{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QGBHQETALB5ACAAEDRMRPKZ4JJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e88a6cffaa7fc220834d985bc1b7d965bff6751535f3a09ff03ff1fb6a4ddc87","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-07-06T15:50:28Z","title_canon_sha256":"69a9aa39ad982a01eea19df12d61d943781167c86f43b75e8a3192489402cffb"},"schema_version":"1.0","source":{"id":"1607.01685","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01685","created_at":"2026-05-18T00:42:32Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01685v3","created_at":"2026-05-18T00:42:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01685","created_at":"2026-05-18T00:42:32Z"},{"alias_kind":"pith_short_12","alias_value":"QGBHQETALB5A","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QGBHQETALB5ACAAE","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QGBHQETA","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:3cd239f0b0ceadc51a0b6a52e8379f378d0b64439e2dc9675304f3591a9c5bf8","target":"graph","created_at":"2026-05-18T00:42:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Bernhard K\\\"ock, Lenny Taelman, Tom Harris","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-07-06T15:50:28Z","title":"Exterior power operations on higher $K$-groups via binary complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01685","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6ad092973dfe31b1b1a18d8cc6fde5989f10e81bfe30537b20547520e57bc68c","target":"record","created_at":"2026-05-18T00:42:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e88a6cffaa7fc220834d985bc1b7d965bff6751535f3a09ff03ff1fb6a4ddc87","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-07-06T15:50:28Z","title_canon_sha256":"69a9aa39ad982a01eea19df12d61d943781167c86f43b75e8a3192489402cffb"},"schema_version":"1.0","source":{"id":"1607.01685","kind":"arxiv","version":3}},"canonical_sha256":"8182781260587a0100041c5917ab3c4a52aa28f615628897f4d024571e34e532","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8182781260587a0100041c5917ab3c4a52aa28f615628897f4d024571e34e532","first_computed_at":"2026-05-18T00:42:32.715462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:32.715462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/0wkNtyKChkXXvCYanSB67Wb4c+vgAMlSGZk2pb3aTLbUkhBH3GCo7hPPagmBdInepYAHO25zJPcKLqmrZKjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:32.716083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01685","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ad092973dfe31b1b1a18d8cc6fde5989f10e81bfe30537b20547520e57bc68c","sha256:3cd239f0b0ceadc51a0b6a52e8379f378d0b64439e2dc9675304f3591a9c5bf8"],"state_sha256":"0f721c3b82608b97590697f9ee3546ca96c8762d66899d63890df4641bcadce8"}