The Strixformes functional

The worst guaranteed safety margin a policy can still promise, given only what the observer actually knows.

RES.99 August 2026developingexploratory

{SF}_{H} (ℐ_{0}) = max_{π} min_{ω} min_{t, i} \frac{h_{i} (Z_{t}^{π, ω})}{s_{i}}

Choose a policy that respects what you actually know. Nature then chooses the worst it is allowed to do. Take the smallest safety margin that occurs, over every constraint and every step. That number is what you can guarantee — and each margin is divided by its own engineering scale first, because a temperature and a clearance cannot be compared until they are.

Pick a policy that respects the information you really have. Nature then picks the worst admissible disturbance, the worst hidden relationship history, the worst sensor errors and the worst sequence of faults. Measure the smallest normalised safety margin that occurs over every constraint and every step of the horizon. The functional is the best value of that quantity you can guarantee.

What the sign means

For a finite, fully specified model the sign answers a yes/no question: a non-negative value means a policy exists that holds every constraint for the whole horizon, and a negative one means none does. That equivalence is the first proposition in the paper, and it is a restatement of established robust viability theory rather than a new result.

In unbounded or continuous spaces the equivalence needs regularity and attainment conditions. A non-negative supremum with no attained admissible policy does not imply that one exists.

What is mine and what is not

The maximin operator is not new. It is the safety game familiar from viability theory and robust control, and claiming it would be claiming Aubin's work and the control-barrier-function literature.

What I am proposing is the naming and the organisation: which parameters belong in the state, that information freshness belongs beside information accuracy, that physical reserve is part of safety rather than a resource question, and that the intended action is a thing to be preserved rather than something to abandon the moment a margin tightens.

It is not a universal constant, a physical force, a probabilistic accident predictor, or a shortcut that computes without specifying the environment.

Safety first, then the mission

The decision rule is ordered, not weighted. First restrict to policies that keep the guarantee non-negative. Only then maximise the guaranteed progress of the action you intended. Only then minimise what the intervention cost.

Ordering them this way has a consequence worth stating plainly: in some states the honest answer is that progress must stop. A weighted objective would quietly trade a little safety for a little progress and never say so.

This is part of a preprint that has not been peer reviewed. 10.5281/zenodo.23372032

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