The 44 Ladder: chemical-family recurrence in a mass-number arrangement of stable nuclides

The periodic table has a mass scale it does not print. A middle row costs about 44 mass units: it spans 18 protons, each adding roughly two and a half units along the valley of stability. The interval was noticed before it was explained. Arranging the 253 nuclides marked stable in NUBASE2020 into 44 ladders places adjacent rungs 44 apart. Ladder 21, for example, climbs through neon-21, copper-65, silver-109, europium-153 and gold-197. Wound, the ladders form a spiral; tilted, a conical helix; unrolled, a 44-column table. A Stride Table writes the mass scale onto the periodic table.

The visual regularity is not the scientific result, and much of it is generic. What distinguishes 44 is chemical-family recurrence: 29 of its 44 ladders carry stable isotopes of three or more elements of one family, against 12, 13 and 14 at 43, 45 and 46. Surrogates keeping key nuclear constraints average 18; none of 10,000 draws at 44 reaches 29, and none of 250 at its best step exceeds 24. They measure rarity under stated controls, not the chance that the recurrence is an accident.

The interval and related arrangements predate this work; no nuclear mechanism is proposed. What is new is a fixed census; a physical scale placing 44 in the climb of a middle row; and, principally, a controlled accounting of which features are generic and which are not. The result is a visual map of stable isotopes on which the recurrence stands apart from what geometry gives for free.