{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:DX54XYYKIWJDXWTSOARPLUVMLW","short_pith_number":"pith:DX54XYYK","schema_version":"1.0","canonical_sha256":"1dfbcbe30a45923bda727022f5d2ac5d81f7c17e4d8e9022f129cac16cd3e371","source":{"kind":"arxiv","id":"2210.04851","version":5},"attestation_state":"computed","paper":{"title":"Pfister's local-global principle for Azumaya algebras with involution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Thomas Unger, Vincent Astier","submitted_at":"2022-10-10T17:08:53Z","abstract_excerpt":"We prove Pfister's local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings, and show in particular that the Witt group of nonsingular hermitian forms is $2$-primary torsion. Our proof relies on a hermitian version of Sylvester's law of inertia, which is obtained from an investigation of the connections between a pairing of hermitian forms extensively studied by Garrel, signatures of hermitian forms, and positive semidefinite quadratic forms."},"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":"2210.04851","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2022-10-10T17:08:53Z","cross_cats_sorted":[],"title_canon_sha256":"1da01a09e5b5477b9e3aa5132d9be3b09227b433ce429e8f4533a1d98f9a3336","abstract_canon_sha256":"0a5d258fd8e468c679ed73eac60216bb6ca39698ca73fff0d36f95ae4bb000dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:01:42.808120Z","signature_b64":"ySHlvmTFrxI0bVrDvPIP32OGi1etEiKYdXskW8DCSHLbeLoDI0ZvWfUPcP8vSheD9acN3kXVNPq2nPqB8hXlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dfbcbe30a45923bda727022f5d2ac5d81f7c17e4d8e9022f129cac16cd3e371","last_reissued_at":"2026-07-05T12:01:42.807704Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:01:42.807704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pfister's local-global principle for Azumaya algebras with involution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Thomas Unger, Vincent Astier","submitted_at":"2022-10-10T17:08:53Z","abstract_excerpt":"We prove Pfister's local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings, and show in particular that the Witt group of nonsingular hermitian forms is $2$-primary torsion. Our proof relies on a hermitian version of Sylvester's law of inertia, which is obtained from an investigation of the connections between a pairing of hermitian forms extensively studied by Garrel, signatures of hermitian forms, and positive semidefinite quadratic forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.04851","kind":"arxiv","version":5},"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/2210.04851/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":"2210.04851","created_at":"2026-07-05T12:01:42.807765+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.04851v5","created_at":"2026-07-05T12:01:42.807765+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.04851","created_at":"2026-07-05T12:01:42.807765+00:00"},{"alias_kind":"pith_short_12","alias_value":"DX54XYYKIWJD","created_at":"2026-07-05T12:01:42.807765+00:00"},{"alias_kind":"pith_short_16","alias_value":"DX54XYYKIWJDXWTS","created_at":"2026-07-05T12:01:42.807765+00:00"},{"alias_kind":"pith_short_8","alias_value":"DX54XYYK","created_at":"2026-07-05T12:01:42.807765+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.22178","citing_title":"Signature maps from positive cones on algebras with involution","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DX54XYYKIWJDXWTSOARPLUVMLW","json":"https://pith.science/pith/DX54XYYKIWJDXWTSOARPLUVMLW.json","graph_json":"https://pith.science/api/pith-number/DX54XYYKIWJDXWTSOARPLUVMLW/graph.json","events_json":"https://pith.science/api/pith-number/DX54XYYKIWJDXWTSOARPLUVMLW/events.json","paper":"https://pith.science/paper/DX54XYYK"},"agent_actions":{"view_html":"https://pith.science/pith/DX54XYYKIWJDXWTSOARPLUVMLW","download_json":"https://pith.science/pith/DX54XYYKIWJDXWTSOARPLUVMLW.json","view_paper":"https://pith.science/paper/DX54XYYK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.04851&json=true","fetch_graph":"https://pith.science/api/pith-number/DX54XYYKIWJDXWTSOARPLUVMLW/graph.json","fetch_events":"https://pith.science/api/pith-number/DX54XYYKIWJDXWTSOARPLUVMLW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DX54XYYKIWJDXWTSOARPLUVMLW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DX54XYYKIWJDXWTSOARPLUVMLW/action/storage_attestation","attest_author":"https://pith.science/pith/DX54XYYKIWJDXWTSOARPLUVMLW/action/author_attestation","sign_citation":"https://pith.science/pith/DX54XYYKIWJDXWTSOARPLUVMLW/action/citation_signature","submit_replication":"https://pith.science/pith/DX54XYYKIWJDXWTSOARPLUVMLW/action/replication_record"}},"created_at":"2026-07-05T12:01:42.807765+00:00","updated_at":"2026-07-05T12:01:42.807765+00:00"}