ImaginaryUnitFalsifier
plain-language theorem explainer
The ImaginaryUnitFalsifier structure packages the three conditions that would refute the derivation of the imaginary unit from eight-tick phase rotations. A physicist examining quantum foundations or the origin of complex numbers in wave equations would cite it when testing the robustness of the Recognition Science account. It is introduced purely as a definition that records the listed propositions and notes one of them is definitionally contradictory.
Claim. A structure whose fields are the propositions that $i^2$ is not equal to $-1$, that physics can be formulated without complex numbers, and that the eight-tick phase cycle is not fundamental, together with the implication that the first proposition yields a contradiction.
background
The module derives $i^2 = -1$ from the eight-tick phase structure of Recognition Science, in which a two-tick rotation corresponds to multiplication by $i$ and a four-tick rotation corresponds to multiplication by $-1$. Composition of two such two-tick rotations therefore yields a four-tick rotation, giving the identity directly. The upstream dependencies supply collision-free properties of empirical programs and algebraic tautologies from simplicial ledgers that underwrite the discrete rotation model.
proof idea
This is a structure definition that simply declares the three propositions and the one-line implication from the first to falsehood; no lemmas are applied and no tactics are used.
why it matters
The definition supplies the explicit falsification criteria for the claim that the imaginary unit arises from eight-tick rotations, closing the module on the origin of complex numbers in quantum mechanics. It directly references the T7 eight-tick octave landmark and the emergence of the Schrödinger equation factor $i$. No downstream theorems are recorded, so the structure functions as a terminal falsifier interface.
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