noble_gas_bp_increases_xe_rn
plain-language theorem explainer
The theorem asserts that the boiling point assigned to xenon exceeds that of radon under the noble gas mapping. Chemists verifying Recognition Science trends in dispersion forces would cite this step to confirm monotonic increase down the group. The proof reduces by unfolding the piecewise definition and evaluating the resulting real-number inequality.
Claim. Let $B(n)$ be the boiling point in kelvin of the noble gas with atomic number $n$. Then $B(54) < B(86)$.
background
The Van der Waals module defines nobleGasBoilingPoint as a piecewise function on atomic numbers of noble gases, returning values in kelvin: He at 2 maps to 4.22, Ne at 10 to 27.07, Ar at 18 to 87.30, Kr at 36 to 119.93, Xe at 54 to 165.05, with Rn at 86 continuing the sequence. The module derives these from Recognition Science mechanisms of ledger fluctuations creating temporary dipoles, polarizability scaling with electron count, and London dispersion scaling as 1/r^6. Upstream results include LedgerFactorization.of for J-cost calibration and PhiForcingDerived.of for the convex minimization underlying the 8-tick dynamics.
proof idea
The term proof applies simp only on the nobleGasBoilingPoint definition to select the matching cases for inputs 54 and 86, then invokes norm_num to compare the concrete real constants.
why it matters
This result supplies the final link in the noble gas sequence and is invoked by the downstream theorem noble_gas_bp_full_ordering that assembles the complete chain. It instantiates the CH-013 prediction that boiling points rise with atomic size via increasing polarizability induced by the 8-tick ledger and J-cost structure. The step aligns with the broader framework landmarks of T7 eight-tick octave and phi-ladder scaling for atomic properties.
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