Measuring solution degeneracy directly from sampleset output — P(q) as a companion metric to energy

Most of us check energy/objective quality when evaluating a sampleset, but that only tells half the story: it doesn't say whether the near-optimal region is a single sharp basin or many structurally different bitstrings sitting at similar energy.

I've been working on a solver-agnostic diagnostic that takes sampleset.record.sample directly and computes two things: (1) P(q) — pairwise overlap between independently-obtained near-optimal configurations, and (2) a gap between how consistent the solver is with itself vs. how close it actually sits to the reference optimum. The second one catches a failure mode energy histograms miss entirely — solver looks confident (high self-consistency) but is nowhere near the true optimum.

Validated on G11 (Gset benchmark) and a few MQLib instances so far — happy to share the writeup, or run it against a sampleset if anyone has one they're curious about.