{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:NG4COWJPFYNVPISL7FNUVBCBAY","short_pith_number":"pith:NG4COWJP","schema_version":"1.0","canonical_sha256":"69b827592f2e1b57a24bf95b4a8441061215b90058001d50025962dfc01c3b63","source":{"kind":"arxiv","id":"2505.00505","version":1},"attestation_state":"computed","paper":{"title":"Generically trivial torsors under constant groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Alexis Bouthier, Federico Scavia, Kestutis Cesnavicius","submitted_at":"2025-05-01T13:22:37Z","abstract_excerpt":"We resolve the Grothendieck-Serre question over an arbitrary base field $k$: for a smooth $k$-group scheme $G$ and a smooth $k$-variety $X$, we show that every generically trivial $G$-torsor over $X$ trivializes Zariski semilocally on $X$. This was known when $G$ is reductive or when $k$ is perfect, and to settle it in general we uncover a wealth of new arithmetic phenomena over imperfect $k$. We build our arguments on new purity theorems for torsors under pseudo-complete, pseudo-proper, and pseudo-finite $k$-groups, for instance, respectively, under wound unipotent $k$-groups, under pseudo-ab"},"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":"2505.00505","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-01T13:22:37Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"2ac89a91b258b0f07a4b694c6bd95ba5e1000622be374221e5aeae0cd4d49f72","abstract_canon_sha256":"1c277c97e03982ab5bc717cfa20d2841fa1cc783c7121859870161add8c0875b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:57:14.639880Z","signature_b64":"P+udAC7PJpBiUHijzAIjO5DJp8IjL+czsEhO4oqA++egNn71HiLi0VErLZ9wANWT1f8yKogZ3b+s+Y5QPxS6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69b827592f2e1b57a24bf95b4a8441061215b90058001d50025962dfc01c3b63","last_reissued_at":"2026-07-05T10:57:14.639475Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:57:14.639475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generically trivial torsors under constant groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Alexis Bouthier, Federico Scavia, Kestutis Cesnavicius","submitted_at":"2025-05-01T13:22:37Z","abstract_excerpt":"We resolve the Grothendieck-Serre question over an arbitrary base field $k$: for a smooth $k$-group scheme $G$ and a smooth $k$-variety $X$, we show that every generically trivial $G$-torsor over $X$ trivializes Zariski semilocally on $X$. This was known when $G$ is reductive or when $k$ is perfect, and to settle it in general we uncover a wealth of new arithmetic phenomena over imperfect $k$. We build our arguments on new purity theorems for torsors under pseudo-complete, pseudo-proper, and pseudo-finite $k$-groups, for instance, respectively, under wound unipotent $k$-groups, under pseudo-ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00505","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.00505/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2505.00505","created_at":"2026-07-05T10:57:14.639531+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.00505v1","created_at":"2026-07-05T10:57:14.639531+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.00505","created_at":"2026-07-05T10:57:14.639531+00:00"},{"alias_kind":"pith_short_12","alias_value":"NG4COWJPFYNV","created_at":"2026-07-05T10:57:14.639531+00:00"},{"alias_kind":"pith_short_16","alias_value":"NG4COWJPFYNVPISL","created_at":"2026-07-05T10:57:14.639531+00:00"},{"alias_kind":"pith_short_8","alias_value":"NG4COWJP","created_at":"2026-07-05T10:57:14.639531+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.01595","citing_title":"Finite abelian subgroups of algebraic groups","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NG4COWJPFYNVPISL7FNUVBCBAY","json":"https://pith.science/pith/NG4COWJPFYNVPISL7FNUVBCBAY.json","graph_json":"https://pith.science/api/pith-number/NG4COWJPFYNVPISL7FNUVBCBAY/graph.json","events_json":"https://pith.science/api/pith-number/NG4COWJPFYNVPISL7FNUVBCBAY/events.json","paper":"https://pith.science/paper/NG4COWJP"},"agent_actions":{"view_html":"https://pith.science/pith/NG4COWJPFYNVPISL7FNUVBCBAY","download_json":"https://pith.science/pith/NG4COWJPFYNVPISL7FNUVBCBAY.json","view_paper":"https://pith.science/paper/NG4COWJP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.00505&json=true","fetch_graph":"https://pith.science/api/pith-number/NG4COWJPFYNVPISL7FNUVBCBAY/graph.json","fetch_events":"https://pith.science/api/pith-number/NG4COWJPFYNVPISL7FNUVBCBAY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NG4COWJPFYNVPISL7FNUVBCBAY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NG4COWJPFYNVPISL7FNUVBCBAY/action/storage_attestation","attest_author":"https://pith.science/pith/NG4COWJPFYNVPISL7FNUVBCBAY/action/author_attestation","sign_citation":"https://pith.science/pith/NG4COWJPFYNVPISL7FNUVBCBAY/action/citation_signature","submit_replication":"https://pith.science/pith/NG4COWJPFYNVPISL7FNUVBCBAY/action/replication_record"}},"created_at":"2026-07-05T10:57:14.639531+00:00","updated_at":"2026-07-05T10:57:14.639531+00:00"}