Prospective Validation of the VxC Regenerative Model through Markov Chains in Territorial Systems

Abstract

This article presents LxC Engineering (Life per Carbon), a regenerative and participatory engineering approach aimed at transforming degradative processes into sustainable, functional, and multi-capital systems. Derived from the IP.IDEAS.S framework, it is grounded in the CRFC (Carbon Regenerative Physicochemical Cycle), whose operative equation states: L = C + 6.5 kWh/kg, where L is regenerated life, C is captured carbon (kg CO2 eq), and 6.5 kWh/kg is the solar energy required per kg of useful biomass. Its methodology integrates tools that support the co-design, implementation, and evaluation of regenerative and participatory processes: DPAV (Decide, Plan, Act, Value): strategic governance cycle for making informed decisions under uncertainty. CUPA (Calculate, Understand, Plan, Act): adaptive operational core structured around technical, creative, and social engagement. ToC (Theory of Constraints): prioritization and measurement logic through five iterative steps to focus action. ADFI (Analyze, Define, Formulate, Implement): participatory engineering methodology that involves stakeholders in every phase from contextual analysis to implemented improvements. 9SP (Nine Strategic Pillars): participatory strategic framework articulating Purpose, Problematic, Potential, People, Proposal, Process, Project, Budget, and Benefit. VxC quantifies regeneration through indicators such as ROP (Return on Process), BM (Marginal Benefit), CM (Marginal Consumption), and PTF (Total Factor Productivity). Its territorial validation is based on the ATA case (Amazon Tambo Hamlet), applying Markov chain simulations and input-output matrices. Results demonstrate the feasibility of reconfiguring degraded territorial processes toward regenerative and sustainable futures through participatory governance and value co-creation.