measurementBasisCount
plain-language theorem explainer
The theorem fixes the number of measurement bases at five in the Recognition Science treatment of quantum collapse. Researchers assembling a formal certificate for wave-function collapse via J-cost minimization would cite this result to anchor the basis dimension. The proof is a direct one-line decision procedure on the enumerated finite type.
Claim. The set of measurement bases, consisting of position, momentum, spin, energy, and angular momentum, has cardinality five: $|$position, momentum, spin, energy, angular momentum$| = 5$.
background
The module models quantum measurement as selection of the J-cost minimum from a superposition. Measurement bases are the five standard observables formalized as an inductive type. This cardinality equals the configuration dimension in the Recognition Science framework. Upstream, the superposition theorem states that J-cost is positive for any ratio r differing from one, while cost definitions from multiplicative recognizers and observer forcing both return non-negative values with equality only at equilibrium.
proof idea
The proof is a one-line wrapper that applies the decide tactic, which directly computes the Fintype cardinality of the inductive type with five constructors and confirms equality to five.
why it matters
This supplies the five_bases field inside waveFunctionCollapseCert, which assembles the complete collapse certificate including positive superposition cost and post-measurement equilibrium. It instantiates the framework assignment of configDim D = 5 to the five observable types, advancing the quantum measurement formalization inside the T0-T8 forcing chain.
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