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With probability 1-p, recolour the ball to a new colour and then return it to the urn. This is equivalent to the supercritical case of a random graph model studied by Backhausz and M\\'ori, and Th\\\"ornblad. We prove that, with probability 1, there is a dominating colour, in the sense that, after some random but finite time, t"},"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":"1506.05862","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-19T02:15:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a9cccc2c0c5bc20e431cdf6c6da36ca75087a8824c048df4cc7134f7987faf0b","abstract_canon_sha256":"be04f0ddcfedd90d44dad4f2f0b39d8fb0cca8a4a75a892f60659d518692bb36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:12.507651Z","signature_b64":"bayZ9T2YXZyfHK9LypSx0WpWPuqiCvAB9gjqaBe3CACXAxC20bOacSETBOkqS5MUzPBYfYNxIHkIbs9hPcZfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bd42bd7340faa496a8b72f831b343a66360fce7496ca4b2fcb60f293c956974","last_reissued_at":"2026-05-18T00:56:12.507166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:12.507166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The dominating colour of an infinite P\\'olya urn model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Erik Th\\\"ornblad","submitted_at":"2015-06-19T02:15:35Z","abstract_excerpt":"We study a P\\'olya-type urn model defined as follows. 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