THE GEOMETRIC ORTHOGONAL TRIAXIAL WARRANTS: A Trisductive Method for Certifying Knowledge Claims, Demonstrated Across 360 Audits in Science, Mathematics, and Philosophy

A claim can be argued well and still be false. Standard verification across the disciplines certifies claims by the quality of a single line of support: a formal proof, a measured correlation, a replicated experiment, an expert consensus. Each of these is one axis of warrant, and each can be strong while the claim is wrong, because a single strong axis cannot detect that it is the only axis, nor that it secretly shares a source with the others. This paper presents a verification method, Trisduction, that certifies a claim by the geometry of its warrant rather than by the strength of any one line of it. A proposition is decomposed onto three structurally independent axes, a formal-structural axis, an empirical-material axis, and an epistemic-registrational axis, and the warrant is certified only when the three stand at mutual right angles and span a genuine three-dimensional volume. The test is closed-form and executable: three warrant vectors are composed through a quaternion product whose scalar part squares to a Gram determinant, and the determinant reads the volume the three axes enclose. A volume near its maximum is a seal. A collapsed volume is a structural break with a named cause. An ill-conditioned volume is an honest under-determination. A second register extends the method to formal and mathematical propositions, separating the part of a problem that is decidable and sealed from the part whose truth is genuinely open, and refusing to read a geometric lock as a proof. The method carries one discipline throughout: social consensus carries zero evidential weight, every verdict states its warrant grade, and the instrument audits itself with no exemption. We demonstrate the method on 360 propositions spanning logic, mathematics, physics, quantum foundations, cosmology, the mind, psychology, the social sciences, geopolitics, and metaphysics, from elementary facts that seal cleanly to celebrated open problems where the honest verdict is that the question remains open and the method says exactly why.

360 Audits.