{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3YACRXXANFRMDMZIHBZDDIOAUR","short_pith_number":"pith:3YACRXXA","schema_version":"1.0","canonical_sha256":"de0028dee06962c1b328387231a1c0a46ccfdfef0896b1f3ea4fa8c8cb4d79de","source":{"kind":"arxiv","id":"1606.05617","version":1},"attestation_state":"computed","paper":{"title":"Algebraic Cycles Representing Cohomology Operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Marie-Louise Michelsohn","submitted_at":"2016-06-17T18:40:52Z","abstract_excerpt":"In this paper we show that certain universal homology classes which are fundamental in topology are algebraic. To be specific, the products of Eilenberg-MacLane spaces ${\\cal K}_{2q} \\equiv K({\\Bbb Z},2) \\times K({\\Bbb Z}, 4) \\times ... \\times K({\\Bbb Z}, 2q)$ have models which are limits of complex projective varieties. Precisely, we have ${\\cal K}_{2q} = \\lim_{d\\to\\infty}{\\cal C}_d^q({\\Bbb P}^n)$ where ${\\cal C}_d^q({\\Bbb P}^n)$ denotes the Chow variety of effective cycles of codimension $q$ and degree $d$ on ${\\Bbb P}^n$. It is natural to ask which elements in the homology of ${\\cal K}_{2q}"},"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":"1606.05617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-06-17T18:40:52Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"10ddd18e57844f4d5cf99b4587ddbe33a51946ff37ad061d1bdeff7480258a45","abstract_canon_sha256":"abb7f4be5aea5d7e37edf7e57a27a11d492ca2e87d470fa0009167c71ab05b44"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:19.328218Z","signature_b64":"TG0Qk5dky2H+tHzmJAVBujQ7a1xMj2DSorY4j5jXY9DeZRkrLgZDpzzvMwf0qnrF24jKq9F/lRUYenaUeqANDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de0028dee06962c1b328387231a1c0a46ccfdfef0896b1f3ea4fa8c8cb4d79de","last_reissued_at":"2026-05-18T01:12:19.327883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:19.327883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic Cycles Representing Cohomology Operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Marie-Louise Michelsohn","submitted_at":"2016-06-17T18:40:52Z","abstract_excerpt":"In this paper we show that certain universal homology classes which are fundamental in topology are algebraic. To be specific, the products of Eilenberg-MacLane spaces ${\\cal K}_{2q} \\equiv K({\\Bbb Z},2) \\times K({\\Bbb Z}, 4) \\times ... \\times K({\\Bbb Z}, 2q)$ have models which are limits of complex projective varieties. Precisely, we have ${\\cal K}_{2q} = \\lim_{d\\to\\infty}{\\cal C}_d^q({\\Bbb P}^n)$ where ${\\cal C}_d^q({\\Bbb P}^n)$ denotes the Chow variety of effective cycles of codimension $q$ and degree $d$ on ${\\Bbb P}^n$. It is natural to ask which elements in the homology of ${\\cal K}_{2q}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05617","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":"1606.05617","created_at":"2026-05-18T01:12:19.327938+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.05617v1","created_at":"2026-05-18T01:12:19.327938+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05617","created_at":"2026-05-18T01:12:19.327938+00:00"},{"alias_kind":"pith_short_12","alias_value":"3YACRXXANFRM","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"3YACRXXANFRMDMZI","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"3YACRXXA","created_at":"2026-05-18T12:29:58.707656+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/3YACRXXANFRMDMZIHBZDDIOAUR","json":"https://pith.science/pith/3YACRXXANFRMDMZIHBZDDIOAUR.json","graph_json":"https://pith.science/api/pith-number/3YACRXXANFRMDMZIHBZDDIOAUR/graph.json","events_json":"https://pith.science/api/pith-number/3YACRXXANFRMDMZIHBZDDIOAUR/events.json","paper":"https://pith.science/paper/3YACRXXA"},"agent_actions":{"view_html":"https://pith.science/pith/3YACRXXANFRMDMZIHBZDDIOAUR","download_json":"https://pith.science/pith/3YACRXXANFRMDMZIHBZDDIOAUR.json","view_paper":"https://pith.science/paper/3YACRXXA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.05617&json=true","fetch_graph":"https://pith.science/api/pith-number/3YACRXXANFRMDMZIHBZDDIOAUR/graph.json","fetch_events":"https://pith.science/api/pith-number/3YACRXXANFRMDMZIHBZDDIOAUR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3YACRXXANFRMDMZIHBZDDIOAUR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3YACRXXANFRMDMZIHBZDDIOAUR/action/storage_attestation","attest_author":"https://pith.science/pith/3YACRXXANFRMDMZIHBZDDIOAUR/action/author_attestation","sign_citation":"https://pith.science/pith/3YACRXXANFRMDMZIHBZDDIOAUR/action/citation_signature","submit_replication":"https://pith.science/pith/3YACRXXANFRMDMZIHBZDDIOAUR/action/replication_record"}},"created_at":"2026-05-18T01:12:19.327938+00:00","updated_at":"2026-05-18T01:12:19.327938+00:00"}