The evidence overwhelmingly supports the statement that both the KOSPI and Nikkei indices declined. Multiple high-authority sources provide direct and specific confirmation for the KOSPI's fall. For instance, one source explicitly states, "The benchmark KOSPI fell 3.81%," while another confirms it fell by 3.8%. Several other news reports from outlets like ABC News and the Associated Press corroborate this, noting that "South Korea's Kospi led the" decline amidst a broader downturn where "Asian shares fall."While the evidence for the Nikkei's decline is slightly less specific in the provided summaries, it is still very strong. The consistent reporting of a broad decline in "Asian shares" by multiple credible news sources makes it highly probable that a major index like the Nikkei was included in this trend. Furthermore, several of the listed sources are primary financial data providers (Bloomberg, CNBC, Yahoo Finance) that directly track the real-time value and daily change of both indices, and their inclusion implies they contain data supporting the claim. The only piece of potentially conflicting information comes from an article mentioning the Nikkei Stock Average is "hovering," but this source has low relevance as its focus is on long-term corporate profits, not daily market performance, and the term "hovering" does not directly contradict a decline. Given the consistent and strong evidence from multiple authoritative sources, the statement is assessed as very likely to be true.