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Let $\\Omega_R$ be the set of rank 1 discrete valuations of $L$ corresponding to codimension 1 points of regular proper models of $\\Spec R$. We prove that a quadratic form $q$ over $L$ satisfies the local-global principle with respect to $\\Omega_R$ in the following two cases: (1) $q$ has rank 3 or 4; (2) $q$ has rank $\\ge 5$ and $R=A[y]$, where $A$ is a complete discrete valuation ring with a not too restrictive condition on the re"},"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":"1010.6038","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-28T18:25:18Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"e5558705883c60b4aabc0de9e462dfc94c06eb737d33f60141acc64a10e72d43","abstract_canon_sha256":"921b1fa19befea20b3ecbbced9510eba6fbc7110b0f22e31ba1cf4a5f36867d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:40.660978Z","signature_b64":"7tIwvIh4Yxjx3czIqqR9olqExCg9/rYafVIjyTz4AsSt5/6vXaa5LU1ci0AlynbjYe860uEpT4QQlLkjvUliAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1630197a6cfeb4896899c13e3bfd6bce7b9d3a57b7420f364ad54b2cf4e4041c","last_reissued_at":"2026-05-18T03:16:40.660482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:40.660482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Yong Hu","submitted_at":"2010-10-28T18:25:18Z","abstract_excerpt":"Let $R$ be a 2-dimensional normal excellent henselian local domain in which 2 is invertible and let $L$ and $k$ be respectively its fraction field and residue field. Let $\\Omega_R$ be the set of rank 1 discrete valuations of $L$ corresponding to codimension 1 points of regular proper models of $\\Spec R$. We prove that a quadratic form $q$ over $L$ satisfies the local-global principle with respect to $\\Omega_R$ in the following two cases: (1) $q$ has rank 3 or 4; (2) $q$ has rank $\\ge 5$ and $R=A[y]$, where $A$ is a complete discrete valuation ring with a not too restrictive condition on the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6038","kind":"arxiv","version":4},"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":"1010.6038","created_at":"2026-05-18T03:16:40.660548+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.6038v4","created_at":"2026-05-18T03:16:40.660548+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.6038","created_at":"2026-05-18T03:16:40.660548+00:00"},{"alias_kind":"pith_short_12","alias_value":"CYYBS6TM722I","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"CYYBS6TM722IS2EZ","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"CYYBS6TM","created_at":"2026-05-18T12:26:06.534383+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/CYYBS6TM722IS2EZYE7DX7LLZZ","json":"https://pith.science/pith/CYYBS6TM722IS2EZYE7DX7LLZZ.json","graph_json":"https://pith.science/api/pith-number/CYYBS6TM722IS2EZYE7DX7LLZZ/graph.json","events_json":"https://pith.science/api/pith-number/CYYBS6TM722IS2EZYE7DX7LLZZ/events.json","paper":"https://pith.science/paper/CYYBS6TM"},"agent_actions":{"view_html":"https://pith.science/pith/CYYBS6TM722IS2EZYE7DX7LLZZ","download_json":"https://pith.science/pith/CYYBS6TM722IS2EZYE7DX7LLZZ.json","view_paper":"https://pith.science/paper/CYYBS6TM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.6038&json=true","fetch_graph":"https://pith.science/api/pith-number/CYYBS6TM722IS2EZYE7DX7LLZZ/graph.json","fetch_events":"https://pith.science/api/pith-number/CYYBS6TM722IS2EZYE7DX7LLZZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CYYBS6TM722IS2EZYE7DX7LLZZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CYYBS6TM722IS2EZYE7DX7LLZZ/action/storage_attestation","attest_author":"https://pith.science/pith/CYYBS6TM722IS2EZYE7DX7LLZZ/action/author_attestation","sign_citation":"https://pith.science/pith/CYYBS6TM722IS2EZYE7DX7LLZZ/action/citation_signature","submit_replication":"https://pith.science/pith/CYYBS6TM722IS2EZYE7DX7LLZZ/action/replication_record"}},"created_at":"2026-05-18T03:16:40.660548+00:00","updated_at":"2026-05-18T03:16:40.660548+00:00"}