Kenneth ChengMathematical modeling

Editorial project overview

Topology at the Edge of Resolution

Which image diagnostic can recover a high-resolution latent melt-pond spanning threshold after blur, downsampling, segmentation error, boundary perturbation, and cropping?

Reproducible studyUpdated 24 Aug 2026
Technical figure from Topology at the Edge of Resolution
A reviewed research figure synchronized from the private technical workspace. The original aspect ratio and labels are preserved.

Editorial overview

Read Topology at the Edge of Resolution for the complete mathematical model, literature review, frozen experiment, observation-error audit, failure analysis, limitations, and ten approved figures.

The study holds each latent pond field fixed while blur, pixel size, a paired one-pixel segmentation-boundary displacement, boundary texture error, and crop change its observed representation. Direct spanning, a discovery-calibrated pond-fraction constant, a fractal-gradient breakpoint, Euler and Betti curves, exact persistence-pruned Betti curves, and a pond-interior distance bottleneck throat are compared against the same high-resolution oracle.

Use the Melt-Pond Topology Lab to explore how nearly unchanged pond area can coexist with a reversed connectivity decision. The public article and lab expose no private source, notebook, raw geospatial file, or coordinate-level image.

Key findings

  • No diagnostic passed every generator-by-observation robustness gate, so the benchmark abstains from naming a universally resolution-robust threshold signal.
  • Raw spanning had the lowest pooled median absolute error at 0.0144 [95% bootstrap interval 0.0124–0.0163], but its p90 was 0.0666 and the worst Matérn segmentation-displacement stratum reached median 0.08555 and p90 0.12913.
  • The bounded MOSAiC case reports aggregate topology on one 71,875-cell common domain; it is not latent truth, and Sentinel-2 was excluded after HTTP 503 requests because its metadata did not declare the floe-motion/co-registration transform needed for controlled pixelwise comparison.

Limitations

  • The synthetic Matérn, germ–grain, and random-field Ising families are controlled morphology tests, not calibrated Arctic climate or drainage models.
  • The latent truth is a finite-window, four-connected pond spanning threshold; other hydraulic, radiative, or ecological definitions can produce different thresholds.
  • The two-date MOSAiC case tests representation sensitivity and cannot identify latent percolation truth, seasonal timing, or a causal melt mechanism.

Technical record

Detailed source, calculations, generated figures, and reproduction instructions are maintained in a private technical workspace. Public articles contain only manually reviewed interpretation and approved figures.

Version history

2026-08-24 — Curated overview reviewed against repository evidence.