GCBM-DCT-HV-Bio-NL-Grow-CHG-CSM-RHEC: A Unified Geometric, Biological, Causal, and Regenerative Framework for Mechanism-Aware Tissue and Connectome Modeling

Abstract

Modern biological prediction problems increasingly require models that go beyond Euclidean feature regression and local graph smoothing. Tissue, cellular, and connectome systems are nonlinear, geometry-dependent, intervention-sensitive, history-dependent, and subject to regenerative or homeostatic constraints. We propose GCBM-DCT-HV-Bio-NL-Grow-CHG-CSM-RHEC, a unified model for mechanism-aware biological prediction. The model integrates geometric connectome dynamics, differentiable charted tissue geometry, Hamiltonian latent transport, nonlinear biological kinetics, nested latent memory, continual growth without overwriting, causal hypergraph structure, causal structure modeling, and regenerative homeostatic error correction. Unlike Euclidean baselines, which treat observations as flat vectors, and local graph baselines, which use neighborhood smoothing without mechanistic structure, the proposed model represents biological states (Trapnell 2015) as coupled geometric, dynamical, causal, and regenerative objects. We evaluate the model on four synthetic toy studies, Toy A-D, designed to reflect increasing biological complexity: local Euclidean structure, nonlinear mechano-chemical interaction, causal intervention response, and out-of-distribution regenerative shift. Compared with Euclidean and local graph baselines, the full model achieves the lowest mean squared error across all four toy studies. Relative to the Euclidean baseline, the full model reduces MSE by approximately 63.0%, 89.1%, 89.0%, and 90.9% on Toy A, Toy B, Toy C, and Toy D, respectively. These results support the value of integrating geometry, mechanism, causal structure, adaptive growth, and regenerative correction into a single predictive architecture (Figure 1). O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=142 SRC="FIGDIR/small/734320v1_fig1.gif" ALT="Figure 1"> View larger version (71K): org.highwire.dtl.DTLVardef@9e9eorg.highwire.dtl.DTLVardef@add398org.highwire.dtl.DTLVardef@1eb1f1org.highwire.dtl.DTLVardef@1346720_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 1.C_FLOATNO GCBM-DCT-HV-Bio-NL-Grow-CHG-CSM-RHEC, a unified model for mechanism-aware biological prediction. C_FIG