This preprint presents The Invisible Window, a security research study of a downstream display-fidelity failure in browser-based proctoring and UI-vision systems. Browser-based proctoring commonly relies on WebRTC getDisplayMedia() under the assumption that captured screen output faithfully represents the physical display. This work shows that documented operating-system display-affinity mechanisms, including Windows SetWindowDisplayAffinity and macOS NSWindow.SharingType.none, can allow visible windows to be omitted from screen-capture output.The paper frames this issue not as an Apple or Microsoft zero-day, nor as an operating-system implementation bug, but as a security-relevant downstream design vulnerability in capture-dependent systems. It presents the threat model, cross-platform proof-of-concept analysis, empirical evaluation, responsible disclosure summary, vendor boundary classification, ethical considerations, and countermeasure analysis. The findings are relevant to online assessment, academic integrity, remote proctoring, and AI-mediated UI-vision workflows. Operational abuse code is not included in this public preprint.