Emoji are widely treated as compact affective tokens whose meaning is summarised by a single sentiment score. We argue that this picture is incomplete. From a corpus of 16{,}575 English tweets and a per-emoji metric we call \emph{stability delta} (within-class minus between-class cosine similarity of sentence embeddings), we show that emojis used in tightly clustered topical contexts also exhibit \emph{more} polarised crowd-sourced sentiment, not less. Validated against the Kralj Novak et al.\ (2015) sentiment lexicon, the central correlation is Spearman $ρ= +0.361$ (Holm $p = 0.015$, 95\% bootstrap CI $[+0.10, +0.59]$); against the independent Ferré et al.\ (2025) Spanish 13-emotion ratings, $ρ= +0.509$ ($p = 0.0003$). The result survives permutation testing, BCa bootstrap, leave-one-out jackknife, partial correlation controlling for emoji frequency, and Holm correction across a four-test family. Topical coherence and affective dispersion are distinct dimensions of emoji meaning. As a downstream check we report leakage-free five-fold cross-validation results for sarcasm classification on the Emoji Sarcasm Dataset; all three baselines (a gated multimodal architecture, fine-tuned BERTweet features, and fine-tuned RoBERTa features) score above 0.97 macro F1, indicating the dataset has saturating emoji-label cues. We frame the classifier as supporting evidence rather than the contribution.
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