Is `long` guaranteed to be at least 32 bits?

By my reading of the C++ Standard, I have always understood that the sizes of the integral fundamental types in C++ were as follows:

sizeof(char) <= sizeof(short int) <= sizeof(int) <= sizeof(long int)

I deduced this from 3.9.1/2:

2. There are four signed integer types: “signed char”, “short int”, “int”, and “long int.” In this list, each type provides at least as much storage as those preceding it in the list. Plain ints have the natural size suggested by the architecture of the execution environment

Further, the size of char is described by 3.9.1/ as being:

1. [...] large enough to store any member of the implementation’s basic character set.

1.7/1 defines this in more concrete terms:

1. The fundamental storage unit in the C + + memory model is the byte. A byte is at least large enough to contain any member of the basic execution character set and is composed of a contiguous sequence of bits, the number of which is implementation-defined.

This leads me to the following conclusion:

1 == sizeof(char) <= sizeof(short int) <= sizeof(int) <= sizeof(long int)

where sizeof tells us how many bytes the type is. Furthermore, it is implementation-defined how many bits are in a byte. Most of us are probably used to dealing with 8-bit bytes, but the Standard says there are n bits in a byte.

In this post, Alf P. Steinbach says:

long is guaranteed (at least) 32 bits.

This flies in the face of everything I understand the size of the fundamental types to be in C++ according to the Standard.