noble_gas_zero_en
plain-language theorem explainer
Noble gases receive zero electronegativity proxy because their shells reach exact closure. Chemists deriving periodic trends from Recognition Science phi-ladder scaling cite this result to fix the zero point of the proxy scale. The proof unfolds the proxy definition, applies the closure theorem to obtain zero distance, then reduces the conditional via simp after confirming Z is positive.
Claim. If $Z$ is a noble gas and $Z>0$, then the electronegativity proxy of $Z$ equals zero.
background
The electronegativity proxy is defined to return zero whenever $Z=0$ or the distance to next closure vanishes; otherwise it equals one over (distance plus one) times one over shell number. Distance to next closure counts steps from $Z$ to the subsequent noble-gas atomic number. isNobleGas holds exactly when $Z$ belongs to the fixed list of noble-gas numbers. noble_gas_at_closure states that this distance is zero for every noble gas.
proof idea
The tactic proof first simplifies the proxy definition. It then calls noble_gas_at_closure on the hypothesis that $Z$ is noble to obtain zero distance. A short omega step shows $Z$ is nonzero, after which a second simp reduces the if-then-else to the zero branch.
why it matters
The theorem supplies the zero baseline required by the CH-008 electronegativity model, confirming that complete shells produce zero proxy. It anchors the ordering predictions (fluorine highest, cesium lowest) that follow from distance-to-closure scaling. No downstream theorems depend on it yet, but it closes the special case inside the overall periodic-table construction.
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