cubeFaces
cubeFaces assigns the constant six as the face count of the recognition cube Q₃. Researchers on the paradigm shift lattice cite it to equate five historical shifts plus the RS shift with this geometric count. The definition is a direct constant assignment that aligns with the spatial dimension three.
claimThe recognition cube $Q_3$ has six faces.
background
The Paradigm Shift Lattice module frames the history of science as five completed shifts (Copernican, Newtonian, Einsteinian, Quantum, Biological) with the sixth slot reserved for the Recognition Science shift. This structural match is expressed as five historical shifts plus the RS shift equaling the face count of the cube Q₃. Upstream results supply the same constant: CardinalitySpectrum defines it as 2 times Dspatial, while FreudenthalTriangulationCert records it as the unit cube face count.
proof idea
The definition is a direct constant assignment of the integer 6.
why it matters in Recognition Science
This definition anchors the claim that five historical shifts plus one RS shift equal six cube faces of Q₃. It feeds directly into CardinalitySpectrumCert (which decomposes Dspatial = 3, Dconfig = 5, and cubeFaces = 2 * Dspatial) and into theorems such as five_plus_one_equals_six and six_is_cubeFaces. It realizes the T8 forcing-chain landmark of D = 3 spatial dimensions.
scope and limits
- Does not prove that exactly five paradigm shifts have occurred historically.
- Does not derive the face count from the Recognition Composition Law or J-cost.
- Does not generalize the count to higher-dimensional cubes or lattices.
- Does not address whether the sixth shift has been realized.
Lean usage
theorem five_plus_one_equals_six : 5 + 1 = cubeFaces := by decideformal statement (Lean)
35def cubeFaces : ℕ := 6