{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:M2F27757NN6QQ5R5Q23K2NHQ5O","short_pith_number":"pith:M2F27757","schema_version":"1.0","canonical_sha256":"668bafffbf6b7d08763d86b6ad34f0ebb353bfbcb230fd8b4008d8a3595f360c","source":{"kind":"arxiv","id":"1802.08507","version":1},"attestation_state":"computed","paper":{"title":"On the classification of rational four-dimensional unital division algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Gustav Hammarhjelm","submitted_at":"2018-02-23T12:53:32Z","abstract_excerpt":"In a paper by E. Dieterich 2017, the category $\\mathscr{C}(k)$ of four-dimensional unital division algebras, whose right nucleus is non-trivial and whose automorphism group contains Klein's four group $V$, is studied over a general ground field $k$ with $\\mathrm{char}\\,k\\neq 2$. In particular, the objects in $\\mathscr{C}(k)$ are exhaustively constructed from parameters in $k^3$ and explicit isomorphism conditions for the constructed objects are found in terms of these parameters.\n  In this paper, we specialize to the case $k=\\mathbb{Q}$ and present results towards a classification of $\\mathscr"},"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":"1802.08507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-02-23T12:53:32Z","cross_cats_sorted":[],"title_canon_sha256":"3e7207877648e79012a10e88836c2bdb0bdbbd0a5e51c74e890dd922ae8340a7","abstract_canon_sha256":"2103080a580b562d4e7d14ced13ab001c427ac2f03c4805c12eaf733e8a2954b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:41.397141Z","signature_b64":"uA1n1cUZFYDpX7s3rp+dTAXWVPT3WWKGXZv0da9jdoGgZlHc2Ci8Q6X0eiMRg2x1kWCOUsggJ1i+FzWlUbuzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"668bafffbf6b7d08763d86b6ad34f0ebb353bfbcb230fd8b4008d8a3595f360c","last_reissued_at":"2026-05-18T00:22:41.396489Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:41.396489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the classification of rational four-dimensional unital division algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Gustav Hammarhjelm","submitted_at":"2018-02-23T12:53:32Z","abstract_excerpt":"In a paper by E. Dieterich 2017, the category $\\mathscr{C}(k)$ of four-dimensional unital division algebras, whose right nucleus is non-trivial and whose automorphism group contains Klein's four group $V$, is studied over a general ground field $k$ with $\\mathrm{char}\\,k\\neq 2$. In particular, the objects in $\\mathscr{C}(k)$ are exhaustively constructed from parameters in $k^3$ and explicit isomorphism conditions for the constructed objects are found in terms of these parameters.\n  In this paper, we specialize to the case $k=\\mathbb{Q}$ and present results towards a classification of $\\mathscr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08507","kind":"arxiv","version":1},"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":"1802.08507","created_at":"2026-05-18T00:22:41.396624+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.08507v1","created_at":"2026-05-18T00:22:41.396624+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08507","created_at":"2026-05-18T00:22:41.396624+00:00"},{"alias_kind":"pith_short_12","alias_value":"M2F27757NN6Q","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"M2F27757NN6QQ5R5","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"M2F27757","created_at":"2026-05-18T12:32:37.024351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.06811","citing_title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M2F27757NN6QQ5R5Q23K2NHQ5O","json":"https://pith.science/pith/M2F27757NN6QQ5R5Q23K2NHQ5O.json","graph_json":"https://pith.science/api/pith-number/M2F27757NN6QQ5R5Q23K2NHQ5O/graph.json","events_json":"https://pith.science/api/pith-number/M2F27757NN6QQ5R5Q23K2NHQ5O/events.json","paper":"https://pith.science/paper/M2F27757"},"agent_actions":{"view_html":"https://pith.science/pith/M2F27757NN6QQ5R5Q23K2NHQ5O","download_json":"https://pith.science/pith/M2F27757NN6QQ5R5Q23K2NHQ5O.json","view_paper":"https://pith.science/paper/M2F27757","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.08507&json=true","fetch_graph":"https://pith.science/api/pith-number/M2F27757NN6QQ5R5Q23K2NHQ5O/graph.json","fetch_events":"https://pith.science/api/pith-number/M2F27757NN6QQ5R5Q23K2NHQ5O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M2F27757NN6QQ5R5Q23K2NHQ5O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M2F27757NN6QQ5R5Q23K2NHQ5O/action/storage_attestation","attest_author":"https://pith.science/pith/M2F27757NN6QQ5R5Q23K2NHQ5O/action/author_attestation","sign_citation":"https://pith.science/pith/M2F27757NN6QQ5R5Q23K2NHQ5O/action/citation_signature","submit_replication":"https://pith.science/pith/M2F27757NN6QQ5R5Q23K2NHQ5O/action/replication_record"}},"created_at":"2026-05-18T00:22:41.396624+00:00","updated_at":"2026-05-18T00:22:41.396624+00:00"}