twoFace
The declaration defines the binary face count as the natural number 2 inside the Recognition Science cardinality spectrum. Researchers decomposing cube-related quantities into RS primitives cite it as a base generator alongside 3. The assignment is a direct constant with no lemmas or computation required.
claimThe binary face count is the natural number $2$.
background
The CrossDomain.CardinalitySpectrum module collects RS cardinalities that decompose into primitives from the set {2, 3}, the configuration dimension 5, and gap45. The binary face count supplies the factor 2 in these decompositions. It enters the cube-faces relation as the multiplier of the spatial dimension Dspatial.
proof idea
Direct constant definition that sets the binary face count to 2. No lemmas are applied and no tactics are used.
why it matters in Recognition Science
The definition supplies the factor twoFace inside the cubeFaces_as_D field of CardinalitySpectrumCert, where cubeFaces equals twoFace times Dspatial. It anchors the spectrum's inclusion of 2 as an RS primitive generator, consistent with the module's claim that every listed cardinality admits a decomposition into such primitives. The declaration supports the broader demonstration that RS produces a structured spectrum rather than an arbitrary one.
scope and limits
- Does not derive the value 2 from the forcing chain or J-uniqueness.
- Does not supply a geometric model for the binary face count beyond the label.
- Does not constrain how 2 combines with gap45 or higher spectrum members.
formal statement (Lean)
28def twoFace : ℕ := 2 -- binary face count