Trisduction Core Stated in Fortran and in Nothing Else: A Verdict Kernel That Determines Totally, Reads Its Rows, and Its Exact Scope
Mohammad Islam · PhilPapers (PhilPapers Foundation) · 2026
A verification kernel reads three warrant rows over N contexts, forms their correlation Gram R, and reports whether the three axes enclose volume. We state what that report determines and what it does not, at the grade each claim carries. Three independent axes intersect in exactly one point: nondegeneracy is linear independence, so the determination is total about its object and no weaker reading survives. The kernel's scalar det R = λ2 is nonetheless blind to the sign of λ, and we show that this blindness is a fact about direction and never about the completeness of the determination, since the intersection is equally unique under every axis reflection. What varies between cases is not the strength of the lock but the provenance of its rows, and we give the three-way partition that follows: rows that are the closure itself, an axis left unpopulated so that no point is determined, and rows furnished by the world. A single-file Fortran implementation carries the theorems as procedures and its own battery of 248 computed checks as the proof of load; every figure quoted was produced by that program at the stated build. Appendix A lists that source verbatim with its hash.