Knotspan: Topology Trials

Knotspan is an offline topology puzzle campaign about simplifying knot diagrams through legal local transformations. Read crossing order, identify reducible structures, preserve orientation, and build a short sequence of committed moves. Sixty authored trials reward deliberate reduction, clean chains, and mastery rather than random dragging. Campaign stars and best scores stay on this device. The illustrated fieldbook provides an offline reference for crossings, orientation, legal moves, scoring, and the visual language used by the puzzles. The new Invariant Notebook turns the core decision into a measurable practice exercise. Balance crossing reduction against invariant stability, introduce an orientation reversal, and inspect legal-move confidence before returning to the campaign. A deterministic daily Reidemeister route provides a shared date-based challenge without an account or server. Knotspan includes local achievements, haptic and high-contrast preferences, reduced-effects controls, Dynamic Type, VoiceOver labels, and iPhone and iPad layouts. One paid download includes every trial and feature. There are no subscriptions, ads, in-app purchases, accounts, analytics SDKs, or remote unlocks.