{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:W7XL5OZV2KF73ADOS5XADY3Y5Y","short_pith_number":"pith:W7XL5OZV","schema_version":"1.0","canonical_sha256":"b7eebebb35d28bfd806e976e01e378ee109e927110033fc2ff1a5997852ec34f","source":{"kind":"arxiv","id":"1602.07739","version":2},"attestation_state":"computed","paper":{"title":"The Artin-Springer Theorem for quadratic forms over semi-local rings with finite residue fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Stephen Scully","submitted_at":"2016-02-24T22:43:28Z","abstract_excerpt":"Let $R$ be a commutative and unital semi-local ring in which 2 is invertible. In this note, we show that anisotropic quadratic spaces over $R$ remain anisotropic after base change to any odd-degree finite \\'{e}tale extension of $R$. This generalization of the classical Artin-Springer theorem (concerning the situation where $R$ is a field) was previously established in the case where all residue fields of $R$ are infinite by I. Panin and U. Rehmann. The more general result presented here permits to extend a fundamental isotropy criterion of I. Panin and K. Pimenov for quadratic spaces over regu"},"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":"1602.07739","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-02-24T22:43:28Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"846d9662f9b72db6e8abeba84d1b2990d7e84584a129cacfb8809751a32ae52b","abstract_canon_sha256":"9f64c3965de75b46d8a5c530be88470603827a7a48f6be6472277c018245352a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:52.847777Z","signature_b64":"tB2tF9DAyAp65U3COuBLJxhTAQRebqOVf/gl9e/jhw/SeXhgmxMqPGKyTM89PObuSBcxFbeAoOSi6o7P09qmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7eebebb35d28bfd806e976e01e378ee109e927110033fc2ff1a5997852ec34f","last_reissued_at":"2026-05-18T01:19:52.847353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:52.847353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Artin-Springer Theorem for quadratic forms over semi-local rings with finite residue fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Stephen Scully","submitted_at":"2016-02-24T22:43:28Z","abstract_excerpt":"Let $R$ be a commutative and unital semi-local ring in which 2 is invertible. In this note, we show that anisotropic quadratic spaces over $R$ remain anisotropic after base change to any odd-degree finite \\'{e}tale extension of $R$. This generalization of the classical Artin-Springer theorem (concerning the situation where $R$ is a field) was previously established in the case where all residue fields of $R$ are infinite by I. Panin and U. Rehmann. The more general result presented here permits to extend a fundamental isotropy criterion of I. Panin and K. Pimenov for quadratic spaces over regu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07739","kind":"arxiv","version":2},"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":"1602.07739","created_at":"2026-05-18T01:19:52.847417+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.07739v2","created_at":"2026-05-18T01:19:52.847417+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07739","created_at":"2026-05-18T01:19:52.847417+00:00"},{"alias_kind":"pith_short_12","alias_value":"W7XL5OZV2KF7","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"W7XL5OZV2KF73ADO","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"W7XL5OZV","created_at":"2026-05-18T12:30:48.956258+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/W7XL5OZV2KF73ADOS5XADY3Y5Y","json":"https://pith.science/pith/W7XL5OZV2KF73ADOS5XADY3Y5Y.json","graph_json":"https://pith.science/api/pith-number/W7XL5OZV2KF73ADOS5XADY3Y5Y/graph.json","events_json":"https://pith.science/api/pith-number/W7XL5OZV2KF73ADOS5XADY3Y5Y/events.json","paper":"https://pith.science/paper/W7XL5OZV"},"agent_actions":{"view_html":"https://pith.science/pith/W7XL5OZV2KF73ADOS5XADY3Y5Y","download_json":"https://pith.science/pith/W7XL5OZV2KF73ADOS5XADY3Y5Y.json","view_paper":"https://pith.science/paper/W7XL5OZV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.07739&json=true","fetch_graph":"https://pith.science/api/pith-number/W7XL5OZV2KF73ADOS5XADY3Y5Y/graph.json","fetch_events":"https://pith.science/api/pith-number/W7XL5OZV2KF73ADOS5XADY3Y5Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W7XL5OZV2KF73ADOS5XADY3Y5Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W7XL5OZV2KF73ADOS5XADY3Y5Y/action/storage_attestation","attest_author":"https://pith.science/pith/W7XL5OZV2KF73ADOS5XADY3Y5Y/action/author_attestation","sign_citation":"https://pith.science/pith/W7XL5OZV2KF73ADOS5XADY3Y5Y/action/citation_signature","submit_replication":"https://pith.science/pith/W7XL5OZV2KF73ADOS5XADY3Y5Y/action/replication_record"}},"created_at":"2026-05-18T01:19:52.847417+00:00","updated_at":"2026-05-18T01:19:52.847417+00:00"}