Applied ITT — The Pressure Recipe: Spectral Shape Fingerprinting via Dimensional Projection Armstrong Knight — intent-tensor-theory. com — 2026 Every 2D pattern produced by a 3D standing wave field carries a measurable spectral signature: k-frequency (energy-weighted mean spectral radius), Xi-complexity (high-frequency energy fraction), and Squeeze ratio (spatial matter density). These three quantities constitute the Pressure Recipe — the acoustic DNA of a shape. This paper defines the three quantities formally, verifies them computationally on five canonical shapes (circle: k=120. 3, Ξ=67. 7; square: k=90. 4, Ξ=56. 8; star N=5: k=136. 5, Ξ=79. 7; hexagon: k=108. 4, Squeeze=0. 144; eye: k=146. 0, Ξ=88. 6), and establishes that the Ξ/k ratio is scale-invariant within a shape class (variance 0. 000004 across 4 circle radii). All results are verified by running code. The Pressure Recipe connects to the ITT pipeline: k-frequency maps to the gradient ordering, Ξ-complexity maps to the bloom quotient Q, and Squeeze maps to the observable density ρₒbs. The library of canonical pressure recipes is a real computational artifact.
Armstrong Knight (Fri,) studied this question.