Paper V · Visual guide
Explore the 40 visuals Read all 40 visuals with 37 original drawings, selectable equations, descriptions, and transcripts of the TikZ labels. Each worked example links to the manuscript passages it illustrates; evidence notes retain their source edition’s scope.
All visual guides Guide contents Search this guide Read paper Switch guide More resources Choose a visual 1 Three objects, three different questions PDF 2 An atlas of the objects PDF 3 Decimation is a permutation, not a loss PDF 4 Refine packets on a common lattice PDF 5 A filter becomes a matrix of actual delays PDF 6 One sample is not one channel step PDF 7 Perfect reconstruction is an operator identity PDF 8 A jump can hide from the first Haar split PDF 9 Lifting preserves information, not energy PDF 10 The second level resolves the hidden change PDF 11 Deleting coefficients is the approximation step PDF 12 A mixed-depth basis must cover every branch PDF 13 Solve every alternative without searching every alternative PDF 14 How far can the costs move before the tree changes? PDF 15 Retain the jump and approximate the other packet PDF 16 Why a Fourier cutoff cannot reproduce this jump pointwise PDF 17 Small location errors, different norms PDF 18 Separate amplitude error from mask error PDF 19 Geometry localizes error while data may leave it ambiguous PDF 20 Two products, two packet laws PDF 21 Nonlinear neighbors cross channel boundaries PDF 22 One reflection circle, four very different impedances PDF 23 A pole is a chart boundary, not a broken group action PDF 24 Residue labels are not impedance averages PDF 25 Sensitivity grows before the pole is reached PDF 26 What the reader can now verify PDF 27 What the extended developments add PDF 28 Six image phases are six exact address classes PDF 29 A positive singular-value gap survives perturbation PDF 30 Nonunitary tree bounds propagate along branches PDF 31 Derivative jumps have their own packets PDF 32 The approximation operator also acts on packet error PDF 33 An overlap matrix is an exact error ledger PDF 34 A shifted step and a shifted ramp have different moduli PDF 35 A strict contrast gap locates every separated jump cell PDF 36 Repeated observations shrink the noise side of the gap PDF 37 Haar sees a jump only through its position in the support PDF 38 Two half-shifted grids remove exact alignment failure PDF 39 Higher differences annihilate polynomial interiors PDF 40 Conditional Gibbs control closes the reconstruction estimate PDF Complete selectable atlas source · Conversion records
