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Moreover, we describe all homology spheres with \\alpha up to four and, as a corollary, all homology spheres with up to eight minimal non-faces. To prove these results we consider the nerve of the minimal non-faces of \\Delta."},"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":"1101.4480","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-24T09:53:29Z","cross_cats_sorted":[],"title_canon_sha256":"20e4d63f12dc515b93d66eb9b874f61d4d3e1dff6bbc81f1a5a9693bc912d15f","abstract_canon_sha256":"01c03919afa0d264fa70f69458b16d83c48e085679ebbfb8080a2eb485398193"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:22.411735Z","signature_b64":"TR+9V/COsxts5ULTDwOUTPVz7RBf3VrCm2x15Qso+jvMximsATMGEov8y7mPSYdbi8uxIaavMwYYlj9rvQPXCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fd304cef5873123628c21de6a8dfdc45967f931ea877d0685fa8e448d7c010d","last_reissued_at":"2026-05-18T03:49:22.411035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:22.411035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On homology spheres with few minimal non faces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lukas Katth\\\"an","submitted_at":"2011-01-24T09:53:29Z","abstract_excerpt":"Let \\Delta be a (d-1)-dimensional homology sphere on n vertices with m minimal non-faces. 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