qftSectors_five
plain-language theorem explainer
The equality asserts that the RS-derived count of distinct QFT sectors equals five. Researchers mapping recognition principles onto quantum field theory would cite this when certifying the five-technique decomposition of the vacuum. The proof reduces immediately to reflexivity on the constant definition of qftSectors.
Claim. The number of distinct sectors in the quantum field theory vacuum, obtained from the RS DFT-8 structure, equals five: $5$.
background
The module QuantumFieldTheoryDepthFromRS encodes the emergence of QFT from recognition science. It identifies the QFT vacuum with the J = 0 ground state and treats renormalization group flow as evolution of J-cost under changes of recognition scale. The upstream definition qftSectors fixes the sector count at five, matching the five canonical techniques (perturbation theory, renormalization, path integral, Feynman diagrams, lattice QFT) and the configuration dimension D = 5.
proof idea
The proof is a one-line reflexivity wrapper that applies rfl directly to the definition of qftSectors.
why it matters
This theorem supplies the sector count required by the downstream QFT depth certificate qftDepthCert. It completes the Lean encoding of the five-technique structure in the B8 Physics section, connecting the J-cost functional equation to the alpha inverse interval (137.030, 137.039) and the overall RS constants. It supports the claim that standard QFT techniques arise without extra axioms once the DFT-8 structure is fixed.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.