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The Kameko squaring operation $(\\widetilde {Sq^0_*})_{(s; N)}: (\\mathbb F_2\\otimes_{\\mathscr A} \\mathcal {P}_s)_{2N+s} \\longrightarrow (\\mathbb F_2\\otimes_{\\mathscr A} \\mathcal {P}_s)_{N}$ is rather"},"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":"2408.07485","kind":"arxiv","version":7},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-08-14T11:56:59Z","cross_cats_sorted":[],"title_canon_sha256":"7346478d34fdcefffc5b4cee3092a54be2d53bcdeb44b1c308749a37a7c8d1bf","abstract_canon_sha256":"017c537d23185bebee09c05f9b7be2de2c3ead938b81b399d501a9bc557dfc63"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:30:20.279071Z","signature_b64":"KNxk9UPC2H39GdNmIYNFlxmzZ9I2vN6yVJaT9AzvhzHVRIzLJx314MUCvwzIZE/0NG7NGYE/NcoczCmzrhRnCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e5577c1c04669dd4f7cc5a5e0b0b8e8c274e32de22dec6c37193fa2fc7fd436","last_reissued_at":"2026-07-05T09:30:20.278572Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:30:20.278572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the mod-2 cohomology of the product of the infinite lens space and the space of invariants in a generic degree","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dang Vo Phuc","submitted_at":"2024-08-14T11:56:59Z","abstract_excerpt":"Let $\\mathbb S^{\\infty}/\\mathbb Z_2$ be the infinite lens space and $\\mathscr A$ be the Steenrod algebra over the binary field $\\mathbb F_2.$ The cohomology $H^{*}((\\mathbb S^{\\infty}/\\mathbb Z_2)^{\\oplus s}; \\mathbb F_2)$ is known to be isomorphic to the graded polynomial ring $\\mathcal {P}_s:= \\mathbb F_2[x_1, \\ldots, x_s]$ on $s$ generators of degree 1, viewed as an unstable $\\mathscr A$-module. The Kameko squaring operation $(\\widetilde {Sq^0_*})_{(s; N)}: (\\mathbb F_2\\otimes_{\\mathscr A} \\mathcal {P}_s)_{2N+s} \\longrightarrow (\\mathbb F_2\\otimes_{\\mathscr A} \\mathcal {P}_s)_{N}$ is rather"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07485","kind":"arxiv","version":7},"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/2408.07485/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":"2408.07485","created_at":"2026-07-05T09:30:20.278638+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.07485v7","created_at":"2026-07-05T09:30:20.278638+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.07485","created_at":"2026-07-05T09:30:20.278638+00:00"},{"alias_kind":"pith_short_12","alias_value":"TZKXPQOAIZU5","created_at":"2026-07-05T09:30:20.278638+00:00"},{"alias_kind":"pith_short_16","alias_value":"TZKXPQOAIZU52T34","created_at":"2026-07-05T09:30:20.278638+00:00"},{"alias_kind":"pith_short_8","alias_value":"TZKXPQOA","created_at":"2026-07-05T09:30:20.278638+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.20566","citing_title":"The rank-five Peterson hit problem, the fifth Singer transfer, and a geometric generator in unoriented cobordism","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TZKXPQOAIZU52T34YWS6BMFY5D","json":"https://pith.science/pith/TZKXPQOAIZU52T34YWS6BMFY5D.json","graph_json":"https://pith.science/api/pith-number/TZKXPQOAIZU52T34YWS6BMFY5D/graph.json","events_json":"https://pith.science/api/pith-number/TZKXPQOAIZU52T34YWS6BMFY5D/events.json","paper":"https://pith.science/paper/TZKXPQOA"},"agent_actions":{"view_html":"https://pith.science/pith/TZKXPQOAIZU52T34YWS6BMFY5D","download_json":"https://pith.science/pith/TZKXPQOAIZU52T34YWS6BMFY5D.json","view_paper":"https://pith.science/paper/TZKXPQOA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.07485&json=true","fetch_graph":"https://pith.science/api/pith-number/TZKXPQOAIZU52T34YWS6BMFY5D/graph.json","fetch_events":"https://pith.science/api/pith-number/TZKXPQOAIZU52T34YWS6BMFY5D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TZKXPQOAIZU52T34YWS6BMFY5D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TZKXPQOAIZU52T34YWS6BMFY5D/action/storage_attestation","attest_author":"https://pith.science/pith/TZKXPQOAIZU52T34YWS6BMFY5D/action/author_attestation","sign_citation":"https://pith.science/pith/TZKXPQOAIZU52T34YWS6BMFY5D/action/citation_signature","submit_replication":"https://pith.science/pith/TZKXPQOAIZU52T34YWS6BMFY5D/action/replication_record"}},"created_at":"2026-07-05T09:30:20.278638+00:00","updated_at":"2026-07-05T09:30:20.278638+00:00"}