BLACK AND GOLD II Barrier-Filtered Guidance and the Navigation Kernel under the Common Integrity Gate

BLACK AND GOLD II Barrier-Filtered Guidance and the Navigation Kernel under theCommon Integrity Gate C. J. TullyIndependent Researcher, Engineer — Tamworth, NSW, AustraliaORCID: 0009-0007-5661-733228th October 2026 ABSTRACT This paper is the second of the black-and-gold series. It places the navigation-and-safety kernel and a barrierfiltered guidance law under the common Quasi-Equivalence Index gate established in Paper I. The kernel maintainsa fused kinematic state, four hard constraints, a polygonal geofences, a dead reckoning bound, and a frozen 36-bytetelemetry frame. Guidance commands are issued by a convex quadratic program that minimally modifies a nominallaw subject to a control-barrier constraint derived from the same index. Under declared Lipschitz and feasibilityassumptions the admissible set is forward invariant. Golden scaling may be composed with either subsystemwithout triggering the gate. External geometric measurements are admitted only when they do not degrade thecertificate. No claim is made that the barrier guarantees performance beyond the stated regularity conditions, northat the kernel has been validated at sea.