Phase 16 · observable completeness
What Are We Not Measuring?
AT-0127 → AT-0134. Phase 15 left one escape from memory accounting: genuine redundancy. This phase tests whether our equivalences are redundancy at all, or just the shape of an incomplete observable set.
The counting argument this phase is built on
COUNTING ARGUMENT, NOT A DISCOVERY: in an n-dimensional microscopic state, any observable set containing fewer than n independent linear measurements leaves an exactly unobserved subspace of dimension n − rank. States separated along that subspace look identical to every declared observable. That equivalence is EXPECTED BY INCOMPLETE OBSERVATION.
RERUNNABLE TOY BENCHMARK, NOT A CLAIM. Seed 127, 12-dimensional microstate: with 2, 4, 6, 8 or 10 generic observables a unit microscopic displacement produces observable change at the floating-point floor (~1e-15). At 12 generic observables the exactly hidden direction disappears and the least-visible unit direction produces a small but nonzero observable change of order 1e-2.
Model controls
Two states can look identical simply because we have not measured the thing that makes them different. Before calling anything 'the same', we have to say what we measured — and then check what happens when we measure more.
What are we not measuring?
Two states can look identical simply because we have not measured the thing that makes them different. Drag the slider to declare more independent measurements on a 12-dimensional microstate and watch the region of “equivalent” states shrink.
- Rank of observable set
- 2
- Exactly hidden dimension
- 10
- Least-visible unit response
- 5.55e-17
- Equivalent radius at τ = 1e-6
- unbounded
With 2 measurements on a 12-dimensional state there are 10 directions along which the state can move arbitrarily far while every declared observable reports zero change. That is dimension counting, not a discovery — status: EXPECTED BY INCOMPLETE OBSERVATION.
Running the observable-completeness audit…