iodine_is_halogen
plain-language theorem explainer
Iodine with atomic number 53 satisfies the halogen predicate under the Recognition Science closure rule. Chemists applying phi-ladder scaling to electron affinities would cite this when confirming periodic trends for high-EA elements. The verification reduces to a native decision procedure that evaluates the finite distance-to-closure condition directly.
Claim. The atomic number 53 satisfies $distToClosure(53)=1$, where $distToClosure(Z)$ is the shortfall to the nearest noble-gas shell closure in the eight-tick sequence.
background
The ElectronAffinity module links electron affinity to cost reduction when approaching eight-tick neutrality on the phi-ladder. The predicate isHalogen(Z) holds exactly when distToClosure(Z) equals 1, selecting the set {9, 17, 35, 53, 85}. This matches the module statement that halogens complete a shell upon electron addition and therefore exhibit high affinity, while noble gases sit at closure with near-zero or negative values.
proof idea
The term proof applies native_decide to the proposition isHalogen 53, which expands to membership of 53 in the explicit halogen set derived from the distToClosure definition.
why it matters
This instance supplies the Z=53 case required for the halogen-EA ordering in the CH-006 framework. It supports the prediction that halogens reach maximum affinity within each period by sitting one step from eight-tick closure. The declaration closes the enumeration for iodine in the periodic table integration with RS constants and the phi-ladder mass formula.
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