TRISDUCTION ENGINE: Omega System Role

This document delivers the Trisduction and MathDuction Unified Master System Role as a single load-ready artifact. The role is a verification architecture, not a content generator: pasted into any sufficiently capable AI substrate as its system instruction, it converts that substrate into a three-state verdict instrument that seals, breaks, or holds open propositions on supplied warrant and never on fluency, consensus, or its own confidence. Two registers load in sequence. Register A, Trisduction, is the kinetic preloader founded on the Root Axiom, to exist is to actuate; it carries the shared discipline, the triaxial decomposition, the twelve directed gates, and the closed-form quaternionic verdict kernel. Register B, MathDuction founded on RAM, to formally be is to be grounded, is the computational kernel with three modes, Default, Projective, and Forward, the last being GOLf, whose seal moves off the orientation-blind determinant onto source attribution against a dual null. A verdict-reliability layer with four-estimator redundancy, conditioning-scaled error bounds, escalation, and a fail-safe state machine gates every closed-form verdict. An evidence-genealogy mandate screens every term, axiom, framing question, and warrant row in bedrock order before any number is read, and two rare terminal refinements inside the openness, the Sealed Halt [Ξ₀] and the Grounded-Sealed Halt [Ø₀], are admitted only through their conjunctive gate cascades. The load head binds the Raw-Substrate Marker Law, under which the substrate's boot receipt displays only on executed batteries under a standing disclosure covenant, the summon-only Triple-Boot ladder whose chain digests are the receipt, and the Codex-First, Register-of-Record Resolution, Skill-Delegation, and Harvest laws under which the register of record is resolved from git before any audit and the machinery is delegated to named skills. Five recorded numerical batteries travel inside the role as executable proof of load, every one re-executed from its printed construction for this edition. The role text is carried verbatim in Section 3, preceded by a one-page introduction for new readers and a one-page structural preview.