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The main result stated in Theorem 3.10 generalizes Theorem 1.10 in K.\\ A.\\ Hardie, \\textit{A generalization of the Hopf construction}, Quart.\\ J.\\ Math.\\ Oxford Ser.\\ (2) \\textbf{12} (1961), 196--204. and concerns to the Hopf invariant of the generalized Hopf construction.\n  We close the paper applying the Gray's construction $\\circ$ (called the Theriault product) "},"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":"1508.06122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-25T11:58:13Z","cross_cats_sorted":[],"title_canon_sha256":"56f7f63c223f43c30324e04a450bfefe4793ec959a4fb84f2cec237de2d68cec","abstract_canon_sha256":"3d58cce2276612616c73bd240c55772a7d96075dcdd60051316a7b2c3202a74a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:46.778607Z","signature_b64":"js5P+7E5wj6uTsXE4jXearSaJam9bCS/OZTiB+4l761Ka4GVBptOml0QjcfB2HGmtmmp8aQbcFbsvQS04vmDBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96b067f91e8364feb6336fba5fc281c40c5c7146019c8eb8084ceac13b0730ee","last_reissued_at":"2026-05-18T01:34:46.777945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:46.777945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the higher order exterior and interior Whitehead products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Marek Golasi\\'nski, Thiago de Melo","submitted_at":"2015-08-25T11:58:13Z","abstract_excerpt":"We extend the notion of the exterior Whitehead product for maps $\\alpha_i:\\Sigma A_i \\to X_i$ for $i=1,\\dots,n$, where $\\Sigma A_i$ is the reduced suspension of $A_i$ and then, for the interior product with $X_i=J_{m_i}(X)$ as well. The main result stated in Theorem 3.10 generalizes Theorem 1.10 in K.\\ A.\\ Hardie, \\textit{A generalization of the Hopf construction}, Quart.\\ J.\\ Math.\\ Oxford Ser.\\ (2) \\textbf{12} (1961), 196--204. and concerns to the Hopf invariant of the generalized Hopf construction.\n  We close the paper applying the Gray's construction $\\circ$ (called the Theriault product) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06122","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":"1508.06122","created_at":"2026-05-18T01:34:46.778045+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.06122v1","created_at":"2026-05-18T01:34:46.778045+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06122","created_at":"2026-05-18T01:34:46.778045+00:00"},{"alias_kind":"pith_short_12","alias_value":"S2YGP6I6QNSP","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"S2YGP6I6QNSP5NRT","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"S2YGP6I6","created_at":"2026-05-18T12:29:39.896362+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/S2YGP6I6QNSP5NRTN65F7QUBYQ","json":"https://pith.science/pith/S2YGP6I6QNSP5NRTN65F7QUBYQ.json","graph_json":"https://pith.science/api/pith-number/S2YGP6I6QNSP5NRTN65F7QUBYQ/graph.json","events_json":"https://pith.science/api/pith-number/S2YGP6I6QNSP5NRTN65F7QUBYQ/events.json","paper":"https://pith.science/paper/S2YGP6I6"},"agent_actions":{"view_html":"https://pith.science/pith/S2YGP6I6QNSP5NRTN65F7QUBYQ","download_json":"https://pith.science/pith/S2YGP6I6QNSP5NRTN65F7QUBYQ.json","view_paper":"https://pith.science/paper/S2YGP6I6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.06122&json=true","fetch_graph":"https://pith.science/api/pith-number/S2YGP6I6QNSP5NRTN65F7QUBYQ/graph.json","fetch_events":"https://pith.science/api/pith-number/S2YGP6I6QNSP5NRTN65F7QUBYQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S2YGP6I6QNSP5NRTN65F7QUBYQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S2YGP6I6QNSP5NRTN65F7QUBYQ/action/storage_attestation","attest_author":"https://pith.science/pith/S2YGP6I6QNSP5NRTN65F7QUBYQ/action/author_attestation","sign_citation":"https://pith.science/pith/S2YGP6I6QNSP5NRTN65F7QUBYQ/action/citation_signature","submit_replication":"https://pith.science/pith/S2YGP6I6QNSP5NRTN65F7QUBYQ/action/replication_record"}},"created_at":"2026-05-18T01:34:46.778045+00:00","updated_at":"2026-05-18T01:34:46.778045+00:00"}