Generative AI models for de novo protein design—principally diffusion networks (RFDiffusion; Watson et al., 2023) and flow-matching architectures (AlphaFold2; Jumper et al., 2021)—optimize statistical loss functions defined exclusively over a Fisher-Riemannian informational manifold. Because these models carry no intrinsic mathematical connector to the thermodynamic admissibility conditions of the aqueous macromolecular environment, they systematically produce structural hallucinations: geometrically coherent outputs that are materially impossible in solution. This paper introduces the Thom-Peirce Viability Filter (TPVF), a differential-geometric and optimal-transport framework that bridges the informational latent space Z with the physical attractor submanifold M_att. The protein configuration space is modeled as a smooth N-dimensional Riemannian manifold (M, G) in which the Entropic Curvature Tensor R_ij^irr is rigorously constructed as the exterior derivative of the entropy production 1-form ω_σ = σ_i dx^i, yielding R^irr = dω_σ with components R_ij^irr = ∂_iσ_j − ∂_jσ_i—a proper differential 2-form on (M, G). A dissipatively penalized Riemannian metric G^diss_ij = G_ij + α R^irr_kl G^ki G^lj explicitly contracts the rank-2 curvature tensor against the base metric inverses, producing a scalar-valued geodesic cost c_R(x,y) that makes the Wasserstein-2 distance sensitive to thermodynamic inadmissibility. The Semiotic Attractor Mapping Γ : Z → M_att, grounded in Thom's structural stability theory and Peirce's operative semiotics, is solved via the corrected intrinsic Wasserstein gradient-flow equation ∂ρ/∂t = ∇_M·(ρ ∇_M(δE/δρ)) using the Jordan-Kinderlehrer-Otto (JKO) implicit time-discretization scheme. The ontic shielding loss L_ontic = λ_1 h(ΔG) + λ_2 L_{SE(3)} + λ_3 L_{topo} replaces Boolean arithmetic with continuous, gradient-optimizable penalty terms, where h(ΔG) = softplus(ΔG/k_BT) is dimensionless. Designs failing the dual stopping criterion d_W2(ρ_z, ρ_{Γ(z)}) > δ_critic or S_irr(Γ(z)) = tr(R^irr(Γ(z)))/N > Ξ_critic are rejected computationally before any synthesis cost is incurred. An executable pipeline with fully normalized pseudocode and an in vitro validation protocol using circular dichroism (CD) and hydrogen-deuterium exchange mass spectrometry (HDX-MS) are provided. The filter is projected to achieve a minimum 20% improvement in empirical folding success over unconstrained generative baselines.
Publication Date: 2026-06-23