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To be more precise, suppose $f\\in{_2\\pi_n^s}$ pulls back to $g\\in{_2\\pi_n^s}P$ through the Kahn-Priddy map $\\lambda:QP\\to Q_0S^0$ such that $g$ projects nontrivially to an element $g'\\in{_2\\pi_n^s}P_{t(n)}$ with $h(g')=0$ where $h:{_2\\pi_*}QP_k\\to H_*QP_k$ is the unstable Hurewicz map, and $t(n)=\\lceil n/2\\rceil$. Then, mod out by elements of ${_2\\pi_*^s}\\simeq{_2\\pi_*}QS^0$ satisfying this property, the Curtis conjecture on the image of $h:{_2\\pi_*}QS^0\\to H_*QS^0$ holds."},"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":"1801.07480","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-23T10:53:17Z","cross_cats_sorted":[],"title_canon_sha256":"71685b324642f717cd776d09bf4eaf08bef554b880e45686acf343553d8e64c1","abstract_canon_sha256":"4c470b821d2ad9c4e45f64a6e688ba8cd91a5668fbf22fa8d911d8150af53369"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:53.614475Z","signature_b64":"qxPGC4viPW4JHCv36Pz74HiyL9vESNlU7z0VCRK7Rc3mmRaTmwysWQMy3Vl1hMgR/vUaLfDGvqY/b10ThxDcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"737165009c3983a40bb0aef4361e81e41b45d882e0bba595943072a51a61e868","last_reissued_at":"2026-05-18T00:17:53.613969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:53.613969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Freudenthal theorem, Kahn-Priddy Theorem, and Curits conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hadi Zare","submitted_at":"2018-01-23T10:53:17Z","abstract_excerpt":"We verify Curtis conjecture on a class of elements of ${_2\\pi_*^s}$ that satisfy a certain factorisation property. To be more precise, suppose $f\\in{_2\\pi_n^s}$ pulls back to $g\\in{_2\\pi_n^s}P$ through the Kahn-Priddy map $\\lambda:QP\\to Q_0S^0$ such that $g$ projects nontrivially to an element $g'\\in{_2\\pi_n^s}P_{t(n)}$ with $h(g')=0$ where $h:{_2\\pi_*}QP_k\\to H_*QP_k$ is the unstable Hurewicz map, and $t(n)=\\lceil n/2\\rceil$. Then, mod out by elements of ${_2\\pi_*^s}\\simeq{_2\\pi_*}QS^0$ satisfying this property, the Curtis conjecture on the image of $h:{_2\\pi_*}QS^0\\to H_*QS^0$ holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07480","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":"1801.07480","created_at":"2026-05-18T00:17:53.614047+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.07480v3","created_at":"2026-05-18T00:17:53.614047+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07480","created_at":"2026-05-18T00:17:53.614047+00:00"},{"alias_kind":"pith_short_12","alias_value":"ONYWKAE4HGB2","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"ONYWKAE4HGB2IC5Q","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"ONYWKAE4","created_at":"2026-05-18T12:32:43.782077+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/ONYWKAE4HGB2IC5QV32DMHUB4Q","json":"https://pith.science/pith/ONYWKAE4HGB2IC5QV32DMHUB4Q.json","graph_json":"https://pith.science/api/pith-number/ONYWKAE4HGB2IC5QV32DMHUB4Q/graph.json","events_json":"https://pith.science/api/pith-number/ONYWKAE4HGB2IC5QV32DMHUB4Q/events.json","paper":"https://pith.science/paper/ONYWKAE4"},"agent_actions":{"view_html":"https://pith.science/pith/ONYWKAE4HGB2IC5QV32DMHUB4Q","download_json":"https://pith.science/pith/ONYWKAE4HGB2IC5QV32DMHUB4Q.json","view_paper":"https://pith.science/paper/ONYWKAE4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.07480&json=true","fetch_graph":"https://pith.science/api/pith-number/ONYWKAE4HGB2IC5QV32DMHUB4Q/graph.json","fetch_events":"https://pith.science/api/pith-number/ONYWKAE4HGB2IC5QV32DMHUB4Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ONYWKAE4HGB2IC5QV32DMHUB4Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ONYWKAE4HGB2IC5QV32DMHUB4Q/action/storage_attestation","attest_author":"https://pith.science/pith/ONYWKAE4HGB2IC5QV32DMHUB4Q/action/author_attestation","sign_citation":"https://pith.science/pith/ONYWKAE4HGB2IC5QV32DMHUB4Q/action/citation_signature","submit_replication":"https://pith.science/pith/ONYWKAE4HGB2IC5QV32DMHUB4Q/action/replication_record"}},"created_at":"2026-05-18T00:17:53.614047+00:00","updated_at":"2026-05-18T00:17:53.614047+00:00"}