Transcriptional Hysteresis and Irreversibility in Periodontitis Revealed by Single-Cell Latent Manifold Modeling

Chronic periodontitis represents one of the most prevalent inflammatory tissue-destructive conditions in humans, yet the molecular thresholds separating reversible inflammation from permanent structural collapse remain undefined. Using single-cell RNA sequencing data from 12,104 cells (GSE152042) spanning three disease states -- healthy gingival tissue, mild periodontitis, and severe periodontitis -- we constructed a variational autoencoder (VAE)-derived 20-dimensional latent disease manifold and applied formal hysteresis quantification to measure transcriptional irreversibility. Chi-square analysis across 9,163 cells occupying transitional pseudotime bins yielded {chi}{superscript 2} = 11,971 (p < 10-300, df = 4), with Cramers V = 0.81, confirming strong state-memory effects inconsistent with freely reversible disease dynamics. Non-negative matrix factorisation (NMF; k = 15) identified biologically coherent gene programs whose co-activation topology was encoded as a hypergraph constraint network; in severe disease, 16 of 76 healthy constraints collapsed by more than 60%, and the Fibroblast-Epithelial coupling (Programs 1-4) was reduced by 84%. A six-agent agentic AI simulation faithfully recapitulated observed shifts in cellular composition and established a temporal threshold beyond which tissue damage trajectories diverge irreversibly. We introduce the Regenerative Permission Index (RPI), a composite single-cell metric (range: 0.060-0.644), whose mean in severe periodontitis (0.323) falls well below the 0.50 permissibility threshold, indicating that all tested biomaterial interventions will fail. Five-fold cross-validated classification achieved 88% accuracy (Random Forest, AUC = 0.992), and permutation testing confirmed that constraint network patterns are biologically specific rather than artefactual (p < 0.01). Together, these findings provide a quantitative basis for understanding periodontal irreversibility and position RPI-guided decision-making as a framework for precision regenerative medicine.