{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JI3WVBST6LTLZWT45WI6NIYMVJ","short_pith_number":"pith:JI3WVBST","schema_version":"1.0","canonical_sha256":"4a376a8653f2e6bcda7ced91e6a30caa4c7036c1965e072115c58813996be419","source":{"kind":"arxiv","id":"1710.07315","version":2},"attestation_state":"computed","paper":{"title":"Dimension functions for spherical fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Cihan Okay, Ergun Yalcin","submitted_at":"2017-10-19T18:45:48Z","abstract_excerpt":"Given a spherical fibration $\\xi$ over the classifying space $BG$ of a finite group we define a dimension function for the $m-$fold fiber join of $\\xi$ where $m$ is some large positive integer. We show that the dimension functions satisfy the Borel-Smith conditions when $m$ is large enough. As an application we prove that there exists no spherical fibration over the classifying space of $\\text{Qd}(p)= (\\mathbb{Z}/p)^2\\rtimes\\text{SL}_2(\\mathbb{Z}/p)$ with $p-$effective Euler class, generalizing the result of \\\"Ozg\\\"un \\\"Unl\\\"u about group actions on finite complexes homotopy equivalent to a sp"},"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":"1710.07315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-19T18:45:48Z","cross_cats_sorted":[],"title_canon_sha256":"574c475c6e8c64edee18cbde0e3640f863dda932c0eea956055da46495241b10","abstract_canon_sha256":"f2a1d35505187d62eac3baea7bf98583c8b2f9c69a7508fb83f9468a59684798"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:05.366095Z","signature_b64":"g5Q4AAIdWrVXP6nFMaqNGrszyyN4gVhJA0AMIKF1UbPZzgSnFhLXrJrxju2ON7LoD78eZaz6tIUNORVBvOqbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a376a8653f2e6bcda7ced91e6a30caa4c7036c1965e072115c58813996be419","last_reissued_at":"2026-05-17T23:58:05.365670Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:05.365670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dimension functions for spherical fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Cihan Okay, Ergun Yalcin","submitted_at":"2017-10-19T18:45:48Z","abstract_excerpt":"Given a spherical fibration $\\xi$ over the classifying space $BG$ of a finite group we define a dimension function for the $m-$fold fiber join of $\\xi$ where $m$ is some large positive integer. We show that the dimension functions satisfy the Borel-Smith conditions when $m$ is large enough. As an application we prove that there exists no spherical fibration over the classifying space of $\\text{Qd}(p)= (\\mathbb{Z}/p)^2\\rtimes\\text{SL}_2(\\mathbb{Z}/p)$ with $p-$effective Euler class, generalizing the result of \\\"Ozg\\\"un \\\"Unl\\\"u about group actions on finite complexes homotopy equivalent to a sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07315","kind":"arxiv","version":2},"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":"1710.07315","created_at":"2026-05-17T23:58:05.365726+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.07315v2","created_at":"2026-05-17T23:58:05.365726+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07315","created_at":"2026-05-17T23:58:05.365726+00:00"},{"alias_kind":"pith_short_12","alias_value":"JI3WVBST6LTL","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JI3WVBST6LTLZWT4","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JI3WVBST","created_at":"2026-05-18T12:31:24.725408+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/JI3WVBST6LTLZWT45WI6NIYMVJ","json":"https://pith.science/pith/JI3WVBST6LTLZWT45WI6NIYMVJ.json","graph_json":"https://pith.science/api/pith-number/JI3WVBST6LTLZWT45WI6NIYMVJ/graph.json","events_json":"https://pith.science/api/pith-number/JI3WVBST6LTLZWT45WI6NIYMVJ/events.json","paper":"https://pith.science/paper/JI3WVBST"},"agent_actions":{"view_html":"https://pith.science/pith/JI3WVBST6LTLZWT45WI6NIYMVJ","download_json":"https://pith.science/pith/JI3WVBST6LTLZWT45WI6NIYMVJ.json","view_paper":"https://pith.science/paper/JI3WVBST","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.07315&json=true","fetch_graph":"https://pith.science/api/pith-number/JI3WVBST6LTLZWT45WI6NIYMVJ/graph.json","fetch_events":"https://pith.science/api/pith-number/JI3WVBST6LTLZWT45WI6NIYMVJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JI3WVBST6LTLZWT45WI6NIYMVJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JI3WVBST6LTLZWT45WI6NIYMVJ/action/storage_attestation","attest_author":"https://pith.science/pith/JI3WVBST6LTLZWT45WI6NIYMVJ/action/author_attestation","sign_citation":"https://pith.science/pith/JI3WVBST6LTLZWT45WI6NIYMVJ/action/citation_signature","submit_replication":"https://pith.science/pith/JI3WVBST6LTLZWT45WI6NIYMVJ/action/replication_record"}},"created_at":"2026-05-17T23:58:05.365726+00:00","updated_at":"2026-05-17T23:58:05.365726+00:00"}