The 44 Ladder: on the hidden whole-number order in the masses of the atoms, and the Isotope Ladder, the new periodic table it reveals

The stable isotopes of matter keep a hidden order in their mass numbers. Step 44 upward in mass number from a stable isotope in the periodic table's midsection and another stable isotope stands there: an isotope of the element one row lower, the starting atom's heavier chemical cousin. From aluminium to lead, and past lead on borrowed time, the steps run 44 and its exact multiples, out to 176 (44 x 4) and 220 (44 x 5). Across the full period-4-to-5 crossing (seventeen vertical element pairs, 285 stable pairings) 44 is the most common stride, hit exactly 43 times, and every exact case is composed of 18 protons and 26 neutrons. The lanthanide-spanning crossing's most common stride is 88, exactly double, though its own recipe is not a doubling of 44's. Extended to complete isotope chains, all 259 mappings inside the evaluated chart land at the exact predicted mass number, and their leftover fractional masses obey a strict sign rule that renders the valley of stability as a contour map. Sorted by remainder of 44 rather than by element, stable matter re-forms into a second periodic table, proposed and named here as the Isotope Ladder: 44 columns, four and five storeys tall, with only four empty addresses in 208, all four the alpha particle's doing. Copper, silver and gold share a single five-storey column ending at gold. The paper reports sixteen observations of this order which, as far as the author's logged searches reach, have not been made before; stakes two falsifiable predictions (the masses of six nuclides nobody has yet weighed, and the persistence of the 82-neutron shell wall below tin, where a school of models says it fails); and proposes the second table. All of it is presented as observation computed from the public AME2020 mass evaluation, checkable in a spreadsheet. Interactive companion plates and live-formula workbooks are deposited with the paper.