Social Hamiltonian and Legal Engineering: A Constructive Approach to the Latent Torus Concept via Quantum Algorithms and Smart Contracts

Abstract

This study quantifies Large Language Models (LLMs) and humanoids as a new labor force and describes the transformation of economic structures brought about by "super-fluid task allocation involving humans," facilitated by tokenized task transactions built on blockchain technology, from the perspective of statistical physics. Furthermore, we devise a constructive approach called "Legal Engineering" and discuss its governance mechanisms. First, we define the price fluctuations of tokenized tasks as "work volatility" and suggest that, within the scope where specific assumptions (existence of information friction, amplification of interactions, and introduction of approximate effective temperature) hold, phase-transition-like behaviors (rapid changes in order similar to bubbles) can occur in the market. Volatility here is interpreted not merely as a statistic but as an operational approximation of "social temperature" that emerges as a result of amplified information friction and interactions. As a governance mechanism to suppress this entropy increase, we propose the "Latent Torus," an information event horizon. The Latent Torus handles internal optimization invisible from the frontend and ensures sustainable social order by recirculating only optimized parameters to smart contracts. Here, by combining quantum optimization with "Semantic Intervention" via "Regulated LLMs," we aim for stabilization based on "semantic depth" rather than apparent liquidity. Furthermore, we propose a "Grand Unified Algorithm" to simultaneously handle economic efficiency (Hamiltonian minimization), humanity (Well-being), and social credit (Proof of Trust) within a single mathematical framework. The scope of this paper is not to advocate for immediate control of society as a whole, but rather to provide a conceptual model for optimizing and auditing trade-offs between indicators in a consistent manner under limited task spaces, participant sets, and operational rules. As a concrete model, we present "Computational Social Contract Theory (CSCT)" and confirm its behavior and limitations under various assumptions through quantitative analysis using multi-agent simulations. Notably, this theory presents a design policy for realizing "verifiable concealment" in governance under certain assumptions (circuitability, computational assumptions, and soundness of key management/operation) using cryptographic techniques such as zero-knowledge proofs (zk-SNARKs). This explores the possibility of hiding the details of internal optimization while maintaining compliance with the Constitutional Core, allowing citizens to verify legitimacy, and examining the operational requirements necessary for such a system. This paper presents a conceptual proposal for institutional design in a post-capitalist society and examines the redesignability of money and law. Note that the quantitative results of this paper are positioned as exploratory simulations and do not directly claim predictive confirmation.