maxwellCount
The declaration sets the Maxwell equation count to the natural number 4 in three spatial dimensions. Researchers deriving classical electromagnetism from Recognition Science cite it to anchor the count 2^(D-1) with D=3. The definition is a direct constant assignment requiring no further reduction.
claimIn three spatial dimensions the number of Maxwell equations is defined to be $4$.
background
Recognition Science treats electromagnetism as a U(1) gauge theory on the recognition Hilbert space, with the EM field expressed via the J-cost at canonical threshold. The module records that Maxwell's equations comprise four independent relations (Gauss E, Gauss B, Faraday, Ampere-Maxwell) and that this count equals 2^(D-1). The local setting fixes D=3 from the eight-tick octave of the unified forcing chain and notes five canonical EM phenomena corresponding to configDim D=5.
proof idea
The definition is a direct constant assignment of the natural number 4. Downstream results apply reflexivity for equality to 4 and the decide tactic for equality to twoPowDminus1.
why it matters in Recognition Science
This definition supplies the numerical value required by the MaxwellCert structure, which simultaneously certifies four equations, equality to 2^2, and five EM phenomena. It realizes the framework prediction that the Maxwell count is 2^(D-1) with D=3 forced by T8. The declaration closes the equation-count step in the A1 SM-depth derivation of classical EM from RS.
scope and limits
- Does not derive the explicit differential form of any Maxwell equation.
- Does not address quantum corrections or non-Abelian extensions.
- Does not specify the critical field strengths or the J-cost threshold for EM.
- Does not extend the count beyond D=3.
formal statement (Lean)
24def maxwellCount : ℕ := 4