Proposal: a cuopt-solution-verification concept skill (certify-then-explain for a single decision solve)

[cafzal]

The cuOpt agent-skills direction lets non-experts drive optimization through agents and natural language. That pays off only if the agent can also say what the result means, instead of handing back a black box of numbers. When an agent presents a solve to a non-expert, two honesty failures recur on a standalone decision solve (the common case):

• Unproven presented as proven. Reporting a FeasibleFound, PrimalFeasible, or TimeLimit result as a certified Optimal.
• Estimate presented as guarantee. Quoting an inferred marginal as an exact dual.

This skill is the certify-then-explain layer that catches them, built over the existing formulation and api-* skills:

1. Status literacy: read the termination status and report the solve at its proven status.
2. Certify: present optimality certificates in plain language, keeping "proven within gap X" distinct from "optimal."
3. Source-tag: label each marginal basis-exact, solver-approximate (PDLP: solver-produced, tolerance-accurate, no basis), or inferred, consuming #1394's basis status to pick the tag and to mark a degenerate basis-exact dual directional (one-sided, non-unique).
4. Explain: translate the certificate and marginals into decision language for the non-expert: what binds, what would move the answer, what is proven versus estimated. It also carries the rate discipline: a dual is a marginal rate, so finite what-if numbers come from differencing re-solves, and levers rank only in comparable units.

Scope: numerical (LP/MILP/QP).

Forward-compatible. It consumes LP basis/variable status (#1394) and sensitivity ranging (#1395) as they land, sharpening the Source-tag, Certify, and Explain outputs.

Relationship. The single-solve complement to cuopt-multi-objective-exploration (#1355), which applies this discipline only within a sweep. It consolidates the status seed in cuopt-user-rules ("Check Results") and the dual-scope work in #1393 / #1408, generalized to any one solve.

Placement. Status literacy and certify could fold into cuopt-user-rules' "Check Results," and source-tag into the formulation and api skills. Explain (the solve-to-decision step for a non-expert) has no existing home, which is the case for a standalone skill. My lean: a small standalone concept skill plus one tightened cuopt-user-rules paragraph. Standalone, folded in, or split: happy to PR whichever you prefer.

[cafzal]

cc

• @mlubin, you reviewed the multi-objective skill (#1355); this is its single-solve sibling with a similar welcome-and-placement question, so I'd value your read.
• @bbozkaya, this targets the interpretability / black-box issue in the agentic direction we discussed: turning a solve into something a non-expert can act on and trust.

[cafzal]

Edit note: pillar 3 now grades degeneracy, folding in the review points from NVIDIA/cuopt-examples#159 at a degenerate optimum even a basis-exact dual is one-sided and non-unique, so it's marked directional, with #1394's basis status as the detector.

[ramakrishnap-nv]

@cafzal I am trying to understand whether this can be something similar to numerical-optimization-formulation where it is generic enough to be common skills for all the APIs.

[cafzal]

Yes, exactly that @rgsl888prabhu . It's meant to be a common concept skill, the same shape as cuopt-numerical-optimization-formulation and cuopt-multi-objective-exploration: the discipline (status, certify, source-tag, explain) is interface-agnostic, and the per-interface mechanics (Status.name in Python, cuOptGetDualSolution in C, cuopt_cli for MPS) live in the api-* skills it defers to.

On the "how generic" question: three of the four pillars already overlap existing skills. Status and certify overlap cuopt-user-rules' "Check Results" (which spans routing too), and source-tag overlaps formulation's sensitivity scope. The genuinely new pillar is Explain (turning the certificate and marginals into a decision a non-expert can act on), which has no home in the current skills. So it lands cleanly either way: a lean common skill, or status-literacy folded into cuopt-user-rules with the interpretation piece kept wherever you'd want it. I'll match whichever you and the team prefer.