The Elements on the Spiral: Nucleosynthesis, Cosmic Time, and the Iron Hinge

The logarithmic spiral e^{(λ+i)θ} that names this series is applied to the chemical elements in three movements. First, as a structural map of the periodic table it fails: shell capacities grow as 2n², a quadratic law, so no single pitch λ is fixed by the data, and the noble-gas axis is a re-description of periodicity rather than a discovered line. Second, as a map of formation time it fits: cosmic element-building spans roughly seventeen decades, from Big Bang nucleosynthesis at three minutes to the present, and a logarithmic axis is the native geometry for that range; the picture corrects a common intuition by showing the primary division is primordial-versus-later, not light-versus-heavy. Third, the lens illuminates one piece of standard stellar physics: a massive star's life read as conserved circulation (i) tightening through successive burning stages to iron's free-energy floor, where rotation yields to irreversible dilation (λ) and the core spirals toward a center it never reaches. The lens re-describes; it derives no new number and does not explain why the floor lies at iron. The parent cosmology's falsification record is reprinted in full.