On the Convergence of Algorithmic Issuance and Thermodynamic Security: A Unified Regenerative Framework

Abstract

AbstractContemporary blockchain architectures face a critical impasse defined herein as the "Tetra-Lemma"—a four-dimensional optimization problem comprising decentralization, security, scalability, and thermodynamic sustainability. Proof-of-Work networks confront diminishing security budgets due to the exhaustion of block subsidies, while Proof-of-Stake systems risk validator centralization. This paper establishes a Unified Monetary-Supply Framework that resolves these structural conflicts by synthesizing the deterministic "Customized Halving" schedule with the probabilistic regeneration logic of the Proof of Rinne (PoR). We demonstrate that by enforcing a "Thermodynamic Statute of Limitations" on dormant assets, the protocol functions as a Non-Equilibrium Thermodynamic Engine. This architecture transforms entropic asset attrition—traditionally viewed as systemic loss—into a regenerative security budget. Using Rincoin as a case study, the model proves that a high-frequency blockchain can maintain a deflationary supply curve while anchoring the effective circulation at a permanent target equilibrium, offering a rigorous blueprint for a closed-loop, regenerative digital economy over a secular horizon. Key Quantitative Findings Asymptotic Convergence: While the effective circulating supply may experience a temporary peak (approx. 27 million RIN), the Dual-Layer Temporal Architecture ensures stabilization below the 21 million threshold (specifically converging to 20.88 million RIN). Perpetual Stability: Beyond the initial mining and transition phases (spanning 443–703 years), the PoR mechanism ensures the indefinite maintenance of the effective circulating supply. This transcends the finite lifecycle of traditional PoW assets by establishing a permanent, self-sustaining regenerative cycle. Thermodynamic Equilibrium: Mathematical verification of the "Golden Ratio" between Reserve, Unrecovered Loss, and Actual Circulation (approx. 77 : 70 : 21). Publication StatusThis manuscript (v1.6.1) serves as the foundational theoretical framework for the Rincoin protocol. Future iterations will formalize the consensus mechanisms required to govern these algorithmic parameters. Integrity & Provenance ArchitectureThe scientific integrity and existence of this document are secured by a Triple-Verification Layer: 1. Academic Provenance: Indexed via Zenodo (DOI: 10.5281/zenodo.17141922). 2. Thermodynamic Timestamping: Anchored to the Bitcoin blockchain via OpenTimestamps. 3. Identity Assurance: Digitally signed by the author via a third-party certification authority (GMO Sign). Note: Verification data and the "Certificate of Authenticity" are available in the supplementary files. CorrespondencePrimary Author: Michiru Tokino (also known as Aevust in the decentralized infrastructure community). Academic Inquiries: [email protected] Community Governance: @aevustus (Discord) / @aevust (X/Telegram) Keywords: Rincoin, Proof of Rinne (PoR), non-equilibrium thermodynamic engine, phase transition of value, dual-layer architecture, customized halving, thermodynamic statute of limitations, regenerative crypto-economics, blockchain tetra-lemma.