Complete supporting proofs

The fifteen operative Bott providers below are included as complete text with their source, TeX, PDF and notices. The Weyl trace lesson uses the included Euclidean symbol, trace and Banach foundation proofs. Earlier supporting collections are retained in full so that their own proof routes and companion assets remain available offline.

Receiving proofs in the principal lessons

• Bott Section 17.1, P261.1–P261.7: The original split metric, its full phase dual, both quantization conversions and the ordered first composition remainder.
• Bott Section 17.2, P261.8–P261.15: Coordinate inverses, subordinate supports and every Green cutoff term.
• Bott Section 17.3, P261.16–P261.20: Linear-first Hilbert representation and the actual compact kernel map.
• Bott Section 17.4, P261.21–P261.23: Dominated convergence and uniform compactness.
• Bott Section 17.5, P261.24–P261.27: Compact primitive decomposition and the connected-domain distribution conclusion.
• Weyl Section 13, TD1–TD4, TG1–TG4, TR1, TO1–TO2: Norm-valued differentiation, every Gaussian and beta factor, and the exact Hermite domains.

Full provider texts

• Metric and topological foundations · Complete source
• Localizing symbols with moving metrics · Complete source
• Banach estimates, quotient spaces and compact parameter arguments · Complete source
• Finite defects under perturbation · Complete source
• Symbols, finite defects, and the index on a closed manifold · Complete source
• Symbols, operators and Sobolev scales · Complete source
• Fourier transforms, finite spectra and convex separation · Complete source
• Two measuring scales, one Weyl product · Complete source
• Detecting regularity without choosing coordinates · Complete source
• Polynomial and contour interfaces for stable boundary models · Complete source
• Changing an interior frame to extend an invertible matrix · Complete source
• When a moving symbol scale controls an operator · Complete source
• Quadratic Fourier multipliers at a moving scale · Complete source
• From Weyl symbols to operators and changes of coordinates · Complete source
• Spectral measures with the original operator domain retained · Complete source

Retained elliptic supporting collection · Retained matrix and foundation collection. Their original published scope and notices remain attached.