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We study the algebraic transfer constructed by Singer using the technique of the hit problem. This transfer is a homomorphism from the homology of the mod-2 Steenrod algebra, $\\text{Tor}^{\\mathcal A}_{k,k+n} (\\mathbb F_2,\\mathbb F_2)$, to the subspace of $\\mathbb F_2{\\otimes}_{\\mathcal A}P_k$ consisting o"},"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":"1609.03006","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2016-09-10T06:30:00Z","cross_cats_sorted":[],"title_canon_sha256":"e72120357ae070cd59c4bdb2f4952f3ace31e3d6b76d437815b4d309b9c1e563","abstract_canon_sha256":"567037a78dda24320f90cc0ca779c985b392fd09be546cce536fc53230d17d11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:00.806991Z","signature_b64":"ohWuhweW2BjeSh9MVxkvxJkVapcEUE1wfy3kKoSflb3xx9udyMepOW3L9ADxETjEz90oA8XHmLOW41Z4XyDlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8330b0e578eced7360af34f4996c1e04a79845f93ab7fb6598895d1074d5b81d","last_reissued_at":"2026-05-18T00:05:00.806587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:00.806587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The squaring operartion and the Singer algebraic transfer","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nguyen Sum","submitted_at":"2016-09-10T06:30:00Z","abstract_excerpt":"Let $P_k$ be the graded polynomial algebra $\\mathbb F_2[x_1,x_2,\\ldots ,x_k]$, with the degree of each $x_i$ being 1, regarded as a module over the mod-2 Steenrod algebra $\\mathcal A$, and let $GL_k$ be the general linear group over the prime field $\\mathbb F_2$ which acts regularly on $P_k$. We study the algebraic transfer constructed by Singer using the technique of the hit problem. This transfer is a homomorphism from the homology of the mod-2 Steenrod algebra, $\\text{Tor}^{\\mathcal A}_{k,k+n} (\\mathbb F_2,\\mathbb F_2)$, to the subspace of $\\mathbb F_2{\\otimes}_{\\mathcal A}P_k$ consisting o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03006","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":"1609.03006","created_at":"2026-05-18T00:05:00.806646+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.03006v3","created_at":"2026-05-18T00:05:00.806646+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03006","created_at":"2026-05-18T00:05:00.806646+00:00"},{"alias_kind":"pith_short_12","alias_value":"QMYLBZLY5TWX","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QMYLBZLY5TWXGYFP","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QMYLBZLY","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/QMYLBZLY5TWXGYFPGT2JS3A6AS","json":"https://pith.science/pith/QMYLBZLY5TWXGYFPGT2JS3A6AS.json","graph_json":"https://pith.science/api/pith-number/QMYLBZLY5TWXGYFPGT2JS3A6AS/graph.json","events_json":"https://pith.science/api/pith-number/QMYLBZLY5TWXGYFPGT2JS3A6AS/events.json","paper":"https://pith.science/paper/QMYLBZLY"},"agent_actions":{"view_html":"https://pith.science/pith/QMYLBZLY5TWXGYFPGT2JS3A6AS","download_json":"https://pith.science/pith/QMYLBZLY5TWXGYFPGT2JS3A6AS.json","view_paper":"https://pith.science/paper/QMYLBZLY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.03006&json=true","fetch_graph":"https://pith.science/api/pith-number/QMYLBZLY5TWXGYFPGT2JS3A6AS/graph.json","fetch_events":"https://pith.science/api/pith-number/QMYLBZLY5TWXGYFPGT2JS3A6AS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QMYLBZLY5TWXGYFPGT2JS3A6AS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QMYLBZLY5TWXGYFPGT2JS3A6AS/action/storage_attestation","attest_author":"https://pith.science/pith/QMYLBZLY5TWXGYFPGT2JS3A6AS/action/author_attestation","sign_citation":"https://pith.science/pith/QMYLBZLY5TWXGYFPGT2JS3A6AS/action/citation_signature","submit_replication":"https://pith.science/pith/QMYLBZLY5TWXGYFPGT2JS3A6AS/action/replication_record"}},"created_at":"2026-05-18T00:05:00.806646+00:00","updated_at":"2026-05-18T00:05:00.806646+00:00"}