A Noble Gas-Centered Coordinate for Within-Period Atomic Property Trends

We introduce a single dimensionless landscape function Jchem(ρ)=cosh(ρlnφ)−1, with φ=(1+5)/2, defined on the noble gas-centred coordinate ρ=d/Lp∈[0,1), and show that it organizes four central within-period atomic observables, first ionization energy IE1, electron affinity EA, Mulliken electronegativity χM, and Pearson chemical hardness η, on a single periodic-table axis. The outward step ΔJchem+ delivers IE1, the inward gap ΔJchem−=Jchem(1)−Jchem(ρ) delivers EA and η, and χM follows from Mulliken’s identity. Benchmarked against NIST and Pearson tabulated atomic data, the framework reproduces the within-period IE1 envelope across periods 2–6 and localizes every upward deviation on the textbook anomaly sites {p3,d5,f7,s2,d10}; it yields two parameter-free golden ratio ionization-energy identities (φ1/4 on heavy noble gas pairs and φ2 on halogen/alkali pairs, agreeing with data to MAD ≈1% and ≈5%); and it provides single-parameter analytical fits for EA (MAE 0.3–0.4 eV), Pearson hardness η, and Mulliken χM (R2=0.73 on a 15-atom 4-class benchmark). By assembling four periodic-table observables under one golden ratio cosh coordinate, the construction provides a compact analytical reference against which relativistic and shell-anomaly corrections can be quantified.