Hydrogen-Fixed Logarithmic Discretization Diagnostics in Elemental and Phase Data: Full-Table Audit with Compton-Profile Cross-Check

This preprint reports an audit-style test of whether tabulated elemental properties can be embedded on a hydrogen-anchored discrete logarithmic ladder in a peak-normalized energy-density coordinate. The ladder is calibrated entirely from hydrogen: a peak anchor is fixed under a scattering/Compton-profile normalization convention, and the ladder stride is determined from hydrogen alone using two independent hydrogen-local routes (edge rescaling at the ionization boundary and envelope-wide spherical closure with an integer period count).With the anchor and stride fixed a priori, the periodic table is treated as the dataset. A conservative full-coverage “envelope proxy” audit maps into a hydrogen-normalized ladder coordinate and evaluates residual concentration and rung occupancy against explicit null controls (paired-input permutation and sham-stride ensembles) and robustness sweeps across global radius conventions. In parallel, a core-sensitive audit uses tabulated Compton profiles to define a hydrogen-normalized core coordinate from an inner-shell tail-slope statistic and tests discretization under the same fixed stride. The core audit exhibits a two-family structure (half-compatible vs quarter-only) with family-aligned residual concentration, and a 10-element external experimental cross-check of total Compton tails shows strong agreement between experimental and computed slopes and an 8/10 family-parity match under a single fixed momentum window.An independent macroscopic consistency check is performed using elemental phase behavior at 1 atm: where tabulations permit, fusion and vaporization boundaries are converted to condensed-phase energy densities and mapped onto the same ladder; separately, a complete 1-atm census treats transition existence/absence as structural outcomes and tests association with ladder coordinates under label-permutation nulls. The work is explicitly diagnostic and does not propose a new chemical ontology or periodic-table replacement; it reports whether discretization diagnostics exceed declared null expectations under fixed inputs and reproducible controls.