Applied ITT — The Pressure Recipe: Spectral Shape Fingerprinting via Dimensional Projection

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 ρ_obs. The library of canonical pressure recipes is a real computational artifact.