Constructive accessibility
An answer can remain possible in principle after the route you are using no longer gets there. Constructive accessibility asks the narrower question: can this process, from this state, still produce the target within the stated limits?
The question can be answered exactly in some constrained systems and estimated in others. In engineering work, it must be judged from the evidence available.
Ask whether this process can still get there.
The ordinary question is whether a valid answer exists somewhere. Constructive accessibility asks whether a particular process can still reach one from the state it has already created, using the time, tools, information, and authority it actually has.
In the 3-SAT benchmark, every remaining completion can be checked, so the answer can be exact. In the AI study, many continuations are sampled, so the result is an estimate for that model and setup—not proof that another answer is logically impossible.
In engineering, the same question becomes practical: what do the drawings, data, test history, constraints, and recovery attempts support saying about the route that remains?
Direct implication
A process can lose its demonstrated route before the goal disappears.
The conclusion should always say whether it was proved, measured, or assessed from incomplete engineering evidence.
It changes what you measure and what you trust.
Not just where validity ends
Do not measure only whether a solution exists. Measure whether the process you are actually using can still reach it.
Not just that the run failed
The important question is whether the evidence changed before the eventual failure became obvious.
Not just which method scores better
A stronger process may keep more routes open. The useful comparison is what a new capability adds: better visibility, better inference, correction, or reversal.
It is not just endpoint validity.
Endpoint validity asks whether a valid completion exists somewhere. Constructive accessibility asks whether the current process can still reach one from the state it has already built. Those can separate in practice.
It is not just an abstract distinction.
It changes a real decision: continue, recover, change the process, gather different evidence, or stop investing in the current route.
Where to go next
Inspect the underlying studies on the research page, use a worksheet before a test or difficult-to-reverse change, or bring one stuck technical decision to the diagnostic.
Use the right kind of evidence for the question.
An exact solver check, a finite set of sampled continuations, and an engineering assessment support different conclusions. Define the target, current state, available actions, and limits before interpreting a result.
Explore the benchmark and explanatory figures · Apply the questions in a decision record