Opoch Kernel Primer
Opoch is a way to turn any problem into a checkable object, then solve it without guessing.
Most systems mix two jobs: proposing an answer and deciding whether it is correct. Opoch separates them. First, the problem is written in a form where any candidate answer can be verified by a clear, finite set of checks. This checker is the center of gravity. Solvers are interchangeable proposal engines that keep generating candidates until one passes the checks, or until the limits are reached.
The Contract
The contract is strict. Every run ends in one of two outcomes:
Verified Answer
A concrete answer plus a concrete witness that passes the checker.
Verified Boundary
When an answer cannot be forced within the available budget, Opoch returns what remains possible and the single cheapest missing check, or resource gap, that would decide it.
The Point
This is the point of the kernel. It makes truth operational.
A claim is only as real as the checks that can separate it from alternatives. If a distinction cannot be verified in principle, it is treated as a story, not as structure.
Opoch then applies the same mechanism across domains:
- In scheduling and planning — it refines by counterexamples: every failure comes with a minimal conflict, and that conflict is turned into the next constraint.
- In optimization — it either returns a verified optimum, or returns a certified frontier that explains exactly what prevented resolution.