QFTDepthCert
plain-language theorem explainer
QFTDepthCert packages two assertions: the inductive type of QFT techniques has cardinality five, and the vacuum decomposes into five sectors. A physicist mapping standard QFT methods onto Recognition Science would cite this record to equate the toolkit with configDim D = 5. The declaration is a bare structure definition whose fields are filled directly by the Fintype cardinality of QFTTechnique and the constant qftSectors.
Claim. Let QFTTechnique be the inductive type whose constructors are perturbation theory, renormalization, path integrals, Feynman diagrams, and lattice QFT. Then QFTDepthCert is the structure asserting that the cardinality of QFTTechnique equals 5 and that the number of QFT sectors equals 5.
background
The module treats the QFT vacuum as the J = 0 ground state whose recognition scale yields five sectors. Five canonical techniques are enumerated by the inductive type QFTTechnique, whose cardinality is required to match configDim D = 5. The upstream definition qftSectors simply returns the constant 5, while the inductive supplies the five distinct methods.
proof idea
This is a structure definition with an empty proof body. It records the two field assertions without invoking any lemmas or tactics; the values are supplied later by qftTechniqueCount and qftSectors_five in the downstream constructor.
why it matters
QFTDepthCert supplies the certificate consumed by qftDepthCert, thereby witnessing that the standard QFT toolkit aligns with the DFT-8 structure of Recognition Science. It directly implements the module claim that five techniques equal configDim D = 5 and closes the link to the J-cost vacuum without addressing the forcing chain steps T0-T8 or the alpha band.
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