Combinadic Compression: An Order-0 Enumerative Byte-Stream Codec with Size-Preserving Encryption

Order-0 enumerative coding represents a fixed-length block not as a self-delimiting bitstream but as a short tuple of integer fields over known finite ranges: each value’s positions form a bitset, reduced to its colexicographic rank, leaving per-symbol counts and ranks. We study this representation, not a particular codec: one structural fact—finite-range integer fields—affords what a self-delimiting bitstream cannot. It is order-0-optimal, reaching the entropy bound up to an O(AlogN) per-block overhead; at matched block sizes it is the most compact block-resetting order-0 coder (Huffman, range, asymmetric numeral systems (ANS)) on narrow alphabets, though a globally modeled coder wins at small blocks. Because every field is an integer over a known range, it also yields an exact compressed size known before encoding, independent random access, and an in-place size-preserving cipher (addition modulo each range) reducing to a standard keystream. Leaving the counts in clear exposes only a block’s count spectrum—an adjustable leakage equal to its entropy, small on the homogeneous streams it best suits. Slower than streaming coders at equal ratio—35–199 MB/s compressing; 9–38 MB/s decompressing—it is not a general-purpose compressor but a structurally transparent design point, suited to record stores and constrained-alphabet data.