improve: If $n=0$, the expression indicates that an oscillator starting with an energy of zero cannot, according to our assumption about the possible energy exchanges, reach the minimum energy of $1/2$. The reverse is also true. 
For this reason, a zero-energy oscillator cannot even absorb standard packets from its surroundings: this is because it does not have the capacity to completely fill the columns of energy states in the triangles. This inadequacy calls into question the feasibility of the quantized  zero-energy model. Therefore, we are faced with two alternatives: either we exclude oscillators with zero energy and terminate our analysis, or we accept the possibility of exchanging semi-standard packets under certain conditions. If we choose to explore the latter scenario and iterate this reasoning $n$ times, we will reach standard packets of size $1/2^n$, accompanied by additional semi-standard energies of size $1/2^{n+1}$. As this infinite regression continues, we eventually converge to a classical oscillator. Therefore, we must discard the existence of zero-energy oscillators. 