Where knowing stops helping
Six ways a perfectly informed observer still fails. These are the results I trust most.
Each of these refutes the strong version of my own hypothesis. I am keeping them at the front rather than in an appendix, because they are the part of the work that is actually settled — they are small enough to check by hand, and they do not depend on any claim of mine being right.
A system whose clearance falls by two every step, with no effective correction available, starting at one. It is unsafe after a single step, and knowing the dynamics perfectly changes nothing. Understanding is not the same as being able to intervene.
Two quantities, one control that helps each at the other's expense. From one state there is exactly one safe action. From a neighbouring state there is none at all — not because anything is unknown, but because the correction cannot move both ways at once. This is a coupling limit, and it is the structure the Lab model is built on.
A certificate that assumes the disturbance is at most one says nothing whatsoever about a disturbance of two. Every guarantee here is conditional on its bounds being correct, and no amount of internal rigour covers a violated assumption.
An exact reading at the moment it is taken can be worthless by the time the actuator responds, if the relationship is allowed to change in between. This is the failure that most resembles the real cases I was originally thinking about.
A diagnostic probe can consume the margin it was meant to protect. If the measurement is compulsory or badly timed, acquiring more information can make the whole strategy less safe — which inverts the usual assumption that more data cannot hurt.
Exact belief-state viability grows combinatorially. Approximating it is fine, but only with sound error bounds: dropping a relationship without bounding what dropping it costs invalidates the safety claim rather than simplifying it.
This is part of a preprint that has not been peer reviewed. 10.5281/zenodo.23372032