People over Segments: A Data-Axis Scaling Law for Person-Identity Contrastive PPG Pretraining

Scaling data is the central lever behind foundation models, but a physiological corpus cannot be scaled like a web corpus: every additional segment must be recorded from a person, so growth is bounded not by what can be scraped but by who can be enrolled. A fixed segment budget therefore splits as K distinct people × M segments per person. Should a collector recruit more people, or record more from each? Both spend the same budget, yet for raw physiological waveforms the question is unsettled. We study this question for person-identity contrastive self-supervised learning on a real-world photoplethysmography (PPG) cohort of 114k people, in over 200 controlled pretraining runs. The number of distinct people seen in training is the stronger axis: segments per person help, but more slowly, and the most people-heavy allocation we sampled is best at every budget. More people do not merely lower the pretraining loss; they change what the representation encodes, separating held-out people more cleanly by identity, in step with better demographic prediction. A fitted scaling law makes the asymmetry quantitative: the people axis buys down its share of the error nearly twice as fast per decade as the segment axis, an ordering that holds across the fitting choices we test. Solving the law for its optimum yields a budget-adaptive acquisition rule: at small budgets it recruits more people than any allocation we sampled, and as the budget grows it shifts toward more segments per person. Training the rule's recommended points confirms it: each matches or beats the best allocation sampled at its budget. The message is simple: grow the number of distinct people before the volume of signal per person.