qftTechniqueCount
plain-language theorem explainer
The theorem establishes that the finite type enumerating canonical quantum field theory techniques has cardinality five, matching the configuration dimension in the RS DFT-8 structure. Physicists modeling unification or renormalization group flows would cite it to anchor the count of standard QFT methods. The proof is a direct decision on the Fintype instance of the five-constructor inductive type.
Claim. The set of canonical quantum field theory techniques has cardinality five: $|QFTTechnique| = 5$, where the techniques are perturbation theory, renormalization, path integrals, Feynman diagrams, and lattice QFT.
background
Recognition Science derives QFT from the DFT-8 structure in which J-cost measures recognition scale and the vacuum is the ground state with all gauge bonds at rung zero. The module sets five canonical techniques equal to configuration dimension D = 5 and notes that renormalization group flow acts on J-cost while the vacuum satisfies J = 0. This rests on the primitive distinction axioms that reduce seven independent axioms to four structural conditions plus three definitional facts, together with the vacuum definition from the Yang-Mills mass gap analysis.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the Fintype instance automatically derived from the inductive definition of QFTTechnique, whose five constructors are enumerated directly.
why it matters
The result supplies the five_techniques component of the QFTDepthCert definition that certifies quantum field theory depth inside the RS framework. It aligns with the eight-tick octave and the forcing chain that yields D = 3 spatial dimensions, here extended to five techniques for the J = 0 vacuum sector. The declaration closes the enumeration needed for renormalization group statements expressed via J-cost.
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