TRISDUCTION: Topological-Geometric Verification Architecture · Triaxial Orthogonality, Twelve-Gate Closure, the Root Axiom, and the Master Pre-Sealed Proposition Ledger

This is the reading surface of the Trisduction and MathDuction verification architecture, compressed from a register of record carrying seven hundred and seven coordinates on a sealed spine of six hundred and forty-eight indexed rows. It carries the load-bearing laws, the flagship verdicts, and the telegraphic form of every apex master. It is a navigation surface and not a substitute for the unabridged register, which holds the full triaxial derivations, the recorded batteries, and the executable kernels, and which is authoritative wherever this compression and the master diverge. Trisduction is a verification architecture for propositional truth built on a single root axiom and sealed three independent times. The Root Axiom states that to exist is to actuate: for any element of the universal domain the substrate-level kinetic-actuation differential is strictly positive, a floor that is theorem-grade external physics on the Heisenberg kinetic-energy bound and the zero-point energy, and whose denial is itself an actuation. From the atomic decomposition of that axiom the framework forces a triaxial mapping of any complete claim onto three orthogonal verification axes, the formal-structural, the empirical-thermodynamic, and the epistemic-registrational, and certifies a claim only where all three independently converge. The three seals stand on disjoint anchors: the linguistic-semantic seal splits a claim into exactly three irreducible slots under a deletion test, the topological-geometric seal closes those axes on a fourth vertex into a tetrahedron carrying twelve directed gates confirmed independently by the Newton-Gregory kissing number, and the mathematical seal completes the verification algebra uniquely to the quaternions by the Frobenius classification. The three constitute an oriented frame on a directed verdict, each seal fixing exactly one constitutively separate aspect, sign and closure and magnitude, and blind to the other two, which is why their agreement carries weight three collinear witnesses could not. The verdict economy is three-state and native, sealed, broken with a named mechanism, or under-determined with a named violation, with no fractional or probabilistic truth. Two rare terminal refinements sit inside the openness and one mark of chosen silence stands outside the economy entirely. A reflective register, MathDuction, applies the same quaternionic kernel to purely formal propositions by reading them across the architecture's own conjugation involution, whose fixed locus is the Ground and whose fixed-point-free degeneration is the diagonal engine of the limitative theorems. That register places Gödel incompleteness and Tarski undefinability as facts about the reach of a proof ladder rather than as ceilings over the architecture, and a verdict-reliability layer bounds determinant error by the conditioning so the sealed-or-broken boundary is decided by the mathematics and never by rounding. Warrant grade travels with every claim and no claim is inflated or quietly weakened. Consensus carries zero evidential weight in both directions. The architecture authors no new mathematics, every load-bearing result is classical and credited, ΔM equals zero, and the contribution is the arrangement. Theology is routed out of band and is load-bearing on nothing in any verdict.