[nayuki]

> this article doesn't explicitly justify is whether the ten-byte zlib string is truly the shortest possible

I know the DEFLATE standard intimately and implemented a decoder and encoder (open source on my website/GitHub).

We know that the smallest image requires 2 bytes - 1 for the row filter and 1 for the pixel(s). For simplicitly, we'll assume the data is (hex) 00 00.

A DEFLATE compressed stream must have at least one block. There are three choices for each block's type - uncompressed, fixed Huffman code, and custom Huffman code. Uncompressed requires 1 byte for {type (2 bits), finality (1 bit), padding (5 bits)} and 4 bytes for the length. So that uses 5 bytes already. Using a fixed Huffman code block lets us encode those 2 bytes as 4 bytes. Using a custom Huffman code requires many, many bytes just to specify the Huffman table. Hence, the OP article's approach is justified.