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We study the algebraic transfer $Tr_k^*$ constructed by Singer using the technique of the Peterson hit problem. This transfer is a homomorphism from the homology of the mod-2 Steenrod algebra $\\mathcal A$, $\\text{Tor}^{\\mathcal A}_{k,k+d} (\\mathbb F_2,\\mathbb F_2)$, to the subspace of $\\mathbb F_2{\\otimes}_{\\mathcal A}"},"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":"1710.07895","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2017-10-22T06:36:58Z","cross_cats_sorted":[],"title_canon_sha256":"ba50afcaf117073a9c979ac33524748759afc822ea92564982254c36adf37033","abstract_canon_sha256":"dd4ced7026f9287f6922705632ef17b6843ca8163033683a82d634d46351a9fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:49:42.256712Z","signature_b64":"zBwLr75v6lvr+ppOGmWMGM3FOVKyPbFCIE5E1zu8wh3clmpJd5c9E2a2Eb9v0sDnhWQL1UhIuQCewRau4u98Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82d1d1181bd319bcb61595c8d63533f7dbcee80c838c505a7896c0d6c88e6a82","last_reissued_at":"2026-07-05T11:49:42.256217Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:49:42.256217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the determination of the Singer transfer","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nguyen Sum","submitted_at":"2017-10-22T06:36:58Z","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 generator $x_i$ being 1, where $\\mathbb F_2$ denote the prime field of two elements, and let $GL_k$ be the general linear group over $\\mathbb F_2$ which acts regularly on $P_k$. We study the algebraic transfer $Tr_k^*$ constructed by Singer using the technique of the Peterson hit problem. This transfer is a homomorphism from the homology of the mod-2 Steenrod algebra $\\mathcal A$, $\\text{Tor}^{\\mathcal A}_{k,k+d} (\\mathbb F_2,\\mathbb F_2)$, to the subspace of $\\mathbb F_2{\\otimes}_{\\mathcal A}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07895","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1710.07895/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1710.07895","created_at":"2026-07-05T11:49:42.256279+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.07895v4","created_at":"2026-07-05T11:49:42.256279+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07895","created_at":"2026-07-05T11:49:42.256279+00:00"},{"alias_kind":"pith_short_12","alias_value":"QLI5CGA32MM3","created_at":"2026-07-05T11:49:42.256279+00:00"},{"alias_kind":"pith_short_16","alias_value":"QLI5CGA32MM3ZNQV","created_at":"2026-07-05T11:49:42.256279+00:00"},{"alias_kind":"pith_short_8","alias_value":"QLI5CGA3","created_at":"2026-07-05T11:49:42.256279+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.23218","citing_title":"An application of the hit problem to the algebraic transfer","ref_index":29,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QLI5CGA32MM3ZNQVSXENMNJT67","json":"https://pith.science/pith/QLI5CGA32MM3ZNQVSXENMNJT67.json","graph_json":"https://pith.science/api/pith-number/QLI5CGA32MM3ZNQVSXENMNJT67/graph.json","events_json":"https://pith.science/api/pith-number/QLI5CGA32MM3ZNQVSXENMNJT67/events.json","paper":"https://pith.science/paper/QLI5CGA3"},"agent_actions":{"view_html":"https://pith.science/pith/QLI5CGA32MM3ZNQVSXENMNJT67","download_json":"https://pith.science/pith/QLI5CGA32MM3ZNQVSXENMNJT67.json","view_paper":"https://pith.science/paper/QLI5CGA3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.07895&json=true","fetch_graph":"https://pith.science/api/pith-number/QLI5CGA32MM3ZNQVSXENMNJT67/graph.json","fetch_events":"https://pith.science/api/pith-number/QLI5CGA32MM3ZNQVSXENMNJT67/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QLI5CGA32MM3ZNQVSXENMNJT67/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QLI5CGA32MM3ZNQVSXENMNJT67/action/storage_attestation","attest_author":"https://pith.science/pith/QLI5CGA32MM3ZNQVSXENMNJT67/action/author_attestation","sign_citation":"https://pith.science/pith/QLI5CGA32MM3ZNQVSXENMNJT67/action/citation_signature","submit_replication":"https://pith.science/pith/QLI5CGA32MM3ZNQVSXENMNJT67/action/replication_record"}},"created_at":"2026-07-05T11:49:42.256279+00:00","updated_at":"2026-07-05T11:49:42.256279+00:00"}