{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:H5PLG676YUFMZW6OY2ZAYHVC43","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a94301af154a1386036c8cbc38dce5e7876b8ad95c9f7ce62666a1d1035dc036","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-05T23:57:31Z","title_canon_sha256":"2e9e0be90b6395f4313fe2d6f5887db143f9ca2805d4c032dcc2279d851c3494"},"schema_version":"1.0","source":{"id":"1203.1075","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1075","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1075v4","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1075","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"H5PLG676YUFM","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H5PLG676YUFMZW6O","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H5PLG676","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:28b0e90a952736f9612b2f561ae54816c6df13f75bdc776957ae0e9d485f014f","target":"graph","created_at":"2026-05-18T02:40:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $K$ be the function field of a $p$-adic curve, $G$ a semisimple simply connected group over $K$ and $X$ a $G$-torsor over $K$. A conjecture of Colliot-Th\\'el\\`ene, Parimala and Suresh predicts that if for every discrete valuation $v$ of $K$, $X$ has a point over the completion $K_v$, then $X$ has a $K$-rational point. The main result of this paper is the proof of this conjecture for groups of some classical types. In particular, we prove the conjecture when $G$ is of one of the following types: (1) ${}^2A_n^*$, i.e. $G=\\mathbf{SU}(h)$ is the special unitary group of some hermitian form $h$","authors_text":"Yong Hu","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-05T23:57:31Z","title":"Hasse Principle for Simply Connected Groups over Function Fields of Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1075","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7c33a4e29a500ab4398b170eea0afb13eed076c300a4fb2ee04d2c88e443e36b","target":"record","created_at":"2026-05-18T02:40:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a94301af154a1386036c8cbc38dce5e7876b8ad95c9f7ce62666a1d1035dc036","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-05T23:57:31Z","title_canon_sha256":"2e9e0be90b6395f4313fe2d6f5887db143f9ca2805d4c032dcc2279d851c3494"},"schema_version":"1.0","source":{"id":"1203.1075","kind":"arxiv","version":4}},"canonical_sha256":"3f5eb37bfec50accdbcec6b20c1ea2e6c1926b3c7bf97375ccd1f641c081a93a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f5eb37bfec50accdbcec6b20c1ea2e6c1926b3c7bf97375ccd1f641c081a93a","first_computed_at":"2026-05-18T02:40:54.423706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:54.423706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"scv6DKTOHywA+NAe/AxRYN+PImdR81LCUfM8g860VdMx99axTk7SvHSt5P84LZK0twLEx5IadEohlcBJQ3uBAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:54.424214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1075","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c33a4e29a500ab4398b170eea0afb13eed076c300a4fb2ee04d2c88e443e36b","sha256:28b0e90a952736f9612b2f561ae54816c6df13f75bdc776957ae0e9d485f014f"],"state_sha256":"bdcefd66b6bc50c8eb960d7494c1c69df5d350dc6db1456d0db3dde97bdc1241"}