Unused Code Words as Handshake Spacers: Delay-Insensitive Request, Timed Release

A p-bit register whose alphabet leaves code words unused can use one of them as the spacer of a four-phase handshake instead of a request wire. For every alphabet the minterm of the spacer detects the request edge (datum to spacer) delay-insensitively, and every cut-based mapping of its and-inverter tree preserves this. The release edge (spacer to datum) has no delay-insensitive detector once the alphabet has more than C(p, floor(p/2)) words, so the timing assumption of bundled data moves from the sender to the receiver; removing it while keeping the data bits costs ceil(log2 L) wires, where L is the number of words in the longest chain of the alphabet seen from the spacer. In an interval alphabet {0,...,m-1} with 2^(p-1) < m < 2^p and c unused words, no two unused words can both follow every datum and be told apart delay-insensitively, but different ones can follow different zones of the data and so tell the receiver up to floor(log2 c) bits of the datum. Among intervals, the only unused word is a spacer with a monotone detector exactly for the Mersenne modulus m = 2^p - 1; this case needs canonical arithmetic, since an end-around-carry adder emits the spacer for about one operand pair in 2^p, and transitions between data that bypass the spacer can present it with probability close to (3/4)^p. Against bundled data the spacer saves one wire per channel for 2p-1 gates and 1.25 to 1.83 times as many bus transitions at p = 8 to 64; in SKY130 its detector has 47-51% of the cell area and 40-47% of the switching energy of a dual-rail valid-phase detector. The archive contains the LaTeX source of the paper, the scripts that regenerate every computed number, finite checks of its theorems, and the provenance of the SKY130 measurements. Run "python3 verify.py" (see README.md) to check everything with one command.