{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QGBHQETALB5ACAAEDRMRPKZ4JJ","short_pith_number":"pith:QGBHQETA","schema_version":"1.0","canonical_sha256":"8182781260587a0100041c5917ab3c4a52aa28f615628897f4d024571e34e532","source":{"kind":"arxiv","id":"1607.01685","version":3},"attestation_state":"computed","paper":{"title":"Exterior power operations on higher $K$-groups via binary complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.KT","authors_text":"Bernhard K\\\"ock, Lenny Taelman, Tom Harris","submitted_at":"2016-07-06T15:50:28Z","abstract_excerpt":"We use Grayson's binary multicomplex presentation of algebraic $K$-theory to give a new construction of exterior power operations on the higher $K$-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a $\\lambda$-ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial functors is the universal $\\lambda$-ring on one generator."},"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":"1607.01685","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-07-06T15:50:28Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"69a9aa39ad982a01eea19df12d61d943781167c86f43b75e8a3192489402cffb","abstract_canon_sha256":"e88a6cffaa7fc220834d985bc1b7d965bff6751535f3a09ff03ff1fb6a4ddc87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:32.716083Z","signature_b64":"/0wkNtyKChkXXvCYanSB67Wb4c+vgAMlSGZk2pb3aTLbUkhBH3GCo7hPPagmBdInepYAHO25zJPcKLqmrZKjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8182781260587a0100041c5917ab3c4a52aa28f615628897f4d024571e34e532","last_reissued_at":"2026-05-18T00:42:32.715462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:32.715462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exterior power operations on higher $K$-groups via binary complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.KT","authors_text":"Bernhard K\\\"ock, Lenny Taelman, Tom Harris","submitted_at":"2016-07-06T15:50:28Z","abstract_excerpt":"We use Grayson's binary multicomplex presentation of algebraic $K$-theory to give a new construction of exterior power operations on the higher $K$-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a $\\lambda$-ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial functors is the universal $\\lambda$-ring on one generator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01685","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":"1607.01685","created_at":"2026-05-18T00:42:32.715550+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.01685v3","created_at":"2026-05-18T00:42:32.715550+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01685","created_at":"2026-05-18T00:42:32.715550+00:00"},{"alias_kind":"pith_short_12","alias_value":"QGBHQETALB5A","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QGBHQETALB5ACAAE","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QGBHQETA","created_at":"2026-05-18T12:30:39.010887+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/QGBHQETALB5ACAAEDRMRPKZ4JJ","json":"https://pith.science/pith/QGBHQETALB5ACAAEDRMRPKZ4JJ.json","graph_json":"https://pith.science/api/pith-number/QGBHQETALB5ACAAEDRMRPKZ4JJ/graph.json","events_json":"https://pith.science/api/pith-number/QGBHQETALB5ACAAEDRMRPKZ4JJ/events.json","paper":"https://pith.science/paper/QGBHQETA"},"agent_actions":{"view_html":"https://pith.science/pith/QGBHQETALB5ACAAEDRMRPKZ4JJ","download_json":"https://pith.science/pith/QGBHQETALB5ACAAEDRMRPKZ4JJ.json","view_paper":"https://pith.science/paper/QGBHQETA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.01685&json=true","fetch_graph":"https://pith.science/api/pith-number/QGBHQETALB5ACAAEDRMRPKZ4JJ/graph.json","fetch_events":"https://pith.science/api/pith-number/QGBHQETALB5ACAAEDRMRPKZ4JJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QGBHQETALB5ACAAEDRMRPKZ4JJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QGBHQETALB5ACAAEDRMRPKZ4JJ/action/storage_attestation","attest_author":"https://pith.science/pith/QGBHQETALB5ACAAEDRMRPKZ4JJ/action/author_attestation","sign_citation":"https://pith.science/pith/QGBHQETALB5ACAAEDRMRPKZ4JJ/action/citation_signature","submit_replication":"https://pith.science/pith/QGBHQETALB5ACAAEDRMRPKZ4JJ/action/replication_record"}},"created_at":"2026-05-18T00:42:32.715550+00:00","updated_at":"2026-05-18T00:42:32.715550+00:00"}