Emergent Continuous Gravity from Lambda-24 Lattice Fluid

Spacetime is modeled as a Sub-Planckian Information Tension Fluid (SPITF) originating from the 24-dimensional Leech lattice (Λ24). The Petersen-Middleton sampling theorem and Pontryagin duality project discrete momentum states onto a 3D macroscopic manifold using a J12 Bessel reconstruction kernel. Topological hysteresis during discrete lattice updates generates temporal viscosity. This viscosity introduces structural damping φ0 and vacuum bulk modulus Kvac into the dissipative Mukhanov-Sasaki equation. High-frequency modes crossing the Hubble horizon undergo a phase random walk dictated by the Fluctuation-Dissipation Theorem (FDT) at the Gibbons-Hawking temperature. Variance accumulation along the holographic boundary yields an amplification factor (H0/f)1/2. The macroscopic integration produces a stochastic gravitational-wave background strain hc ~ O(10-15) with a f-1/2 scaling profile. In the extreme gravitational limit, the J12 kernel truncates the continuous manifold outside the event horizon. A Gibbs surface forms at rh + 16.7 lP. The inner reflection boundary imposes a -π/2 phase shift. Iyer-Will high-order WKB matching evaluates the smooth photon sphere potential. The outer reflection phase shift φout(a) is determined by the complex Gamma function argument arg(Γ(1/2 + ia)). The Bohr-Sommerfeld quantization condition defines the black hole echo spectrum fn ∝ (n + Δ). The topological phase offset Δ shifts continuously. The value evaluates to Δ = 5.25 at peak resonance (a &to; 0). The value evaluates to Δ = 5.50 in the deep WKB limit (a ≫ 1). The frequency spectrum exhibits dynamical dispersion chirping.