Conformal Non-Coverage Risk Control (CNCRC): Pairwise Cost-Weighted Nonconformity Scores for Risk-Aware Prediction Sets

Split-conformal prediction gives marginal coverage for any fixed nonconformity score, but it does not determine which alternatives a prediction set retains. We study CNCRC as an orientation-aware score-design family for fixed-label multiclass prediction with a supplied, bounded pairwise ambiguity-cost matrix. Its row and column forms are dual design choices: the row form supports conditional retained-set accounting, whereas the column form weights candidate admission by incoming cost. MAX and SUM provide peak-sensitive and accumulation-sensitive reductions while leaving the calibration template unchanged. We separate generic coverage and bounded-cost omission from the retained-set accounting properties induced by each score. In a validation-only, matched-coverage clinical benchmark, both orientations yield comparable composition metrics, with the column MAX form attaining AmbCost 0.293 and Hazard 10.1%. The poison stress test and the large-label clinical benchmark are interpreted as operating-point evidence about set composition. A poison-class control with the same recall and average set size shows lower poison-label admission on benign examples than random set inflation. The risk-budget sweep and a synthetic cost-matrix perturbation analysis characterize the operating range and sensitivity of the score family. These results characterize oriented score design for the stated benchmark without claiming a universal safety or downstream-utility guarantee.