Fusion Density Under Ambiguity

Fusion Density Under Ambiguity Preserving Useful Density Under Unresolved Fringe Counts Can a fusion diagnostic provide a useful plasma-density estimate before its fringe counts are uniquely resolved? This engineering note examines that question for two-color interferometer–polarimeter systems in magnetic-confinement fusion. It develops a model-conditional framework that retains multiple plausible integer phase branches and evaluates their consequences for density estimation, rather than treating unique fringe-count identification as a prerequisite for every usable measurement. The approach combines branch-weighted density estimation with a decision criterion based on the probability of exceeding a specified density-error tolerance. It distinguishes posterior error probability from a conservative risk bound and accounts explicitly for probability mass outside a finite candidate search. Reproducible numerical examples explore prototype and ITER-relevant parameter regimes. In the prototype simulation, branch marginalization reduces large-error events relative to hard branch selection. The tested cases do not demonstrate an additional acceptance advantage for the proposed risk-bound gate over the count-confidence comparator when both use the same estimator. The note separates these findings and sets out falsifiable tests for calibration, bound validity, and experimental replay. This is a numerical and methodological contribution, not an experimentally validated diagnostic or a demonstrated control-system safety guarantee. Its conclusions depend on the stated measurement, noise, prior, and candidate-search assumptions. The release includes the engineering note, a standalone reproduction script, pinned dependencies, reference output, and file checksums.