The age of the cloth was determined by Carbon-14 dating.
FORBES: Ancient Burial Cloth Provides Clues To Bronze Age Trade
Carbon-14 decays into nitrogen at predictable rates, which is how it can be used to determine the age of an object.
FORBES: Scientists Use Ion Beams To Detect Forged Art
This allowed him to age or "date" a person by examining the brain cells a high carbon-14 count means the person was conceived in the era of atomic testing.
NPR: How A-Bomb Testing Changed Our Trees
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