{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CV25UYRAQADYHEFK63ROYDVVSP","short_pith_number":"pith:CV25UYRA","schema_version":"1.0","canonical_sha256":"1575da622080078390aaf6e2ec0eb593f39b1d0b8edc16d9330e09a5faf4c17b","source":{"kind":"arxiv","id":"1401.7265","version":2},"attestation_state":"computed","paper":{"title":"Multiplicative quadratic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Matthias Gr\\\"uninger","submitted_at":"2014-01-28T17:18:00Z","abstract_excerpt":"In this paper we prove that a multiplicative quadratic map between a unital ring $K$ and a field $L$ is induced by a homomorphism from $K$ into $L$ or a composition algebra over $L$. Especially we show that if $K$ is a field, then every multiplicative quadratic map is the product of two field homomorphisms. Moreover, we prove a multiplicative version of Artin's Theorem showing that a product of field homomorphisms is unique up to multiplicity."},"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":"1401.7265","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-28T17:18:00Z","cross_cats_sorted":[],"title_canon_sha256":"2cd82129f8c79818c79f87043472f0fb0a395181296c463b27defbdbcc79b698","abstract_canon_sha256":"279ad1d413b07e18a3aa10d7b8a5d156afcd67cb4e71b7aad0913defc1e101ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:30.970260Z","signature_b64":"pWJnCL5bYNJQvdvftiM7wlZBViJQXl0pudZidENiXh9Mv3xT0LMM2QfeQwouuED3L5+6FrtPVrdgNkT2yhRIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1575da622080078390aaf6e2ec0eb593f39b1d0b8edc16d9330e09a5faf4c17b","last_reissued_at":"2026-05-18T02:46:30.969823Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:30.969823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplicative quadratic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Matthias Gr\\\"uninger","submitted_at":"2014-01-28T17:18:00Z","abstract_excerpt":"In this paper we prove that a multiplicative quadratic map between a unital ring $K$ and a field $L$ is induced by a homomorphism from $K$ into $L$ or a composition algebra over $L$. Especially we show that if $K$ is a field, then every multiplicative quadratic map is the product of two field homomorphisms. Moreover, we prove a multiplicative version of Artin's Theorem showing that a product of field homomorphisms is unique up to multiplicity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7265","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":"1401.7265","created_at":"2026-05-18T02:46:30.969891+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.7265v2","created_at":"2026-05-18T02:46:30.969891+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7265","created_at":"2026-05-18T02:46:30.969891+00:00"},{"alias_kind":"pith_short_12","alias_value":"CV25UYRAQADY","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"CV25UYRAQADYHEFK","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"CV25UYRA","created_at":"2026-05-18T12:28:25.294606+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/CV25UYRAQADYHEFK63ROYDVVSP","json":"https://pith.science/pith/CV25UYRAQADYHEFK63ROYDVVSP.json","graph_json":"https://pith.science/api/pith-number/CV25UYRAQADYHEFK63ROYDVVSP/graph.json","events_json":"https://pith.science/api/pith-number/CV25UYRAQADYHEFK63ROYDVVSP/events.json","paper":"https://pith.science/paper/CV25UYRA"},"agent_actions":{"view_html":"https://pith.science/pith/CV25UYRAQADYHEFK63ROYDVVSP","download_json":"https://pith.science/pith/CV25UYRAQADYHEFK63ROYDVVSP.json","view_paper":"https://pith.science/paper/CV25UYRA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.7265&json=true","fetch_graph":"https://pith.science/api/pith-number/CV25UYRAQADYHEFK63ROYDVVSP/graph.json","fetch_events":"https://pith.science/api/pith-number/CV25UYRAQADYHEFK63ROYDVVSP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CV25UYRAQADYHEFK63ROYDVVSP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CV25UYRAQADYHEFK63ROYDVVSP/action/storage_attestation","attest_author":"https://pith.science/pith/CV25UYRAQADYHEFK63ROYDVVSP/action/author_attestation","sign_citation":"https://pith.science/pith/CV25UYRAQADYHEFK63ROYDVVSP/action/citation_signature","submit_replication":"https://pith.science/pith/CV25UYRAQADYHEFK63ROYDVVSP/action/replication_record"}},"created_at":"2026-05-18T02:46:30.969891+00:00","updated_at":"2026-05-18T02:46:30.969891+00:00"}