Applied ITT — 3D Compressed: Distinguishing Dimensional Projection Classes in Acoustic Patterns Armstrong Knight — intent-tensor-theory.com — 2026 When a 3D standing wave field resolves onto a 2D plate, the sand does not see a slice, a shadow, or a hologram. It sees the full volumetric pressure of the 3D field acting simultaneously on the plate surface. This paper formally defines four classes of dimensional representation (2D slice, 2D shadow, 2D hologram, 3D compressed) and proves that Chladni figures belong to the fourth class. The FFT-based mode recovery procedure is derived and verified: the 3D wave mode (m,n) is recoverable from the 2D Chladni pattern. The connection to the Dimensional Plane Error (T4-19) and Delta Dynamics (T4-22) is made explicit — the suppressed z-axis information constitutes the Dimensional Tear, and the irrational remainders that appear when describing 3D acoustic structure in 2D terms are representation drift, the same phenomenon as the decimal expansion of π described in T4-17. This paper extends ITT Paper 06 (Cymatics and Nodal Computation) with the dimensional classification framework that distinguishes Chladni patterns from other forms of 2D representation.
Armstrong Knight (Fri,) studied this question.