Dimineața Cubului: The First Original Melody Composed Natively in Z₇³ Toroidal Harmonic Space

We document the composition and analysis of "Dimineața Cubului" (Morning of the Cube), an original melody composed natively in Z₇³ harmonic space — not transcribed or adapted from existing music, but constructed directly as a path through the 343-node toroidal lattice defined by f(x,y,z) = 256·(3/2)ˣ·2ʸ·(7/4)ᶻ.The melody is encoded in D Dorian via the Z₇³ x-axis (scale degree), y-axis (octave register), and z-axis (harmonic color). Its six-phrase structure — question, descent, ascent, resolution, low echo, final cadence — traces a closed toroidal path through the lattice, returning to its origin node. This closure was not designed; it emerged from the musical requirements of a satisfying cadence.The document includes the full score in Z₇³ coordinates, Western notation, structural analysis, harmonic frequency table for each visited node, the complete JavaScript implementation, and composition notes from both authors.The melody is released into the public domain. It is implemented as the default intro sequence in CUBICUM JOY v3–v5 (companion artefact on Zenodo).