From Geometry to Behavior: A Smoothness-Certified Digital-Twin Framework for Information Management, Sustainability, and Resilience in Built Heritage Conservation

Existing heritage digital twins document geometry and monitor condition with high fidelity, but rarely model the behavioral process through which owners, authorities, and peer-exchange networks jointly determine the long-run conservation profile of a historic district, and therefore cannot answer the subsidy-design questions heritage authorities face. This paper supplies that missing behavioral layer. We formalize heritage conservation credit systems (indivisible credits, capped holdings, balanced aggregate stock) as a matching model and establish four analytical guarantees for twin operation: predictions exist, are unique, are globally stable, and vary continuously differentiably with policy parameters. Global stability acts as a resilience certificate, guaranteeing recovery from any shock within roughly twenty annual cycles, and smoothness bounds prediction uncertainty in closed form. These certificates are properties of the behavioral engine, established analytically; they are not claims about field-validated operation. A three-layer architecture embeds the engine behind a state-synchronization loop that re-estimates behavioral parameters from registry observables at a cadence set by the data source rather than by the model; in a controlled in silico sensing experiment the synchronized twin reduces post-disruption tracking error by 71% relative to a static twin, and a window-length sweep shows the loop dominates the static twin by 62–71% at every cadence tested. Calibrated to a traditional village in the Mount Tai Piedmont and verified against an agent-based Monte Carlo counterpart, the twin yields three model-dependent policy results: a subsidy trap (higher subsidy rates activate conservation exchange yet reduce steady-state top-tier counts), the dominance of within-tier cooperation over cross-tier mentorship, and an inverted-U sustainability frontier locating Mount Tai villages in the under-funded regime. All outputs consolidate into a single HBIM-compatible information-management deliverable. We report the framework as a specified and in-silico-verified behavioral twin whose sensing interfaces await field deployment, and we state explicitly which components remain conceptual.