"beyond the threshold of" is a grammatically correct phrase and can be used in written English.
It can be used when describing something that is outside or surpasses a certain limit or boundary. Example: The beauty of the mountains was beyond the threshold of anything I had ever seen before.
The virus seems to have gone far beyond the threshold of outbreak and ignited an epidemic.
"We are now beyond the threshold of risk," Mr Castel-Branco says.
I walked out to just beyond the threshold of the store, turned to face him and opened the bag.
"At that moment, I suddenly realized that I was going beyond the threshold of consciousness," Senna said.
Or there's the grim Goodbye Door at the Jewish Montessori, beyond the threshold of which the dropping-off parent is forbidden to pass.
Pnin hurled the towel into a corner and, turning away, stood for a moment staring at the blackness beyond the threshold of the open back door...
In models of infectious diseases, the tipping point represents the threshold of infections beyond which a disease becomes an epidemic.
Mohsen and Rezazadeh Karsalari (2011) observe a negative relationship between private investment and the real interest rate beyond the threshold level of 5to6%6 %, but the impact of real rates on private investment turns positive within this threshold level.
Because the risk increases rapidly beyond the threshold value of σ, these results suggest that an essential component of risk management is to carefully minimize erratic fluctuations in the patient's CSF input flow rate at all times.
This observed increase depends on CF length and becomes more pronounced at and beyond the threshold loading of the HDPE/G composite.
According to our simulation for patient muscle, the sodium conductance of the omega pores may be high enough to depolarize the membrane beyond the mechanical threshold of −40 mV and thereby induce muscle contracture.
