What does it take for “neo-Fisherism” to be wrong?

"Neo-Fisherism" is based on the Fisher relationship in the long run, which is written: Nominal interest rate = Real interest rate + Inflation If: Central banks control nominal interest rates at all maturities in the long run , which is more or less the case; The real interest rate in the long run returns to an equilibrium level that depends on the structural characteristics of the economy (savings-investment equilibrium, therefore propensity to save, need for investment, technological progress, etc.); then in the long run inflation depends on the nominal interest rate; a lasting fall in the nominal interest rate leads to a fall in inflation, which may come as a shock . For this not to be true, there must be high inflation and a low nominal interest rate in the long run , and therefore a permanently very negative real interest rate. But the real return on corporate capital is highly positive. For the real interest rate to be highly negative in the long term, there must therefore be no arbitrage between bonds and assets representing corporate capital. If there is arbitrage, the real interest rate on bonds will converge towards the real return on corporate capital, and there is neo-Fisherism. The absence of arbitrage may result from: Either permanent bond purchases by central banks; Or strong financial repression that forces banks and institutional investors to hold bonds and not assets representing corporate capital.