Rank-1 analog · Shields 2026a §5

Analog bench

Complete remainder → one decay instant T*. Unread remainder → a waiting-time law. Reading more of the true remainder must shrink the uncertainty. Dummy variables must not.

Schema result

Holds

Analog only — not a nucleus

Is the hypothesis accurate?

In the analog, yes. A complete individual state fixes one first-exit time. Withholding the remainder recovers a waiting-time spread. Revealing more of the true remainder shrinks both variance and error to the true instant. Dummy variables do not. That is exactly Einstein’s kinetic-theory relation, made numerical.

It does not show that a real nucleus, or nature, is built this way. Rank-1 is supported as a schema. Nature still needs a characterized analog whose background you can actually read. Pass rules and frozen JSON: Verify. Definitions: Math.

2026a §5.1Pass

Repeatability

Same phases, eight integrations. Spread 0.0000. The law has no primitive chance.

2026a §5.2Pass

Individuality

120 different remainders, 120 distinct T*. Std 10.91. The unread structure actually moves the instant.

2026a §5.3Pass

Statistical shadow

Unread phases spread T* (mean 17.85, n=120). Exponential is a guide, not a requirement — KS vs exp is poor, and that is allowed.

2026a §5.4Pass

Conditional narrowing

Axiom A6. Variance 77.2 → 0.0 as all eight phases are revealed. This is the kill test, and it passed.

2026a §5.4Pass

Dummy control

Reading a vector that is never fed to the ODE does not collapse variance (49.7 → 58.5). Narrowing is not a generic curve.

2026a §7Pass

Noisy readout

Phase measurement error grows the prediction error. A lab analog needs a clean enough diagnostic of S⊥.