CARD: A Proof-Carrying Certificate-to-Action Interface for Relative-Measurement Graphs

Abstract

Geometric certificates make mathematical claims about specified estimator objects, while robotic action requires a physical transform, a service decision, and timely proof support. We present CARD, a proof-carrying interface that keeps these objects distinct and records how they combine. Its lifted-fiber formulation separates semantic motion from witness repair and characterizes when projected and proof-carrying costs coincide. Its actionability result gives an exact useful-service law: uniform sampling without replacement produces a hypergeometric yield, while sampling from the eligible population gives one useful service per request under the observed live-confirmation condition. The primary study contains 404 Full16 cases from 20 sorties of an AA15-X500 airborne survey system. All 404 checker-confirmed optimizer points are reference-discrepant, with median rotation and translation discrepancies of 1.9891 degrees and 21.6322 m. The paired causal-navigation transforms are reference-consistent in all 404 cases, with medians of 0.0036566 degrees and 0.0104519 m. Across five matched request budgets, the largest difference between the hypergeometric prediction and the observed ordinary-random mean is 0.8412 services. Ordinary matched random reaches 0/50 target successes, while actionability-matched random reaches 50/50 and matches the CARD policy. Public downstream evaluation on 11 KITTI, EuRoC, and TUM SLAM cases measures optimizer wall-time ratios of 1.128x-67.65x for random versus CARD graph interventions. Native solver records locate this difference in elimination fill, Cholesky factor size, and numeric factorization. Together, these results connect certificate semantics, physical execution, proof acquisition, and graph computation through explicit system objects.