A MUX with select probability 1/2 outputs z = (x + y)/2: scaled addition, the stochastic computing convention. Measured over 200,000 slices per point:
| x | y | exact (x+y)/2 | measured |
|---|---|---|---|
| 0.1 | 0.3 | 0.2000 | 0.1998 |
| 0.25 | 0.5 | 0.3750 | 0.3761 |
| 0.5 | 0.9 | 0.7000 | 0.7004 |
| 0.8 | 0.8 | 0.8000 | 0.8014 |
Worst deviation 0.0014 (counting noise). Subtraction is addition with a complemented input; multiplication is the coincidence gate (verified in /transport); comparison is the degree checked comparator. That set is an ALU for rate coded words, and every element is a routine gate.
Every Nth event of a Poisson stream defines a tick. Interarrival of ticks is Erlang(N): mean N/lambda, relative jitter exactly 1/sqrt(N). Measured over 20,000 ticks per point:
| divide by N | predicted jitter | measured |
|---|---|---|
| 1 | 1.0000 | 0.9937 |
| 10 | 0.3162 | 0.3165 |
| 100 | 0.1000 | 0.1008 |
| 1000 | 0.0316 | 0.0318 |
| 10000 | 0.0100 | 0.0100 |
A machine that wants a 0.1 percent clock spends 10^6 decays per tick and simply has one: the same precision law that prices readout prices time. There is no crystal oscillator because none is needed; the randomness is the metronome, averaged.
A self exciting loop through a saturable stage: x' = Gamma x/(1+x) per pass, seeded by a SET pulse at pass 5. The fixed points are 0 and Gamma minus 1; the written bit survives if and only if loop gain Gamma exceeds one:
| loop gain Gamma | state 40 passes after SET | verdict |
|---|---|---|
| 0.7 | 0.000 | signal death |
| 0.95 | 0.007 | signal death |
| 1.05 | 0.058 | latched |
| 1.5 | 0.500 | latched |
| 3.0 | 2.000 | latched |
Below Gamma = 1 the bit decays geometrically (signal death); above it the loop latches at Gamma minus 1 and holds indefinitely against the saturable ceiling. This is the amplification condition of the keystone criterion reappearing as the memory regeneration requirement, the same reason DRAM needs sense amplifiers: a computer's working memory is an application of gain. The isomer registers of the crystal cell store without gain (they are nonvolatile), so the machine has memory today; what waits on the keystone is memory the computation itself can rewrite through a loop.
A valve keys one internal emission line on and off (contrast m = 0.4, per the valve note); an external counter integrates for T per symbol and thresholds. Detected budget 10,000 counts per second on the line. Simulated bit error rate, 20,000 symbols per point:
| symbol time T | counts per symbol | measured BER | bits/s |
|---|---|---|---|
| 0.3 ms | 3/2 | 3.47e-01 | 3,333 |
| 1.0 ms | 10/6 | 2.42e-01 | 1,000 |
| 3.0 ms | 30/18 | 1.11e-01 | 333 |
| 10.0 ms | 100/60 | 1.42e-02 | 100 |
| 30.0 ms | 300/180 | 1.00e-04 | 33 |
At 30 ms symbols the measured error rate is 10^-4 at 33 bits per second; pushing to a 10^-9 grade link at this budget and contrast costs roughly 100 ms per symbol, ten fully reliable bits per second through a sealed wall, with no antenna, no cable, and no emission in any conventional radio band, carried by a γ line that passes through steel, soil, and vacuum. The receiver is any spectrometer; the transmitter is the machine deciding what its own glow says. Rate scales linearly with detected budget: 10^6 counts per second on the line is a kilobit link at the same reliability.