radon_is_noble
plain-language theorem explainer
The atomic number 86 satisfies the noble gas predicate, confirming radon as a shell closure point under eight-window neutrality. Chemists working with the fit-free periodic table scaffold would cite this to validate the forced sequence of closures. The proof is a one-line native decision procedure that checks membership in the precomputed noble gas set.
Claim. The atomic number 86 belongs to the set of noble gas atomic numbers, i.e., $86$ achieves cumulative valence cost zero under the eight-window neutrality condition.
background
The Periodic Table Engine maps the eight-tick octave to chemistry via phi-tier rails and fixed block offsets for s/p/d/f shells. Noble gases are defined as the exact points where the running valence sum returns to zero modulo eight, providing the chemical realization of ledger balance without per-element parameters. The predicate isNobleGas holds precisely when Z lies in nobleGasZ, the set of such closure points. This setting rests on the upstream successor operation for cyclic phases in the eight-tick scheduler.
proof idea
The proof is a term-mode one-liner that invokes native_decide on the decidable instance of isNobleGas. This evaluates set membership of 86 in nobleGasZ by direct computation of the pre-listed closure points.
why it matters
The result instantiates the Noble Gas Closure Theorem (P0-A0) for Z=86, verifying that radon completes an eight-tick valence cycle. It supports the module claim that the full set {2, 10, 18, 36, 54, 86} is forced by eight-window neutrality and connects to the T7 eight-tick octave in the forcing chain. No downstream uses are recorded, leaving it available for external chemistry predictions.
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