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In this note, we find a recursive way to depict how {\\it some} of these parameters $c$ appear in the interval $[0, 2]$ and show that $\\liminf_{n \\to \\infty} (\\log N_n)/n \\ge \\log 2$ and this result is generalized to a class of one-parameter families of continuous real-valued maps tha"},"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":"1405.7167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-28T09:10:57Z","cross_cats_sorted":[],"title_canon_sha256":"351b1247c3e39e2b1bc68a2689706307ec71e3f3dd39da511c30b228fcf36b18","abstract_canon_sha256":"d1a174cf17d1bd66d065893f22303ca70491fa3cfae6e53a26db88c258a92715"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:59.040661Z","signature_b64":"mi6+WjXsDcIhkJzWNFk9GGcTNcvkHTye3ni0IuM21UjNmx6kEvN4k3B8kqdFP3Wm816uP3QgJRSo2esn1YY0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83a9dd19cfba54d63de8ea255a619755843e6f7e66ed3b1a8897e39602c77eaa","last_reissued_at":"2026-05-18T02:50:59.039902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:59.039902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the number of parameters $c$ for which the point $x=0$ is a superstable periodic point of $f_c(x) = 1 - cx^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bau-Sen Du","submitted_at":"2014-05-28T09:10:57Z","abstract_excerpt":"Let $f_c(x) = 1 - cx^2$ be a one-parameter family of real continuous maps with parameter $c \\ge 0$. 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