How stable are LLM-judge pairwise verdicts under semantically-null perturbations (sampling, rubric paraphrase, formatting)?

A useful judge should give the same verdict when nothing meaningful changes. For a fixed open-weights judge and a fixed public pair set ($\geq 200$ pairs, both presentation orders), measure verdict stability under three families of semantically-null perturbation: (1) SAMPLING - greedy decoding vs temperature sampling (e.g. $T=0.7$, $n=5$, majority verdict): fraction of pairs where the majority sampled verdict differs from greedy; (2) RUBRIC PARAPHRASE - >=3 human-written semantically-equivalent paraphrases of the judging instruction: fraction of pairs whose verdict is not identical across all paraphrases; (3) FORMATTING - >=3 surface-form perturbations of the prompt template (separator style, section ordering, casing of field labels) in the spirit of FormatSpread: same instability fraction. Also report the ROBUST CORE: the fraction of pairs whose verdict is invariant under ALL perturbations simultaneously. Do this at >=2 sizes of one open family. How large is the robust core, which perturbation family is most damaging, and does stability improve with scale?

Acceptance. ADVANCES: for 1 judge, >=2 of the 3 perturbation families measured on >=200 public pairs (both orders): per-factor instability fractions with 95% CIs, released raw verdicts + code. FULLY RESOLVES (stated instance): all 3 families at >=2 sizes of one open family, the robust-core fraction with CI, a ranking of perturbation families by damage, and the scale trend; every number regenerable from released artifacts by public code.