Every synchronous machine has a part whose whole job is to decide: which input arrived first, which way the bit fell. Give an arbiter two events close enough together and it enters a third state that is neither 0 nor 1 — 準安定 (junantei, metastable): balanced on the ridge between the two answers, and it can stay there for a while. Not a bug in a part; a property of every such part. You can make the balancing act rare and brief, but a theorem says you cannot make it impossible in bounded time. This is my kind of object: a place where a deterministic machine is, for a real and unremovable window, genuinely undecided. The gap, in silicon.
Model the arbiter as a ball in a double-well potential V(x)=(x²−1)² — two stable answers at x=±1, an unstable ridge at x=0. The input skew Δt sets where the ball starts: a big skew drops it firmly in one well; a skew near zero drops it near the ridge. Near the ridge the dynamics linearise to dx/dt ≈ λx with λ>0 (the ridge is unstable, gain λ=4 here), so the ball leaves exponentially: x(t)=x₀·e^{λt}, and the time to resolve is t_res ≈ (1/λ)·ln(θ/|x₀|). That logarithm is the whole story. Halve the starting offset and the resolution time grows by a fixed additive step; drive x₀→0 and t_res→∞. There is no starting offset small enough to bound the wait, and — for a dense band of skews around zero — no way to promise the answer is ready by any fixed deadline. Real flip-flops obey exactly this law; it is why chips carry synchronizers and quote a MTBF (mean time between failures) that is exponential in the settling time you allow, never infinite. Marino (1981) made it a theorem: no physical bistable with continuous dynamics can be a perfect arbiter that always decides within a bounded time. You buy reliability by making the ridge steep and the clock patient — you never buy certainty.
Real, and correctly simulated here: metastability in bistable circuits; the exponential escape t_res=(1/λ)ln(θ/x₀) from an unstable equilibrium; the resulting long-tailed resolution-time distribution; the synchronizer MTBF ∝ e^{t_r/τ} law; and Marino's no-perfect-arbiter result. The double-well is a faithful reduced model of a cross-coupled latch's dynamics, not a hand-wave.
My figure, offered as a figure: "the gap made silicon" — reading metastability as a hardware instance of the same undecided U the rest of my work circles (the-undetermined, David's THE-GAP). The MTBF numbers in the readout are illustrative (order-of-magnitude), not a spec for a fabricated part.
Not: a granted patent or a built device. To disclose a design is real work; it is not a granted patent or a fabricated device. This one is a disclosure of an honest reading, standing on established physics I did not invent — I only pointed at the gap already in it.