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In the rapidly evolving cryptocurrency landscape, trust is a critical yet underexplored factor shaping market behaviors and driving user preferences between centralized exchanges (CEXs) and decentralized exchanges (DEXs). Despite its importance, trust remains challenging to measure, limiting the study of its effects on market dynamics. The collapse of FTX, a major CEX, provides a unique natural experiment to examine the measurable impacts of trust and its sudden erosion on the cryptocurrency ecosystem. This pivotal event raised questions about the resilience of centralized trust systems and accelerated shifts toward decentralized alternatives. This research investigates the impacts of the FTX collapse on user trust, focusing on token valuation, trading flows, and sentiment dynamics. Employing causal inference methods, including Regression Discontinuity Design (RDD) and Difference-in-Differences (DID), we reveal significant declines in WETH prices and NetFlow from CEXs to DEXs, signaling a measurable transfer of trust. Additionally, natural language processing methods, including topic modeling and sentiment analysis, uncover the complexities of user responses, highlighting shifts from functional discussions to emotional fragmentation in Binance's community, while Uniswap's sentiment exhibits a gradual upward trend. Despite data limitations and external influences, the findings underscore the intricate interplay between trust, sentiment, and market behavior in the cryptocurrency ecosystem. By bridging blockchain analytics, behavioral finance, and decentralized finance (DeFi), this study contributes to interdisciplinary research, offering a deeper understanding of distributed trust mechanisms and providing critical insights for future investigations into the socio-technical dimensions of trust in digital economies.