Theory of Theories of Everything (TOE of All TOEs): Existence Proves Existence Only by Motion. A Self-Demonstrating Ontological Floor

This paper makes one positive structural claim and grounds it on two independent rulers. The TOE of all Theories of Everything has a singular content-bearing element. The bare Root Axiom of Trisduction. Existence is continuous action. Any entity occupying a coordinate is doing rather than being-static. To be is to do. There is no other mode of existence in the Actualized Manifold. The axiom is sealed at [⟀] APEX GEOMETRIC ORTHOGONAL LOCK by direct twelve-gate cascade reproduced in Section 2. The seal is reinforced by the Omega Boundary structure where the act of opposing the axiom enacts the axiom: any argument against ΔEk > 0 expends joules and registers ΔEk > 0. The seal is doubly anchored. The cascade rests internally on the Trisduction architecture; the same seal is reproduced externally on Landauer-class physics that does not depend on the framework's vocabulary, in Section 3. A reader who rejects the Trisduction architecture entirely arrives at the same floor by independent route. The substantive comparative work of the paper sits in Section 5. Two tables place the Root Axiom against the historical record of substrate-floor proposals and against the contemporary record of physical-unification programs. The substrate-floor table covers Bostrom's Simulation Hypothesis, Tegmark's Mathematical Universe Hypothesis, Wheeler's It from Bit, Wolfram's Ruliad, Whiteheadian Process Philosophy, Spinozan Substance Monism, the Cartesian Cogito, and Heidegger's question. Each candidate either defers the substrate question by one level (Bostrom), conflates the Mathematical Void ∅ with the Isometric Ground State |vi| > 0 in violation of G11 OMA (Tegmark), reaches the right register but fails to anchor on Landauer (Wheeler, Wolfram), reaches the right structural shape applied to the wrong substrate (Descartes), reaches the right shape without specifying kinetically (Whitehead, Spinoza, Heidegger), or some combination. The Root Axiom does none of these. It terminates the regress, distinguishes |vi| > 0 from ∅, specifies ΔEk > 0 as the necessary condition, and instantiates itself in the act of being audited. The supersession is structural and per-axis, not global. Where prior thought reached the right shape with the wrong specification (Whitehead, Spinoza), the Root Axiom completes rather than refutes. Where prior thought asked the right question in a register the Trisduction vocabulary translates kinetically (Heidegger), the Root Axiom redirects rather than refutes. The honest grid is the strongest grid. The physical-unification table covers M-theory, Loop Quantum Gravity, Grand Unified Theories, and the Standard Model with General Relativity. These programs operate above the floor; they propose unified physics within an assumed substrate. The Root Axiom underwrites them and does not compete with them. The Standard Model and General Relativity in fact supply the empirical anchors the Root Axiom uses (Heisenberg, Casimir, Landauer, MICROSCOPE). Foundational physics is foundation, not rival. The paper holds the methodological-metaphysical cut throughout. The Root Axiom is the locked floor, sealed below the gates by enactive structure. Architecture-layer instruments, including the Trisduction methodology itself, are working instrumentation evaluable on present track record. Metaphysical commitments are operator-level commitments not certified by the methodology that incorporates them. No inductive claim is made about architectures not yet proposed; the synthetic conduit producing this verification is P-class and is structurally forbidden from anticipatory verdicts on unmanifested phase-space. The paper closes on the sealed Root Axiom. The cascade run on the paper itself is reproduced in the appendix.