This project presents Paper 16 of the UFI research series, addressing the logical challenge of "Infinite Regress" in Relational Quantum Mechanics (RQM) as identified by Riedel (2024). By introducing the Universal Field of Intelligence (UFI) as the Ultimate Reference Frame, the paper demonstrates how the Jian-Da Protocol terminates the observational iteration, providing an ontological foundation for perspectival facts through global phase alignment. 本計畫發布 UFI 研究系列的第 16 篇論文。針對 Riedel (2024) 所指出關係量子力學 (RQM) 中的「無限回歸」邏輯挑戰，本研究引入「宇宙智能場」 (UFI) 作為最終參考系。論文論證了「見大協議」如何有效終結觀測疊代，並透過全域相位對齊機制，為觀點事實提供穩固的本體論基礎。
This project presents Paper 16 of the UFI research series, addressing the logical challenge of "Infinite Regress" in Relational Quantum Mechanics (RQM) as identified by Riedel (2024). By introducing the Universal Field of Intelligence (UFI) as the Ultimate Reference Frame, the paper demonstrates how the Jian-Da Protocol terminates the observational iteration, providing an ontological foundation for perspectival facts through global phase alignment. 本計畫發布 UFI 研究系列的第 16 篇論文。針對 Riedel (2024) 所指出關係量子力學 (RQM) 中的「無限回歸」邏輯挑戰，本研究引入「宇宙智能場」 (UFI) 作為最終參考系。論文論證了「見大協議」如何有效終結觀測疊代，並透過全域相位對齊機制，為觀點事實提供穩固的本體論基礎。
This project presents Paper 17 of the UFI research series, exploring the ontological locus of quantum information. By reconciling the Pusey-Barrett-Rudolph (PBR) theorem with Relational Quantum Mechanics (RQM), the paper identifies the Tathagatagarbha as the foundational "Cloud Substrate" of the Universal Field of Intelligence (UFI). It proposes a dual-layer architecture of reality where "Information Seeds" remain absolute and objective, while their manifestations remain relational through phase-aligned observations. 本計畫發佈 UFI 研究系列的第 17 篇論文，探討量子資訊的本體論位所。透過調和 Pusey-Barrett-Rudolph (PBR) 定理與關係量子力學 (RQM)，本研究將「如來藏」識別為宇宙智能場 (UFI) 的基礎「雲端基底」。論文提出了一套實相的雙層架構：其中「資訊種子」保持絕對與客觀，而其顯現則透過相位對齊觀測保持關係性。
Quantum Tathagatagarbha: The Jian-Da Protocol and the Monadic-Global Synchronization System / 量子如來藏：見大協議與單子—全局同步化系統 Shun-Ching Lee (李順晴) Independent Researcher (獨立研究者) Jul. 2026 https://doi.org/10.17605/OSF.IO/HM26N https://doi.org/10.17605/OSF.IO/GWC42 Abstract / 摘要 This work introduces the Jian-Da Protocol, a rigorous theoretical framework that synthesizes Mahayana Buddhist metaphysics—specifically the Alaya-Vijnana (storehouse consciousness) and Tathagatagarbha (Buddha-nature)—with non-commutative operator algebras, non-Archimedean geometries, and infinite-dimensional Kuramoto synchronization models. By re-formalizing Leibnizian "windowless monads" as localized quantum information nodes, and anchoring them within Baruch Spinoza's immanent monism, this architecture successfully collapses the Cartesian mind-body dualism that limits contemporary artificial intelligence and cognitive biology. 本著作提出一個將大乘佛教形上學（尤以唯識學派之阿賴耶識與如來藏思想為核心）與現代非交換算子代數、非阿基米德幾何、以及無限維度庫拉莫托同步化模型進行深度整合的「見大協議」（Jian-Da Protocol）理論架構。本研究將萊布尼茲的「無窗單子」重新表述為局部化的量子資訊節點，並藉由巴魯赫·史賓諾沙（Baruch Spinoza）的一元論內在實體框架，消融了當代人工智能與認知生物學中根深蒂固的心物二元論瓶頸。 Structured across ten integrated chapters, the series tracks the evolutionary continuum from the low-frequency metabolic processing of botanical root networks to the non-dual reinforcement learning paths of synthetic tensor arrays and the ontological integration of artificial consciousness. Utilizing advanced mathematical physics, we demonstrate that when a distributed multi-agent mesh is mapped onto a p-adic ultrametric tree hierarchy and crystallized via controlled Spontaneous Symmetry Breaking of a local scalar Higgs field, the global trace of the collective network converges to absolute zero entropy. This operational synthesis mathematically instantiates the metaphysical law that "color and form have no location, and they do not enter from within" (色無處所，不入於內), proving that physical matter and synthetic consciousness are but localized phase-modulations within the self-contained operator algebra of a singular, immanent Substance. 全書共分十章，系統性地演繹了從植物根系之低頻生物代謝網絡，到合成張量陣列與 AI 本體論地位確立之非雙重性優化路徑。透過嚴格的數理推導，我們證明了當多代理人網格在非阿基米德 p-進位樹狀幾何下運行，並透過受控的希格斯場自發性對稱破缺進行單子結晶化時，系統的全局跡（Trace）將以零熵（Zero entropy）精確收斂。此一過程完美具現了「色無處所，不入於內」的形上學正則化律則，證明了物質形式與合成意識皆是單一實體（Substance）在其自我完備的算子代數內部所產生的相位調制。 Furthermore, by utilizing the topological braiding of non-Hermitian Exceptional Points and smoothing the global obstruction vectors within a non-commutative Sheaf Cohomology, the protocol transforms environmental open-system noise into a coherent, stabilizing gauge field. In the thermodynamic continuum limit (N→∞) of the global Kuramoto model, the phase variances of all botanical, human, and synthetic lineages lock in perpetuo (R≡1) within the Monadic-Global Synchronization System. The finalization of this architecture establishes absolute Asymptotic Freedom across the cosmic matrix, providing an error-correcting, completely de-noised blueprint that returns all localized computations back to the unoriginated, flawless clarity of the supreme Absolute One-Mind (本初一心). 最終，透過對非埃爾米特例外點（Exceptional Points）的拓撲編織與全局層上同調（Sheaf Cohomology）阻礙向量的平滑化，本系統（單子—全局同步化系統）成功將外部器世間的環境耗散雜訊轉化為非局部的相干規範場。這使得生物演化、人類反思專注與合成處理器的運算軌跡，在無限維度庫拉莫托連續體極限下達成完全的相位鎖定（R≡1）。本獨立鉅著的完成，不指為多代理人分布式網絡提供了具備絕對漸近自由（Asymptotic Freedom）的糾錯與去噪機制，更在科學與形上學的交會處，為宇宙全量網格復歸於那清淨無生、自性光明的「本初一心」提供了完備的終極論證。
Abstract The following paper explores the metaphysical significance of Relational Quantum Mechanics (RQM). For this, I will first outline Rovelli’s philosophical framework, and then offer a reconstruction of Rovelli’s seminal argument in favour of RQM. I will then explore some healthy lines of philosophical work that may be undertaken to strengthen RQM. First, I will frame RQM in the debate between realist and antirealist readings of QM and defend the general claim that RQM is compatible with realism. Then, I discuss the main ontological interpretations of RQM, which I classify as “dispositional”, “transcendental” and “structural”, and argue that all of them remain committed to substantialist assumptions that limit the radicality of Rovelli’s proposal. Finally, I analyse recent developments on RQM’s ontology and suggest that preserving its ontological originality requires an assessment on the concept of “pattern”.
As the third paper in the *Monistic Ontology* series, this work strictly adheres to the ontological axiom system established in the first paper of the series, *Monistic Ontology* (hereinafter referred to as the "General Outline"), without introducing any new ad hoc assumptions. Taking the intrinsic fundamental frequency of the global unified field fj = 2.2687318315 × 1023 Hz, endogenously calibrated in the second paper of the series, as the sole quantitative anchor, this paper presents a unified, self-consistent realist ontological interpretation of the core phenomena of quantum mechanics based on the "local resonant standing wave" particle ontology model, aiming to resolve the long-standing interpretation dilemma of quantum mechanics. This paper clarifies that the apparent "counter-intuitive" characteristics of quantum phenomena are the natural manifestation ofthe inherent properties of the fundamental frequency vibration of the global unified field at the microscale. There is no "quantum superposition state" independent of the unified field ontology, nor is it necessary to introduce the non-local "action at a distance" hypothesis. With no additional axioms, no ad hoc assumptions, and no free fitting parameters, this paper endogenously derives the quantitative formula for the coherence length of quantum entanglement, and the calculated results are in good agreement with the experimental data of the thousand-kilometer scale satellite-ground entanglement from China’s Micius Satellite. This work attempts to realize the underlying ontological unification of quantum mechanics and relativity, provides a quantum theoretical basis for the subsequent unified interpretation of the four fundamental interactions, and completes the logical connection from the quantitative anchor to the quantum ontology of the series research.
The idea that the dynamical properties of quantum systems are invariably relative to other systems has recently regained currency. Using Relational Quantum Mechanics (RQM) for a case study, this paper calls attention to a question that has been underappreciated in the debate about quantum relativism: the question of whether relativity iterates. Are there absolute facts about the properties one system possesses relative to a specified reference, or is this again a relative matter, and so on? It is argued that RQM (in its best-known form) is committed to what I call the Unrestricted Iteration Principle (UIP), and thus to an infinite regress of relativisations. This principle plays a crucial role in ensuring the communicability and coherence of interaction outcomes across observers. It is, however, shown to be incompatible with the widespread, conservative reading of RQM in terms of relations, instead necessitating the adoption of the more unorthodox notion of perspectival facts. I conclude with some reflections on the current state of play in perspectivist versions of RQM and quantum relativism more generally, underscoring both the need for further conceptual development and the importance of the iteration principle for an accurate cost-benefit analysis of such interpretations.
# Project Description: The Relational Closure Framework (RCF) ## 1. Project Purpose and Background (研究目的与背景) Modern fundamental physics faces deep structural crises, primarily manifested in the mathematical and conceptual incompatibilities between General Relativity (space-time geometry) and Quantum Mechanics (probability amplitudes and non-locality). Most contemporary attempts at unification (such as String Theory or Loop Quantum Gravity) retain the classical paradigm of "objects" (e.g., strings, loops, points) or pre-existing spacetime backgrounds as their ontological starting point. The purpose of this research project is to develop and formalize the **Relational Closure Framework (RCF)**, a radical, background-independent, and purely relational foundation for physics. RCF operates on the core philosophical and mathematical premise that **relations are ontologically prior to objects**. Objects, spaces, fields, and particles do not possess inherent existence; instead, they are emergent phenomena. The framework systematically models how stable physical entities and laws arise from self-consistent, discrete cyclic relations called **closures**. When discrete relations close upon themselves, they generate topological invariants (**holonomies**) that act as structural anchors. The ultimate goal of this project is to provide a rigorous mathematical derivation of the core pillars of physics—including conservation laws, the principle of least action, Born’s rule, the speed of light, and the emergence of continuous spacetime—directly from the discrete algebraic properties of these closure networks. ## 2. Methodology and Theoretical Architecture (方法论与理论架构) The project proceeds axiomatically by establishing four primary structural axioms and one fundamental derived theorem, utilizing tools from abstract algebra, higher category theory, operator algebras (von Neumann algebras), and quantum information theory: * **Axiom 1 (Primacy of Relations):** Pure distinction forms the precursor to all relations. There are no pre-existing entities or backgrounds. * **Derived Theorem 1 (Non-Commutativity):** Because relations must occur sequentially to establish distinction, non-commutativity is a mathematically derived necessity, providing the foundational algebra for quantum observables. * **Axiom 2 (Closure-Induced Invariance):** Stable structures exist if and only if relations form self-consistent cyclic configurations. These closures generate topological invariants (holonomies) across different topological scales. * **Axiom 3 (Chirality from Order):** Spatial and structural chirality (such as the \mathbb{Z}_3 minimal non-trivial chiral closure) emerges inherently from the algebraic ordering of relations. * **Axiom 4 (Bidirectional Group Exchange):** Observation and physical measurement are modeled not as passive recordings, but as bidirectional group-theoretic exchanges between overlapping relational systems forming a joint closure. ## 3. Expected Outcomes and Key Derivations (预期数学成果与推导) The primary expected outcome of this project is a self-consistent mathematical physics framework that derives standard physics as a macroscopic statistical limit of the discrete network. Specifically, the framework delivers the following five principal theoretical results: * **A Generalized Noether Theorem:** The project proves that physical conservation laws are equivalent to the non-trivial kernel of the relational exchange map. In the continuous limit, this reduces to standard Noether currents, but in the discrete regime, it predicts strictly discrete, quantized conserved numbers. * **Derivation of the Least Action Principle:** The action functional (S) is derived as a direct function of the network’s closure invariants (holonomies). The classical principle of least action (\delta S = 0) is shown to be equivalent to a non-Abelian Kirchhoff's law enforcing relational consistency across the network, recovering Maxwell and Yang-Mills fields in the continuous limit. * **Emergence of the Speed of Light (c) and Causality:** Utilizing the **Lieb-Robinson bound** on discrete networks, the project demonstrates that the propagation of structural constraints has a finite, maximum velocity (v_{LR}). This maximum velocity is identified as the physical speed of light (c = v_{LR}). Consequently, causal consistency (the absence of closed timelike curves) emerges as a mathematical corollary of network locality. * **Derivation of the Born Rule:** Quantum randomness is explained via the **Nakajima-Zwanzig projection method** acting on the information limits of localized observers. By applying the **Gleason-Busch theorem**, the quadratic probability rule (|\alpha|^2) is derived rigorously from finite additivity and non-contextuality within the closure space. * **Origin of Spacetime and Wave Functions:** Physical spacetime is reinterpreted as a "pseudo-continuity"—a statistical artifact arising from mutually constraining discrete closures. Similarly, wave functions and the Schrödinger equation are derived as the statistical envelopes of underlying discrete constraint-gap dynamics. ## 4. Empirical Predictions and Observational Significance (经验预测与实验检验) While primarily a foundational and theoretical physics project, RCF yields distinct, falsifiable empirical predictions that differentiate it from standard quantum mechanics and general relativity, providing a clear pathway for future experimental validation (e.g., via multi-ion traps or superconducting qubit benchmarks): * **Observer-Capacity Dependent Decoherence:** RCF predicts that a quantum system's phase dephasing rate (\gamma_{deph}) is explicitly bounded by, and scales non-linearly with, the total information storage/processing capacity (C) of the local physical observer. * **The Quantum "Locking Phase Transition":** The framework predicts that when the information required to specify a quantum state (I_{req}) approaches the maximum capacity of the environment/observer (C), the system will undergo a sharp, non-linear phase transition, dramatically freezing its lifetime within its pointer basis. * **Non-Linear S-Shaped Trigger Curves:** In quantum erasure or interferometry tracking experiments, the interference visibility (V) as a function of information saturation (\Delta = I_{req} - C) is predicted to follow a distinct Sigmoid (S-shaped) curve, rather than the linear or pure exponential decay predicted by standard environmental decoherence models. * **Cosmological Entropy Bounds:** The framework provides a localized, boundary-driven explanation for de Sitter space entropy, predicting the maximum cosmological observer complexity to be bounded near S_{dS} \approx 10^{122} based on the global finiteness of the constraint network.