CRB Framework Makes Testable Predictions at 1-10 Degree Range Through N-Dependent Precision Scaling

Plants don't have eyes or ears, but they do know which way is down — and they're remarkably good at it. Tiny starch-filled granules called statoliths settle to the bottom of specialized cells like a biological snow globe, telling the plant which direction gravity is pulling. But how precise is this system, and what sets its limits? That's where an elegant theorem from statistics steps in. The Cramér-Rao bound is a fundamental result from information theory — it sets a hard mathematical floor on how imprecise any measurement system can be, given the amount of 'signal' it has to work with. Think of it as the universe's rule about how much you can squeeze out of noisy data. This hypothesis proposes applying that framework to plant gravity sensing: specifically, it predicts that a mutant plant with fewer statoliths (called pgm1) should show exactly 2.6 times more variability in its gravitropic response compared to normal plants — and crucially, this ratio should stay constant regardless of the angle you tilt the plant. That angle-independence is the key fingerprint: no existing biological model predicts it, only the statistical theory does. To test this, researchers would tilt plants at a range of angles — from a gentle 2 degrees to a steep 60 degrees — and carefully measure how consistently each plant bends back upright. If the ratio of variability between mutant and normal plants stays locked at roughly 2.6 across all those angles, it would be strong evidence that plants are operating right up against a fundamental information-theoretic limit, the same kind of limit that governs everything from radar systems to medical imaging.

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