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The Harmonic Operator Materials Manual – Aligned Edition (Version 3) is the definitive engineering‑scale reformulation of the Harmonic Operator framework, rebuilt so that every claim is explicitly aligned with A General Theory of Curvature, Q, and Toroidal Boundaries (Version 7). This edition replaces the speculative physics of Version 1 with a rigorous, falsifiable design language grounded in topology, curvature budgets, circulation classes and boundary closure, and it establishes a modular operator framework that engineers can actually use at the bench. The manual clarifies the population‑regime scope, withdraws aperture‑scale relations, and reconstructs the operator’s three terms directly from canonical geometry, showing which sectors are engineerable and which are fixed by topology alone. It introduces a precise vocabulary of motifs, anchors and functioners, rewrites the design rules around curvature conservation and matching order, and provides worked examples that demonstrate how to route behaviour through geometry rather than through forbidden dynamics. With explicit provenance tags, exclusion lists, boundary‑state corrections and a mandatory falsification section, this edition is both stricter and more powerful than its predecessor: a complete, auditable, engineering‑ready language for designing curvature‑structured matter.

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