Inner Geometry: A Single-File Browser App for Measuring Observer-Axis Alignment and Structured Pareidolia

Inner Geometry is a self-contained, single-file browser application (one HTML file; no installation, server, accounts, or network access) that teaches and measures Geometry G — a minimal cognitive model in which an internal vertical observer-axis (I), a collapse operator terminating at an identity pixel (p), and a graded compression state (c) act as a projective frame over ambiguous external shapes. The core of the app is a real, pixel-based measurement rather than an illustration. For any shape — five built-ins or any image the user uploads and thresholds to a silhouette — the app extracts the negative space, computes the orientation of its principal axis by covariance analysis, and evaluates the model's signature condition live: f(E) = I if and only if align(A(E), I) < τ and c > θ, where align = |α − 90°| is the axis's deviation from vertical, τ is an adjustable tolerance, and θ is a fixed compression threshold. Beyond exploration, the app includes a blind, randomized data-collection mode: silhouettes are presented one at a time with the computed answer hidden, participants judge whether a vertical axis is present, and every response is logged with the shape, its design condition, the computed metrics, and the current parameters. A results screen pools responses across sessions, reports aligned-versus-control detection rates with a two-proportion z-test, and exports data as CSV or a full JSON backup. All data stays in the user's browser. The application is intended as an instrument, not a finding. It is designed to gather the n>1 evidence needed to test whether the alignment effect exceeds baseline symmetry salience — the empirical question the model raises — and it accompanies the Geometry G papers. Additional features: four visual themes, a shared compression-state variable across modules, a timeline and event-reconstruction tool, and a signature-equation showcase linking each term to its module. Requirements: any modern desktop browser (Canvas 2D and localStorage). Open inner-geometry.html directly; works fully offline. Keywords: structured pareidolia, observer-axis, negative space, symmetry perception, principal axis, cognitive geometry, interactive instrument, single-file web app, predictive coding, Gestalt. Contact: [email protected]