It might be not so clear for you, however, this does not mean that you or these biased mathematicians are correct heheheh.
The indicator they used is quite simple: the 6 month correlation between the Bitcoin price and the S&P 500. So there is not much room for mistakes.
Bitcoin's value was 0.18, Gold 0.06, other commodities 0.29, EV Equities 0.57, and US High yield bonds 0.69. It was a bit surprising to me to see that commodities' prices have also a certain correlation with the S&P 500, higher than Bitcoin's.
The only thing I don't like in their report is that they used a 10 year average. This is imo too long, because in 2016 investment behavior was very different in the Bitcoin space than now. They should have used a 5 year average instead to see the correlation in the market conditions after major institutional involvement. Major correlations between Bitcoin and S&P 500 were only seen from 2020 onwards.
here's the report, it's on page 8.
Of course this doesn't tell us the future, it's still a measure about the past. I have often looked at patterns themselves, and US stock market movements (above all the Nasdaq) often have influenced Bitcoin during some periods, but mainly for minor price movements, like deciding if we go up 2% or down 2% in a single day. The major Bitcoin price movements, in contrast, were often "contrarian" to the stock price movement. The best example is last year's Bitcoin crash. There was no correlation with a stock market movement at all.
Here's a chart comparing Bitcoin and S&P 500 for the last years. It can be clearly seen that the October/November crash was during a first slightly bullish and later sideways phase of the S&P 500. The most significant correlation, in contrast, was in April/May 2026 when both indicators were slightly bullish. The most recent time when instead a significant downwards movement affected both the S&P 500 and Bitcoin was the March 2025 dip, caused probably by the trade wars and US tariff policy.

Also, if the AI bubble pops, it will certainly cause fear on the market and cause less liquidity and more outflows, including outflows from the cryptospace market.
I could indeed imagine a short dip like in 2020 caused by a panic, but we saw then later that the outcome of the year 2020 was overwhelmingly positive even if it was a desaster for the economy.
On the failure of passage of the Clarity act, you might correct that bitcoin might not be very much affected only if an anticrypto administration decides that he will not go after the whole cryptospace including bitcoin. The clearer framework that the Clarity act will bring on the cryptospace will be the protection from the possibility of a Gensler 2.0.
The next US presidential elections are in 2028. I think here we are discussing a shorter timeframe (until 2027 maybe), aren't we? I don't rule out that a 2028 administration change, depending on the proposals floating around, could have indeed bearish consequences. But it's way too early.