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Our main result is that, if the degree distribution is a power-law with exponent $\\tau\\in(2,3)$, then, as the number of vertices tends to infinity and with high probability, one of the infection types will occupy all but a finite number o"},"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":"1306.6467","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-27T11:28:44Z","cross_cats_sorted":[],"title_canon_sha256":"e555aec0b9465b232027a5081073636216dfe6429fb976388495e927781d3122","abstract_canon_sha256":"9ba3aeac3872382974e1ef7eebc5df6771e6067f299439c40ca5fca567793967"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:30.055628Z","signature_b64":"eq5cRe3qnDPRTlF0izXRqywkVJ6JDEbajRZCFrcuEWekGrYsHyAw5ZLx36kTJhlUncC6RrMDXd403M/tHQETBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bacfddfbb25a766bef7e79a7df2b206adcaf8f1a9cd0e45e760a6bb5fdf8bf3","last_reissued_at":"2026-05-18T01:23:30.055076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:30.055076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The winner takes it all","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Maria Deijfen, Remco van der Hofstad","submitted_at":"2013-06-27T11:28:44Z","abstract_excerpt":"We study competing first passage percolation on graphs generated by the configuration model. 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