How do I know the Fed is not our central banker?

This chart reveals the dirty secret.  How did the excess reserves match the reserve portfolio of treasuries so well? This is an accurate double entry accounting in the Fed balance sheet. And iot obeys the constrained flow conditions, so someone did a BlackScholes. But it wasn't Bernanke because he pre-announced his purchases (red line). The excess reserves (blue line) was always adjusted after some time to re-align with the portfolio. The adjustment was done using the ten year yield.

Once you understand what happened then you have the aha moment,  Goldman Sachs or JP Morgan is our new central banker. Dunno exactly which one, but they share their banker bot with their partners, (read member banks). The Fed actually got fired somewhere in 1988, or a bit earlier, likely when Greenspan took over. The Fed has actually never set the interest rate since Volcker left, the data shows that. The one year treasury is the benchmark, and it is being set somewhere in some urine infested back alley in New York City.

What are the other options here?

Treasury could have adjusted its debt sales to make the reserves match portfolios. Or, the Theory of Everything, which says that some people, conscious or unconscious always runs a generalized Black Scholes in aggregate adapted statistics. In other words, this match had to happen to keep the ruler straight, otherwise we would have second dipped; (and we almost did).