Independent research · Regeneron STS · 2026
Transit sampling
How many finite exposures determine a transit model uniquely—and what happens when one observation is lost?
A finite schedule, a continuous problem
I studied an exposure-averaged, three-parameter transit model. A measurement is an integral over an exposure window—not the brightness at a single instant. The question is whether distinct parameter choices can produce the same vector of measurements.
The proof pipeline combines piecewise-rational analysis, exact rational arithmetic, strong monotonicity, and Bernstein polynomial certificates. It certified all 568 parameter-space cells for the selected schedule.
Minimal observations and repairs
I screened 557,361 eligible schedules from a fixed catalog of 20 slots with a required baseline anchor. Every smaller eligible schedule failed a necessary identification condition; the selected schedule established a minimum of 10 exposures under these constraints.
After each possible single-exposure loss, I proved minimum static repairs requiring one to three additional observations. The three hardest repaired maps involved 484,788 continuous cell-pair proof obligations, all resolved.
Uniqueness at a singularity
At a contact singularity, the measurement Jacobian has rank two, while the parameters remain globally unique. An explicit radical decoder yields a sharp ½-Hölder inverse stability law on the specified closed three-cell region.
Prepared for Regeneron STS. The minimum is specific to the catalog and anchor constraints; the stability result is specific to the stated region. A public writeup and original figures are not currently linked.