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Moreover we compute the total I^j-cohomology and Chow-Witt rings of P^q x P^r for all q,r greater than or equal to 1 and of BG_m x BG_m."},"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":"2508.13605","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2025-08-19T08:12:02Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"cbdb36abf01dd5c6b5e33571eeba53fde0fc7c55f3d6452f1124f078fe56de09","abstract_canon_sha256":"e8e7a7b92a3acab211a4c89a6097bfd039e05ca5aa6c4ac8485bf6ef7c79ec4e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:55:51.001965Z","signature_b64":"FQjxFohw1cisLwXCcCFT4+kzUKeU0ZQ7eB55kvbiI/TDCuSbhJgMQwX0Z6Im7ulEvwbTtyTuz1swPUHf9cejBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fac595d5c67fc302081fc5a4952610887cf45106133eddb6abe562fec54d3d1a","last_reissued_at":"2026-07-05T11:55:51.001581Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:55:51.001581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chow-Witt Rings of Classifying Spaces of Products of Multiplicative and Cyclic Groups","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Andrea Lachmann","submitted_at":"2025-08-19T08:12:02Z","abstract_excerpt":"We compute the total Chow-Witt rings of the classifying space B\\mu_n of the roots of unity, as well as the products BG_m x B\\mu_n and B\\mu_m x B\\mu_n for all m,n greater than or equal to 1 based on the strategy by di Lorenzo and Mantovani (2023) for B\\mu_n with n even. 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