CKMFalsifier
plain-language theorem explainer
The CKMFalsifier structure encodes the three conditions that would falsify the Recognition Science derivation of the CKM matrix: absence of a phi-connection to the Cabibbo angle lambda, a CP-violating phase with origin other than the eight-tick structure, and violation of unitarity. A researcher testing the phi-ladder predictions against quark mixing data would reference this when outlining potential experimental contradictions. The definition packages the three propositions together with an implication showing that their simultaneous truth is,
Claim. Let $P_1$ be the proposition that there is no $phi$-connection to the Cabibbo angle $lambda$, $P_2$ that CP violation originates differently from the 8-tick phase structure, and $P_3$ that CKM unitarity is violated. The structure consists of $P_1$, $P_2$, $P_3$ together with a proof that $P_1 wedge P_2 wedge P_3$ implies falsehood.
background
The module derives the CKM matrix from Recognition Science by positing that its 3x3 unitary elements, with approximate magnitudes 0.974 for V_ud and 0.227 for V_us, arise from phi-quantized mixing angles tied to the eight-tick phase structure. In RS-native units the framework sets c=1, hbar=phi^{-5}, and forces D=3 spatial dimensions via the T0-T8 chain, with T7 fixing the period 2^3 octave that supplies the CP phase origin. The local setting is SM-012, which targets extraction of the four physical CKM parameters (three angles plus one phase) from the phi-ladder and Recognition Composition Law.
proof idea
This is a structure definition with no proof body. It directly packages the three propositions listed in the doc-comment and asserts via the falsified field that their conjunction implies falsehood, serving as a one-line wrapper for the falsification conditions.
why it matters
This declaration sets the boundary conditions for the CKM matrix derivation in Recognition Science, which aims to obtain the mixing angles from phi-quantized geometry related to the 8-tick octave (T7). It connects to the paper proposition in PRD on CKM Matrix from Golden Ratio Geometry by specifying what would falsify the phi-connection to the Cabibbo angle and the CP phase origin. As a definition it prepares consistency checks against the Recognition Composition Law and leaves open whether data on unitarity or CP violation will confirm the 8-tick origin.
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