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 the
Common Integrity Gate

C. J. Tully
Independent Researcher, Engineer — Tamworth, NSW, Australia
ORCID: 0009-0007-5661-7332
28th 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 maintains
a fused kinematic state, four hard constraints, a polygonal geofences, a dead reckoning bound, and a frozen 36-byte
telemetry frame. Guidance commands are issued by a convex quadratic program that minimally modifies a nominal
law subject to a control-barrier constraint derived from the same index. Under declared Lipschitz and feasibility
assumptions the admissible set is forward invariant. Golden scaling may be composed with either subsystem
without triggering the gate. External geometric measurements are admitted only when they do not degrade the
certificate. No claim is made that the barrier guarantees performance beyond the stated regularity conditions, nor
that the kernel has been validated at sea.