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Let $A$ be a mixed characteristic DVR, $G$ a reductive group scheme over $A$, $X$ an irreducible smooth projective $A$-scheme, $\\mathcal G$ a principal $G$-bundle over $X$. Suppose $\\mathcal G$ is generically trivial. We prove that in this case $\\mathcal G$ is Zariski locally trivial. This result confirms the conjecture."},"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":"2302.02842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-02-06T15:05:52Z","cross_cats_sorted":[],"title_canon_sha256":"ff9152911c8e3e94c05ec567d429f58127933a332c4834d535154a16aebf753d","abstract_canon_sha256":"2843ea7a36cdc9e93a1aadc8d654be2a8712ff336db99278ab20b7472f66b2a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:39:07.327355Z","signature_b64":"EgXwSaTdo+CQJNL2Ih5Bcm1rji5slqQk1jahjyYMi9pHCPcUfEuYH1ujmJWBCFHpd8cc8LWI8b82PdtD83/PBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7ce2620948b7146e845d8f0af770654c4aed3e854e6f601d7d010c79d2a400c","last_reissued_at":"2026-07-05T05:39:07.326960Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:39:07.326960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Grothendieck--Serre conjecture for projective smooth schemes over a DVR","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ivan Panin, Ning Guo","submitted_at":"2023-02-06T15:05:52Z","abstract_excerpt":"The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group scheme $G$ over a regular local ring $R$ is trivial. 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