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Let I denote the image of this map.\n  We prove that if (K,v) is henselian and its completion is a separable extension, then:\n  - I is locally closed in Y(K);\n  - the induced surjection X(K)-->I is a principal bundle with group G(K) (also topologized by the valuation)."},"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":"1309.6430","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-25T08:53:45Z","cross_cats_sorted":[],"title_canon_sha256":"6ccb93c05475588113e329b9ecf7554f183a288ec5748a0690fee7513b51f6ea","abstract_canon_sha256":"f982447da6ffe0dbeef6c14bef88b16a030343e99f73f99dbe820310edfcf63b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:05.703436Z","signature_b64":"t3T5y8SPCnHdVfz0gex/vc1+ptxe1Y66u5yDw0H90dmwRI3kYli0xe8tjnJu2fzZDUgDEfMZlHkmP2PXotkLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92097ce2774f1832340cf8918c737b080db1314a9a0acb0c41ff54fcbda97eb8","last_reissued_at":"2026-05-18T02:47:05.702835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:05.702835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fibr\\'es principaux sur les corps valu\\'es hens\\'eliens","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Laurent Moret-Bailly, Ofer Gabber, Philippe Gille","submitted_at":"2013-09-25T08:53:45Z","abstract_excerpt":"Let (K,v) be a valued field, Y a K-variety, G an algebraic group over K (not necessarily smooth), and f: X->Y a G-torsor over Y. We consider the induced map X(K)-->Y(K), which is continuous for the topologies deduced from the valuation. Let I denote the image of this map.\n  We prove that if (K,v) is henselian and its completion is a separable extension, then:\n  - I is locally closed in Y(K);\n  - the induced surjection X(K)-->I is a principal bundle with group G(K) (also topologized by the valuation)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6430","kind":"arxiv","version":3},"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":"1309.6430","created_at":"2026-05-18T02:47:05.702912+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.6430v3","created_at":"2026-05-18T02:47:05.702912+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6430","created_at":"2026-05-18T02:47:05.702912+00:00"},{"alias_kind":"pith_short_12","alias_value":"SIEXZYTXJ4MD","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SIEXZYTXJ4MDENAM","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SIEXZYTX","created_at":"2026-05-18T12:27:59.945178+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/SIEXZYTXJ4MDENAM7CIYY433BA","json":"https://pith.science/pith/SIEXZYTXJ4MDENAM7CIYY433BA.json","graph_json":"https://pith.science/api/pith-number/SIEXZYTXJ4MDENAM7CIYY433BA/graph.json","events_json":"https://pith.science/api/pith-number/SIEXZYTXJ4MDENAM7CIYY433BA/events.json","paper":"https://pith.science/paper/SIEXZYTX"},"agent_actions":{"view_html":"https://pith.science/pith/SIEXZYTXJ4MDENAM7CIYY433BA","download_json":"https://pith.science/pith/SIEXZYTXJ4MDENAM7CIYY433BA.json","view_paper":"https://pith.science/paper/SIEXZYTX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.6430&json=true","fetch_graph":"https://pith.science/api/pith-number/SIEXZYTXJ4MDENAM7CIYY433BA/graph.json","fetch_events":"https://pith.science/api/pith-number/SIEXZYTXJ4MDENAM7CIYY433BA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SIEXZYTXJ4MDENAM7CIYY433BA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SIEXZYTXJ4MDENAM7CIYY433BA/action/storage_attestation","attest_author":"https://pith.science/pith/SIEXZYTXJ4MDENAM7CIYY433BA/action/author_attestation","sign_citation":"https://pith.science/pith/SIEXZYTXJ4MDENAM7CIYY433BA/action/citation_signature","submit_replication":"https://pith.science/pith/SIEXZYTXJ4MDENAM7CIYY433BA/action/replication_record"}},"created_at":"2026-05-18T02:47:05.702912+00:00","updated_at":"2026-05-18T02:47:05.702912+00:00"}