Polar glacier monitoring faces a dual challenge: the high nonlinearity of calving dynamics and the scarcity of labelled observational data. We introduce a computational framework inspired by a new information-geometric construction—the Arithmetic Fisher Manifold—in which the glacier boundary state space is modelled as a non- Euclidean manifold whose curvature encodes structural stability. We introduce a geometrically inspired framework in which analysis of a theoretical Perceptual Operator on this manifold suggests that spectral collapse of its first eigen-gap should precede structural failure. This motivates a computationally tractable surrogate—the variance of the boundary entropy field, denoted Δ(̂)_spec—which we monitor as an early-warning index. The resulting ICE-SAP segmentation pipeline dynamically adapts its loss landscape to the local manifold geometry via a lightweight Meta-Net. Validation on two Vatnajökull outlet glaciers—Breiðamerkurjökull (122 scenes, 14 calving events) and Skeiðarárjökull (106 scenes, 12 events; 64.0558° N, 17.2081°W)—shows that ICE-SAP achieves consistent Boundary-IoU improvements of 8.7–8.9 percentage points over a standard U-Net baseline. Precursor signals are detected at a median 18.3 h in advance (Breiðamerkurjökull) and 17.1 h (Skeiðarárjökull), with a combined detection rate of 21/26 events (Fisher exact test: p < 0.001). Sentinel-2 data are sourced from the Copernicus Programme, and calving events are identified using MEaSUREs glacier velocity data. INT8-quantised deployment on a Raspberry Pi 4 achieves 320 mW peak power at 2.3 s per 512×512 tile, demonstrating viability for autonomous in-situ monitoring.