{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:BNJMB7WF32JWU4VZMZJVZLDMKE","short_pith_number":"pith:BNJMB7WF","schema_version":"1.0","canonical_sha256":"0b52c0fec5de936a72b966535cac6c51317ade653c3797a1e3c6d1488fc85b2d","source":{"kind":"arxiv","id":"1005.5326","version":3},"attestation_state":"computed","paper":{"title":"Selectivity in Quaternion Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Benjamin Linowitz","submitted_at":"2010-05-28T16:14:42Z","abstract_excerpt":"We prove an integral version of the classical Albert-Brauer-Hasse-Noether theorem regarding quaternion algebras over number fields. Let $\\mathfrak A$ be a quaternion algebra over a number field $K$ and assume that $\\mathfrak A$ satisfies the Eichler condition; that is, there exists an archimedean prime of $K$ which does not ramify in $\\mathfrak A$. Let $\\Omega$ be a commutative, quadratic $\\mathcal{O}_K$-order and let $\\mathcal{R}\\subset \\mathfrak A$ be an order of full rank. Assume that there exists an embedding of $\\Omega$ into $\\mathcal R$. We describe a number of criteria which, if satisfi"},"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":"1005.5326","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-28T16:14:42Z","cross_cats_sorted":[],"title_canon_sha256":"de9ead40c14d7d100706f2935d82d35ebc7a647b8c6705d9ca75a377dffe9a24","abstract_canon_sha256":"783b9220bfaf1c020a4415a29d7f80e9cdf3036ca6e37ea8c19d316c61c6215d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:36.307788Z","signature_b64":"46l3JgEKtxUTH2HPngrDYIbLMsY2kiAIOTiwxc/J/OP8JvLKeZTK3YZsOg3YyzHv5a799Pc3PiTNzeqWMc1eAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b52c0fec5de936a72b966535cac6c51317ade653c3797a1e3c6d1488fc85b2d","last_reissued_at":"2026-05-18T04:02:36.307241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:36.307241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Selectivity in Quaternion Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Benjamin Linowitz","submitted_at":"2010-05-28T16:14:42Z","abstract_excerpt":"We prove an integral version of the classical Albert-Brauer-Hasse-Noether theorem regarding quaternion algebras over number fields. Let $\\mathfrak A$ be a quaternion algebra over a number field $K$ and assume that $\\mathfrak A$ satisfies the Eichler condition; that is, there exists an archimedean prime of $K$ which does not ramify in $\\mathfrak A$. Let $\\Omega$ be a commutative, quadratic $\\mathcal{O}_K$-order and let $\\mathcal{R}\\subset \\mathfrak A$ be an order of full rank. Assume that there exists an embedding of $\\Omega$ into $\\mathcal R$. We describe a number of criteria which, if satisfi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5326","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":"1005.5326","created_at":"2026-05-18T04:02:36.307328+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.5326v3","created_at":"2026-05-18T04:02:36.307328+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5326","created_at":"2026-05-18T04:02:36.307328+00:00"},{"alias_kind":"pith_short_12","alias_value":"BNJMB7WF32JW","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BNJMB7WF32JWU4VZ","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BNJMB7WF","created_at":"2026-05-18T12:26:05.355336+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/BNJMB7WF32JWU4VZMZJVZLDMKE","json":"https://pith.science/pith/BNJMB7WF32JWU4VZMZJVZLDMKE.json","graph_json":"https://pith.science/api/pith-number/BNJMB7WF32JWU4VZMZJVZLDMKE/graph.json","events_json":"https://pith.science/api/pith-number/BNJMB7WF32JWU4VZMZJVZLDMKE/events.json","paper":"https://pith.science/paper/BNJMB7WF"},"agent_actions":{"view_html":"https://pith.science/pith/BNJMB7WF32JWU4VZMZJVZLDMKE","download_json":"https://pith.science/pith/BNJMB7WF32JWU4VZMZJVZLDMKE.json","view_paper":"https://pith.science/paper/BNJMB7WF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.5326&json=true","fetch_graph":"https://pith.science/api/pith-number/BNJMB7WF32JWU4VZMZJVZLDMKE/graph.json","fetch_events":"https://pith.science/api/pith-number/BNJMB7WF32JWU4VZMZJVZLDMKE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BNJMB7WF32JWU4VZMZJVZLDMKE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BNJMB7WF32JWU4VZMZJVZLDMKE/action/storage_attestation","attest_author":"https://pith.science/pith/BNJMB7WF32JWU4VZMZJVZLDMKE/action/author_attestation","sign_citation":"https://pith.science/pith/BNJMB7WF32JWU4VZMZJVZLDMKE/action/citation_signature","submit_replication":"https://pith.science/pith/BNJMB7WF32JWU4VZMZJVZLDMKE/action/replication_record"}},"created_at":"2026-05-18T04:02:36.307328+00:00","updated_at":"2026-05-18T04:02:36.307328+00:00"}