Projection onto xyztRQ: Construction and Machine Verification of the Map and Inverse Map from the Discrete Dual System to Spacetime Coordinates (Dual Geometry of Wavelength and Frequency Spaces, Paper 15)

Paper 15 of the series Dual Geometry of Wavelength Space and Frequency Space. We construct the explicit projection and inverse projection from the discrete dual system's state data onto the spacetime coordinates (x,y,z,t) and the ledger coordinates (R,Q), and machine-verify every stage. Spatial coordinates are mixed-radix quarter-digit expansions read from transcription-line phase classes by peeling decode; the only genealogy whose digits close within the digital alphabet is the ternary one. Time is a derived quantity (norm clock) with no independent inverse map. R and Q require no map: the image is the codimension-2 constraint surface R^2=s, Q=epsilon. The inverse map is constructive for space (loss below the censorship quantum; composite round trip 500/500). The projection commutes with the conservation ledger: s read from the record alone is additive across decays (60/60), and charge-like conservation is a parity-arithmetic theorem enforced by transport (39.2% of raw combinations violate; zero amplitude-carrying paths do). The 4D lift is exhaustively verified (diagonal quotient by the even-sign-flip group; parity-mixed composites decode 256/256). Uniform motion is a digit odometer: the amplitude spectrum, wavelength content, R and Q do not evolve (deviation 1e-15); only phases rotate, linearly, at rate f*v — velocity exists only in the sequence of records. Originally reviewed and accepted as Paper 13 of the series; renumbered to 15 upon insertion of the new Papers 13-14, with citations redirected. Japanese and English full texts. No physical identification is made.