On the Convergence of Regenerative Thermodynamic Security and Economic Incentives

Abstract

Version: v1.6.4 (June 2026) Major additions in this version: phased migration protocol with cryptographic quarantine (Section 6.4.4), sensitivity boundaries delineating the statistical decoupling threshold up to mu = 1.9% (Section 6.7), and integration of recent empirical MEV findings (Mancino & Rezzoli, 2025). Abstract Contemporary blockchain architectures face a critical impasse defined herein as the "Tetra-Lemma"—a four-dimensional optimization problem encompassing decentralization, security, scalability, and thermodynamic sustainability. Legacy Proof-of-Work networks confront diminishing security budgets due to the exhaustion of block subsidies, while Proof-of-Stake systems inherently risk oligarchic 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. The remainder of the abstract, covering the SDE and Fokker-Planck validation, the ZKP owner recovery model, and the resulting equilibrium, is in the manuscript. Data & Code AvailabilityThe mathematical models and high-precision stochastic simulations (e.g., Monte Carlo paths, SDE convergence, and Fokker-Planck distributions) presented in this manuscript are fully reproducible. The corresponding Python simulation suite and open-source models are made available at the author's GitHub repository (rincoin-regenerative-simulations) to ensure scientific transparency. Integrity & Provenance This document is anchored to the Bitcoin blockchain via OpenTimestamps. The proof file verification_data_v1.6.4.ots, included in the files below, covers the SHA-256 digest of Tokino_Rincoin_v1.6.4.pdf: 5269207ea7e363e8df312ed50c00afc119b43e6fa5d3c717e6a7d8fc9863147b The archived proof is in its as-submitted form: it commits the digest to the public OpenTimestamps calendars and does not itself embed the Bitcoin attestations. Completing it against those calendars — which both verification paths below do automatically — yields three Bitcoin attestations, the earliest in block 952366. An OpenTimestamps proof carries no wall-clock time of its own — any date reported for it is read from a Bitcoin block header. To verify, upload the PDF and the .ots file to opentimestamps.org, or with a Bitcoin node: ots verify -f Tokino_Rincoin_v1.6.4.pdf verification_data_v1.6.4.ots — the -f flag is required because the proof's filename differs from the document's. The provenance of this document is recorded in a separate signed artifact, the Rincoin Provenance Certificate (10.5281/zenodo.21415730), which binds this whitepaper to the digest above and is the reference for the full anchoring detail. That certificate carries its own OpenPGP signature, Bitcoin anchor, and PAdES signature; this whitepaper itself carries the OpenTimestamps proof only. Zenodo archival gives this record a persistent identifier and an independent retrieval path; it is not itself a cryptographic control. Validation_Scientific_Provenance_v1.6.4.pdf in the files below is an earlier certificate edition, retained as evidence. It is superseded by the record cited above. Correspondence & AffiliationPrimary Author: Tokino, Michiru (時乃 満)Affiliation: Rincoin Core Research Academic Inquiries: [email protected] Community Governance: @aevustus (Discord) / @aevust (X/Telegram) Keywords: Rincoin, Proof of Rinne (PoR), regenerative crypto-economics, non-equilibrium thermodynamics, non-equilibrium steady state (NESS), stochastic differential equations (SDE), Fokker-Planck equation, recirculation incentive mechanism, macroeconomic homeostasis, Nash equilibrium, cryptographic vault, zero-knowledge proofs (ZKP), modular blockchain architecture, account abstraction, blockchain tetra-lemma, MEV mitigation, sandwich attack resistance, sensitivity analysis, statistical decoupling threshold, phased migration protocol