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We show that if the value on $(0,0,\\ldots,0)$ is set to $x=X/L$ then $\\Theta/L$ converges in law as $L\\to\\infty$"},"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":"1304.0246","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-31T19:27:00Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"03139f74116db0d10cad5b908091b230aca7f80b7142460268c357566a72b276","abstract_canon_sha256":"0fa4f6a66d38ed27a73ed401eeb9dcfde985068c93e07c4bfe0db7cd45c7ef26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:08.885471Z","signature_b64":"UIl3GYqqWitnFFmeTLJWFMlWnTue4HKqNPyw8VEQyijHqAvDbDki+hYxpPP7o1SBxsa2fn8uXFBERhTYfSxECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8780aa44ad535a8a3f74dbf7337cf82d2f84370e188fef13ca57f860f8ab76e","last_reissued_at":"2026-05-18T01:21:08.884863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:08.884863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The number of accessible paths in the hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"math.PR","authors_text":"\\'Eric Brunet, Julien Berestycki, Zhan Shi","submitted_at":"2013-03-31T19:27:00Z","abstract_excerpt":"Motivated by an evolutionary biology question, we study the following problem: we consider the hypercube $\\{0,1\\}^L$ where each node carries an independent random variable uniformly distributed on $[0,1]$, except $(1,1,\\ldots,1)$ which carries the value $1$ and $(0,0,\\ldots,0)$ which carries the value $x\\in[0,1]$. 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