Information-Geometric Phase Transition Predicts Mutant-Specific Threshold Shifts in Gravitropic Dose-Response

Plants know which way gravity pulls them, and they respond by bending roots downward and shoots upward. This sensing ability comes from tiny starch-filled granules inside special cells — imagine microscopic ball bearings that roll toward the bottom of the cell when the plant tilts, triggering a chemical signal. What's puzzling is that plants seem to have a threshold: they ignore tiny tilts but respond sharply past a certain angle. Nobody fully understands why this threshold exists or where it comes from. This hypothesis borrows a powerful framework from a completely different world — the mathematics of optimal estimation. Engineers and statisticians use something called 'Fisher information' and the Cramér-Rao bound to figure out the absolute best precision any sensor can achieve, given noise in the system. Think of it as a cosmic speed limit for measurement accuracy. The idea here is that plant cells might be operating right at this mathematical limit, and the geometry of that limit — literally, the curvature of an abstract mathematical space called a statistical manifold — predicts a sharp 'phase transition' in sensing behavior at a very specific tilt angle: 0.29 degrees. Below that angle, the plant is essentially guessing; above it, sensing kicks in with full precision. The math even generates a formula predicting how genetically modified plants with wider or narrower cells should shift that threshold. This is genuinely unusual science — it's not an analogy between fields, but an exact mathematical equivalence applied across the boundary between abstract statistics and living plant cells. If it holds, it would mean plants aren't just vaguely sensitive to gravity; they're operating at a fundamental mathematical limit, the same way the best human-engineered sensors do.

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