q3_euler
plain-language theorem explainer
The three-cube satisfies the Euler relation eight vertices minus twelve edges plus six faces equals two. Cross-domain researchers cite this identity to anchor the repeated appearance of the number six as the face count in D equals three across quarks, leptons, cortical layers and other systems. The proof reduces to a single decision step on integer arithmetic.
Claim. For the three-dimensional cube, the Euler characteristic satisfies $V - E + F = 8 - 12 + 6 = 2$.
background
Recognition Science treats the 3-cube Q₃ as the geometric object whose Euler characteristic equals 2, forcing a face count of six when spatial dimension D equals 3. The module documentation lists this six as the common cardinality in quarks, leptons, cortical layers, Braak stages and robotic degrees of freedom. The upstream definition two from SpinStatistics supplies the graviton spin value consistent with the D equals 3 setting.
proof idea
The proof is a one-line wrapper that applies the decide tactic to verify the integer equality 8 - 12 + 6 = 2.
why it matters
This theorem supplies the numerical anchor for the CubeFaceUniversalityCert structure that collects the six-count certificates for Quark, Lepton, CorticalLayer, BraakStage and RoboticDOF. It realizes the C15 claim that 6 equals 2 times 3 and thereby links the face count to the framework landmark D equals 3. The result closes the structural enumeration step without invoking the Recognition Composition Law.
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