A hyperbolic topological atlas reveals polyamine steering of a shared developmental manifold in Arabidopsis

High-throughput plant phenotyping captures development at scale, yet image-rich screens are still often reduced to static trait summaries. We tested whether nutrient availability, polyamine priming, concentration, and their transport reshape Arabidopsis rosette development by generating distinct morphologies or by changing residence along a common trajectory. We analyzed 138,223 time-resolved rosette images from Col-0 and five mutants involved in polyamine transport (put1-5) primed to putrescine, spermidine, spermine, dose, and nutrient regimes using a self-supervised vision backbone, Poincare embedding, hyperbolic Mapper, and manifold straightening. The data form a single connected developmental manifold with 410 nodes and 746 edges, organized from an early, low-nutrient-biased hub through high-betweenness transition corridors to two late, nutrient-enriched terminal regions. Polyamine identity stratifies this manifold by developmental phase: putrescine enriches early states, spermidine occupies transition corridors, and spermine marks late compact rosettes. Nutrient richness and dose change distal occupancy, whereas put genotypes alter dwell time within shared regions rather than producing separate topologies. Manifold straightening resolves these effects into a short early lateral deflection followed by convergence, yielding two scalar readouts, early transverse offset and distal occupancy, that summarize treatment action on a common morphodynamic scale. The framework converts large image screens into interpretable developmental geometry for image-based phenomics.