Existence vs reachability
A valid answer can still exist even when the route you are following no longer gets there. “Does a solution exist?” and “Can this process still reach it from here?” are different questions.
That difference is exact in the SAT benchmark, estimated by sampling in the AI study, and assessed from evidence in engineering work.
The destination can remain valid after the route stops working.
Existence asks whether a valid endpoint is still out there somewhere. Reachability asks whether a particular process can still get there from its present state, with the time, tools, information, and authority available. A system can satisfy the first condition while failing the second.
In random 3-SAT, every remaining completion can be checked. In AI, sampled continuations estimate how often the target answer is still produced under a stated setup. In engineering, the answer is limited by the quality of the records and the recovery options that have actually been tested.
The distinction matters most in forward, commitment-heavy work: search, scheduling, routing, optimization, planning, structured decoding, or any process where going backward is costly or impossible.
Plain-language test
If a team can still truthfully say “a valid answer exists” while its evidence supports “this process, under this contract, has no demonstrated route from here,” you are looking at the existence–reachability split.
Three operational patterns
Supported access can disappear before the symptom.
A process can keep moving after the available evidence says the current route is no longer working. The visible failure may arrive much later.
Healthy local metrics can still mislead.
A state can look locally fine while the useful options ahead have narrowed sharply. Recovery may still be possible, costly, or simply untested.
Stronger methods do not just score better.
They can change what remains possible. The real question is what they add: more visibility, more time, a correction route, or a way to reverse course.
For research
The distinction makes it possible to study not only whether a target exists, but when a particular process loses reliable access to it.
For engineering
The distinction turns vague failure into three concrete questions: what can still be done, what recovery has been tested, and what should change next?
Creating access
A different capability can change what is reachable.
A limitation of the present process need not be a limitation of every possible process. A better measurement, another tool, a preserved configuration, or a different sequence may change the available routes. Each possibility still needs evidence in the situation being examined.
Building requires commitments. The practical question is what a choice makes possible, what it consumes, and what would justify continuing or changing course.