EQUATION REGISTRY

∂²t ψL − c²∇²ψL = 0 ; ω² = c²|k|²

The compatibility symbol ψL here denotes the source-free linear density channel σ=-∇·uL. Homogeneous long-wave regime and compatible boundaries; retain its 1/k² kinetic kernel rather than introducing a new scalar constitutive law.

Theory · EFFECTIVE MODELEquation version 1.1

Based on the final manuscript · Chapters 4 and 5

ASD-WEB-WAV-001
∂t2ψL−c2∇2ψL=0,ω2=c2∣k∣2\partial_t^2\psi_L-c^2\nabla^2\psi_L=0,\quad\omega^2=c^2|\mathbf k|^2

The compatibility symbol ψL here denotes the source-free linear density channel σ=-∇·uL. Homogeneous long-wave regime and compatible boundaries; retain its 1/k² kinetic kernel rather than introducing a new scalar constitutive law.
Chapter reference: Ch. 5 (5.4.6), source-free density channel; (5.4.8)–(5.4.10) · ASD-BOOK-ddbade997b45

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Ch. 5 (5.4.6), source-free density channel; (5.4.8)–(5.4.10)

Registered formula checked individually against the final manuscript; source-grounded scope note synchronized

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  • The compatibility symbol ψL here denotes the source-free linear density channel σ=-∇·uL. Homogeneous long-wave regime and compatible boundaries; retain its 1/k² kinetic kernel rather than introducing a new scalar constitutive law.

Source locators: p2030 · p2035–2040

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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