{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7I3S3FJHSN3P7FMPES4LFR7BGT","short_pith_number":"pith:7I3S3FJH","schema_version":"1.0","canonical_sha256":"fa372d95279376ff958f24b8b2c7e134def701caa478c6debc146c7576ffe6ab","source":{"kind":"arxiv","id":"1607.01095","version":1},"attestation_state":"computed","paper":{"title":"On the generators of the polynomial algebra as a module over the Steenrod algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dang Vo Phuc, Nguyen Sum","submitted_at":"2016-07-05T02:33:28Z","abstract_excerpt":"Let $P_k:= \\mathbb F_2[x_1,x_2,\\ldots,x_k]$ be the polynomial algebra over the prime field of two elements, $\\mathbb F_2$, in $k$ variables $x_1, x_2, \\ldots, x_k$, each of degree 1. We are interested in the Peterson hit problem of finding a minimal set of generators for $P_k$ as a module over the mod-2 Steenrod algebra, $\\mathcal{A}$. In this paper, we study the hit problem in degree $(k-1)(2^d-1)$ with $d$ a positive integer. Our result implies the one of Mothebe [4,5]."},"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":"1607.01095","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2016-07-05T02:33:28Z","cross_cats_sorted":[],"title_canon_sha256":"f1300f3ead1caf4dde665d10f703ef5babf4c967db17787a04cf7fa5734b1b38","abstract_canon_sha256":"b94b1ab53242dd0bb81296698b03461a781dda1b163efd45c09e16783bd2d8b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:30.161256Z","signature_b64":"/JiiWeg6UhRDI0mobQfVpgNf8TvYQLy38qHDkYsGRcQYAORyKFoARoUjYrcWMW4RrfhxOpV3JWXxDRE7ktXlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa372d95279376ff958f24b8b2c7e134def701caa478c6debc146c7576ffe6ab","last_reissued_at":"2026-05-18T01:11:30.160926Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:30.160926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the generators of the polynomial algebra as a module over the Steenrod algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dang Vo Phuc, Nguyen Sum","submitted_at":"2016-07-05T02:33:28Z","abstract_excerpt":"Let $P_k:= \\mathbb F_2[x_1,x_2,\\ldots,x_k]$ be the polynomial algebra over the prime field of two elements, $\\mathbb F_2$, in $k$ variables $x_1, x_2, \\ldots, x_k$, each of degree 1. We are interested in the Peterson hit problem of finding a minimal set of generators for $P_k$ as a module over the mod-2 Steenrod algebra, $\\mathcal{A}$. In this paper, we study the hit problem in degree $(k-1)(2^d-1)$ with $d$ a positive integer. Our result implies the one of Mothebe [4,5]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01095","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":"1607.01095","created_at":"2026-05-18T01:11:30.160981+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.01095v1","created_at":"2026-05-18T01:11:30.160981+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01095","created_at":"2026-05-18T01:11:30.160981+00:00"},{"alias_kind":"pith_short_12","alias_value":"7I3S3FJHSN3P","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7I3S3FJHSN3P7FMP","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7I3S3FJH","created_at":"2026-05-18T12:30:04.600751+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/7I3S3FJHSN3P7FMPES4LFR7BGT","json":"https://pith.science/pith/7I3S3FJHSN3P7FMPES4LFR7BGT.json","graph_json":"https://pith.science/api/pith-number/7I3S3FJHSN3P7FMPES4LFR7BGT/graph.json","events_json":"https://pith.science/api/pith-number/7I3S3FJHSN3P7FMPES4LFR7BGT/events.json","paper":"https://pith.science/paper/7I3S3FJH"},"agent_actions":{"view_html":"https://pith.science/pith/7I3S3FJHSN3P7FMPES4LFR7BGT","download_json":"https://pith.science/pith/7I3S3FJHSN3P7FMPES4LFR7BGT.json","view_paper":"https://pith.science/paper/7I3S3FJH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.01095&json=true","fetch_graph":"https://pith.science/api/pith-number/7I3S3FJHSN3P7FMPES4LFR7BGT/graph.json","fetch_events":"https://pith.science/api/pith-number/7I3S3FJHSN3P7FMPES4LFR7BGT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7I3S3FJHSN3P7FMPES4LFR7BGT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7I3S3FJHSN3P7FMPES4LFR7BGT/action/storage_attestation","attest_author":"https://pith.science/pith/7I3S3FJHSN3P7FMPES4LFR7BGT/action/author_attestation","sign_citation":"https://pith.science/pith/7I3S3FJHSN3P7FMPES4LFR7BGT/action/citation_signature","submit_replication":"https://pith.science/pith/7I3S3FJHSN3P7FMPES4LFR7BGT/action/replication_record"}},"created_at":"2026-05-18T01:11:30.160981+00:00","updated_at":"2026-05-18T01:11:30.160981+00:00"}