312503cc1e4bc2aad0a33a3cdcefba061ee49f22910fb6a57e3454","source":{"kind":"arxiv","id":"0705.2830","version":1},"attestation_state":"computed","paper":{"title":"The K(\\pi, 1) problem for the affine Artin group of type \\widetilde{B}_n and its cohomology","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Davide Moroni, Filippo Callegaro, Mario Salvetti","submitted_at":"2007-05-19T17:26:33Z","abstract_excerpt":"In this paper we prove that the complement to the affine complex arrangement of type \\widetilde{B}_n is a K(\\pi, 1) space. We also compute the cohomology of the affine Artin group G of type \\widetilde{B}_n with coefficients over several interesting local systems. In particular, we consider the module Q[q^{\\pm 1}, t^{\\pm 1}], where the first n-standard generators of G act by (-q)-multiplication while the last generator acts by (-t)-multiplication. Such representation generalizes the analog 1-parameter representation related to the bundle structure over the complement to the discriminant hypersu"},"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":"0705.2830","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2007-05-19T17:26:33Z","cross_cats_sorted":[],"title_canon_sha256":"8a4e9951aa0f8393e55900f5e916323f62e4fcdaa514c2fb321d1ab96afc0855","abstract_canon_sha256":"596f333a7999a16b86c8e67fbda319a1061ddbb52bc54cbebeaaa0577963df00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:24.936243Z","signature_b64":"NXdywqlZ4TCKH7sGeS6e2OXBIH+bAACCKeJotZOF0KxYRdE0nm/v568UPHRMqBsHRPQaBXQew1X/ZEVPVfQrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ff6974877312503cc1e4bc2aad0a33a3cdcefba061ee49f22910fb6a57e3454","last_reissued_at":"2026-05-18T03:44:24.935647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:24.935647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The K(\\pi, 1) problem for the affine Artin group of type \\widetilde{B}_n and its cohomology","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Davide Moroni, Filippo Callegaro, Mario Salvetti","submitted_at":"2007-05-19T17:26:33Z","abstract_excerpt":"In this paper we prove that the complement to the affine complex arrangement of type \\widetilde{B}_n is a K(\\pi, 1) space. We also compute the cohomology of the affine Artin group G of type \\widetilde{B}_n with coefficients over several interesting local systems. In particular, we consider the module Q[q^{\\pm 1}, t^{\\pm 1}], where the first n-standard generators of G act by (-q)-multiplication while the last generator acts by (-t)-multiplication. Such representation generalizes the analog 1-parameter representation related to the bundle structure over the complement to the discriminant hypersu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.2830","kind":"arxiv","version":1},"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":"0705.2830","created_at":"2026-05-18T03:44:24.935751+00:00"},{"alias_kind":"arxiv_version","alias_value":"0705.2830v1","created_at":"2026-05-18T03:44:24.935751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.2830","created_at":"2026-05-18T03:44:24.935751+00:00"},{"alias_kind":"pith_short_12","alias_value":"T73JOSDXGESQ","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"T73JOSDXGESQHTA6","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"T73JOSDX","created_at":"2026-05-18T12:25:56.245647+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/T73JOSDXGESQHTA6JPBKVUFDHI","json":"https://pith.science/pith/T73JOSDXGESQHTA6JPBKVUFDHI.json","graph_json":"https://pith.science/api/pith-number/T73JOSDXGESQHTA6JPBKVUFDHI/graph.json","events_json":"https://pith.science/api/pith-number/T73JOSDXGESQHTA6JPBKVUFDHI/events.json","paper":"https://pith.science/paper/T73JOSDX"},"agent_actions":{"view_html":"https://pith.science/pith/T73JOSDXGESQHTA6JPBKVUFDHI","download_json":"https://pith.science/pith/T73JOSDXGESQHTA6JPBKVUFDHI.json","view_paper":"https://pith.science/paper/T73JOSDX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0705.2830&json=true","fetch_graph":"https://pith.science/api/pith-number/T73JOSDXGESQHTA6JPBKVUFDHI/graph.json","fetch_events":"https://pith.science/api/pith-number/T73JOSDXGESQHTA6JPBKVUFDHI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T73JOSDXGESQHTA6JPBKVUFDHI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T73JOSDXGESQHTA6JPBKVUFDHI/action/storage_attestation","attest_author":"https://pith.science/pith/T73JOSDXGESQHTA6JPBKVUFDHI/action/author_attestation","sign_citation":"https://pith.science/pith/T73JOSDXGESQHTA6JPBKVUFDHI/action/citation_signature","submit_replication":"https://pith.science/pith/T73JOSDXGESQHTA6JPBKVUFDHI/action/replication_record"}},"created_at":"2026-05-18T03:44:24.935751+00:00","updated_at":"2026-05-18T03:44:24.935751+00:00"}