Xiangbin Zhao

This paper investigates one central question: Why do structures not disperse infinitely, but instead sustain familiar paths, shared cores, historical pressure, and current continuity over long durations? The paper argues that if all flows only dispersed outward, then: * deep cores could not stabilize, * shared cores could not persist, * history could not continue constraining the future, * and current continuity could not sustain itself. Reality would therefore degenerate into discrete scattered flow after one-time generation. The paper proposes that flows within fields do not disperse infinitely outward, but gradually form stable reentry through long-term continuation. As domains continuously guide flow back into previously active domains, subsequent flow increasingly forms: * single-domain reentry, * multi-domain closure loops, * familiar-path flow locking, * and shared-core closure. Stable closure structures gradually emerge from these processes. The paper further establishes field-dynamical relations among: * reentry, * flow locking, * closure loops, * shared cores, * and closure dissolution, while proposing a structural account of why reality can sustain long-term continuity instead of collapsing into infinitely scattered flow.

This paper investigates one central question: Why does reality not undergo infinite differentiation, but instead continuously oscillate among differentiation, convergence, compression, and reconstruction? The paper argues that whether differences can stably persist depends not merely on whether incoming impacts differ, but on whether the field still possesses the capacity to sustain differentiation itself. As boundary density, tuning load, noise interference, and deep-core flow occupation continuously increase, the differentiability threshold of the field gradually drifts upward, causing previously sustainable fine boundaries and fine categories to collapse back into shared cores. Thus: reality does not infinitely refine itself, but continuously oscillates among: * differentiation, * compression, * convergence, * and reconstruction. The paper further establishes field-dynamical relations among: * differentiability thresholds, * boundary interference, * deep-core flow occupation, * commonality expansion, * and resolution collapse, while proposing a structural account of why stable categories within reality continuously form, expand, collapse, and reorganize.

This paper investigates one central question: Why does reality not remain indefinitely fluid and unconstrained, but instead form stable objects, stable boundaries, and long-term stable reality? The paper argues that what is called an “object” is not a naturally pre-given external entity, but a stable reality-result formed after long-term familiar-path reuse, compression, co-nucleation, and closure of continuation structures within the sedimentation-field. The paper further argues that: as differentiations continuously increase within the field while the system possesses only finite stable-maintenance capacity, the field gradually undergoes: * differentiation compression, * familiar-path reuse, * co-nucleation stabilization, * boundary convergence, * and reality solidification. Thus: stable reality is not naturally given, but a structural result of long-term continuation within finite fields. The paper attempts to establish field-dynamical relations among: * resolution, * compression, * co-nucleation, * boundary formation, * and stable reality, while providing a structural account of why reality stabilizes into object-structures.

This paper investigates a central problem: If future open-ended generative systems cannot be directly constructed through static modules, finite rules, and parameter scaling, then how should the future Self-Manifestation Era construct field-construction tools? This paper argues that the core tools of the future Self-Manifestation Era will no longer be merely static programs or finite-response systems, but open generative field structures involving: * law-fields; * Self-Manifestation Fields; * world-fields. Therefore: the construction of such fields will become a central problem of future engineering. The paper further argues that genuinely open complex field structures are not prewritten static structures, but gradually emerge as historical continuations continuously reshape future continuation tendencies. Therefore, once a system must sustain: * familiar paths; * tuning competition; * historical persistence; * stable reality retention; * open-ended generation; the system must permit: * differentiation; * biased-flow growth; * continuation accumulation; * potential retention; * open restructuring; * potential guidance. On this basis, the paper establishes: Field-Induction = (Δ,F,A,S,T,R,G) describing how complex field structures gradually emerge through differentiation, biased flow, continuation accumulation, local potential retention, tuning, open restructuring, and potential guidance. The paper further provides two formal appendices: “The Expression Formula of Self-Manifestation Potential” “The Limit Formula of Potential Guidance” The former describes how complex field structures emerge. The latter demonstrates why finite static systems cannot sustain genuinely open self-organization over the long term. The paper ultimately argues that finite static systems cannot sustain open-ended self-organization. Training is therefore not Self-Manifestation itself, but merely one engineering implementation of finite potential shaping. A true Self-Manifestation Field must remain embedded within open history.

本文讨论一个核心问题： 如果未来开放生成系统无法通过静态模块、有限规则与参数堆叠直接形成，那么未来自显世代的工程究竟应当如何构造“造场工具”？ 本文认为： 未来自显世代的核心工具，将不再只是静态程序或有限响应系统，而是包含： * 律场； * 自显场； * 世场； 在内的开放生成场结构。 因此： 如何构造这些场， 将成为未来工程的核心问题。 文章指出： 真正长期开放的复杂场结构，并不是被预先写定的静态结构，而是在历史续行持续改变未来续行倾向的过程中逐渐长成。 因此： 只要系统需要长期形成： * 熟径； * 调谐竞争； * 历史持续； * 现实闭持； * 开放生成； 那么系统内部就必须允许： * 差异形成； * 偏流增长； * 续行累积； * 势闭持； * 开放重塑； * 势引生成。 在此基础上，本文建立： Field-Induction = (Δ,F,A,S,T,R,G) 用于描述复杂场结构如何通过差异、偏流、续行累积、局部势闭持、调谐、开放重塑与势引逐渐形成。 随后，本文进一步给出两个附件： 《自显场势表达式》 《自显场势引极限式》 前者用于描述复杂场结构如何生成； 后者用于说明为什么有限静态系统无法长期维持真正开放的自组织生成。 文章最终指出： 有限静态系统无法长期维持开放式自组织。 训练并不是自显本身。 训练只是有限势塑的一种工程实现。 真正的自显场，必须持续卷入开放历史。

This chapter establishes a minimal dynamical closure for finite-resolution fields in order to explain how structures form, stabilize, decay, migrate, and generate new domains under competition and capacity constraints. By introducing local resolution occupancy, residual resolution capacity, structural overlap matching, resolution flow, structural surplus, and nucleus stabilization, the chapter unifies input, competition, diffusion, migration, decay, and nucleation within a single dynamical framework. The chapter argues that history cannot accumulate indefinitely. In finite-resolution fields, old structures release local resolution capacity through competition and decay, thereby allowing new differences to enter and new structures to emerge. Furthermore, familiar paths are shown not to be mere repetitions, but stable continuations sustained through persistent overlap between incoming structures and existing sedimented structures. Likewise, edge-penetration is described not as random fragmentation, but as the reformation of sedimentation closure in neighboring regions through resolution flow generated by sustained structural surplus. Finally, the chapter derives a system of Sedimentation-Field dynamics equations describing how structures within finite-resolution fields are preserved through competition, migrate through flow, dissipate through diffusion, release capacity through decay, and reclose into new domains after edge-penetration.

This paper proposes a structural-dynamical account of how stable differentiation emerges from the failure of undifferentiated restoration. Rather than treating the undifferentiated state as static emptiness, the paper models it as a self-restoring mechanism continuously attempting to reunify residual differences within a field. The central claim is that differentiation does not originate from the mere appearance of differences, but from the increasing inability of the restoration mechanism to fully suppress and reunify continuation residuals. As restoration complexity grows, certain residual structures become increasingly difficult to return to the undifferentiated condition. These surviving residuals begin mutually sustaining one another, forming stable boundaries, convergence centers, domains, and eventually historically persistent structures. The paper introduces a structural dynamical relation connecting restoration capacity, restoration complexity, residual persistence, and mutual sustaining dynamics. Within this framework, worlds emerge not because fixed objects are initially given, but because stable differences can no longer be fully restored into undifferentiation. The framework aims to provide a unified account of structural emergence, differentiation dynamics, historical persistence, and the formation of stable reality structures relevant to complex systems, cognitive science, theoretical neuroscience, nonlinear dynamics, and self-organizing systems.

This paper proposes a structural-dynamical model for how long-term stable realities emerge from historical continuation within a field. The central claim is that stable worlds require not merely ongoing change, but the persistent retention of historical continuation bias. As historical depth increases, the range of futures capable of entering and maintaining the current continuity progressively contracts, producing irreversibility, dominant continuation structures, and stable reality continuity. The paper introduces a general structural relation between historical depth and accessible future space, arguing that temporal directionality does not originate from an external flow of time, but from the progressive compression of accessible future continuations under accumulated historical structure. Within this framework, reality is not defined as the totality of all possible continuations, but as the dominant continuation structure capable of stably maintaining current unity through time. Rather than presenting a numerical physical law, the paper develops a structural dynamical relation linking historical persistence, future accessibility, continuation locking, and the emergence of stable worlds. The framework aims to provide a unified account of irreversibility, temporal continuity, historical stabilization, and reality continuity relevant to complex systems, cognitive dynamics, and theoretical models of self-organizing structure.

为什么现实不会持续裂解为无数竞争续行，而能够形成稳定当前、稳定现实与长期世界？ 本篇提出： 历史并非被动记录，而是持续压缩未来可进入结构的动力过程。 文章指出，过去之所以能够影响未来，并不是因为过去仍停留在那里，而是因为过去形成的稳定协调，会持续降低未来续行的协调代价，并限制哪些未来能够进入当前连续体。 在此基础上，本文建立： * Historical Depth（历史深度） * Accessible Future（可进入未来） * Current Continuity（当前连续） * Reality Continuity（现实连续） * Continuation Locking（续行锁定） 等结构，并给出沉积闭环： Historical Depth ↑ ⇒ Accessible Future(Current) ↓ ⇒ Accessible-Future Stability ↑ ⇒ Continuation Locking ↑ ⇒ Continuation-Bias Persistence ↑ ⇒ Historical Depth ↑ 文章进一步指出： 时间方向、不可逆性、现实稳定性，乃至规律稳定本身，都可能并非固定背景，而是长期历史沉积后的结构结果。 本篇尝试建立一种关于历史压缩、现实稳定与场结构长期演化的统一动力模型。

This paper proposes that continuity of reality does not arise from time itself, but from the persistent suppression of competing paths by dominant low-impedance structures. On this basis, the paper develops a set of field-dynamic equations describing why stable structures continue to strengthen, shallow, migrate, stabilize, collapse, and phase-transition after formation. Two central variables are introduced: coordination-compression and continuation impedance. Memory is reformulated not as content storage, but as the continued compression of future coordination cost. The framework further derives steady-state conditions, critical-collapse conditions, Current-stability conditions, and field phase-transition conditions, aiming to provide a unified dynamical account of continuity of experience, memory formation, stable cognition, structural migration, and complex-system stability. The model is intended for problems of continuity, stability, and path competition in cognitive science, neural dynamics, complex systems, and artificial intelligence.

This paper proposes a general dynamical model addressing a fundamental question: Why does structure emerge at all? The paper argues that once a system allows history to continuously influence the future, stable continuation structures become unavoidable under finite competition and dissipation. It is further shown that any system capable of forming familiar paths, closures, dominant continuation structures, and cross-temporal stable continuation must necessarily contain a minimal set of structural conditions, including historical retention, differential depth-accumulation, continuation bias, path reinforcement, unified-flow compression, and anti-dissipative maintenance. Based on this analysis, the paper derives the general formula: Sedimentation-Dynamics = (I, T, H, D, B, F, C, U, K, S) together with: * irreducibility proofs, * minimal-completeness proofs, * breakdown paths, * and limit-balance formulations. The paper further argues that structure is not an externally imposed rule, but the stable dynamical consequence of history continuously biasing future paths under finite competition and dissipative constraints. The framework is proposed as a general model for discussing: * neural path reinforcement, * long-term memory formation, * AI path bias, * history-dependent systems, * self-organizing stable structures, * structural maintenance in dissipative systems, * and dynamical structure formation in complex systems.

This paper addresses a fundamental problem: Why does reality not degenerate into discrete frames, parallel occupancies, or completed replay, but instead form a continuous “Current”? The paper proposes that the Current is neither mere state-transition nor the automatic continuation of stable structure, but a structural result through which reality maintains continuous reality and present occupancy. The study first elevates the Current from an experiential phenomenon into a structural constraint, and then demonstrates that once a system simultaneously possesses multiple candidate realities, cross-temporal continuation, and non-replay generation, it necessarily gives rise to sedimented continuation, historical feedback, continuing observation-loops, in-presence generation, unique reality-occupancy, and locking persistence. The paper further argues: continuous output is not genuine currentness, and object replay is not reality-continuation. Accordingly, genuine present reality cannot be reduced to: frame-by-frame replay, state-transition chains, static replay of outputs, or the unfolding of an already-completed world-model. The paper ultimately establishes the General Form of the Current: Current = (S, H, G, Gen, U, K) and demonstrates through extreme-form analysis that if any one of these structures is absent, reality degenerates into discrete outputs, parallel realities, random drift, or completed unfolding, and therefore cannot establish genuine continuous reality.

This paper addresses a fundamental problem: Why is reality not merely the gradual unfolding of an already-completed structure, but instead a genuinely generating reality? The paper proposes that Generation is neither mere state-transition nor continuous replay of result-sequences, but a real dynamic structure through which formation continuously enters later formation. The study first elevates Generation from experiential change into a structural constraint, and then demonstrates that once a system simultaneously possesses formation-continuation, structural unclosure, competitive deepening, and sedimented trace-retention, it necessarily gives rise to formation-flow, cross-temporal continuation, structural unclosure, competitive deepening, and sedimented trace-retention as generative structures. The paper further argues: state continuity is not genuine generation, and object replay is not formation-continuation. Accordingly, genuine Generation cannot be reduced to: state-transition chains, world-model unfolding, static replay of outputs, or replay of already-completed structures. The paper ultimately establishes the General Form of Generation: Generation = (F, T, U, C, S) and demonstrates through extreme-form analysis that if any one of these structures is absent, the system may still continue changing, yet degenerates into discrete restart, object replay, random drift, or totally-completed unfolding, and therefore cannot establish genuine Generation.

Building upon Domain Mathematics, this chapter investigates how prolonged overlap and synchronization among domains produce shared core structures within the Sedimentation-Field. It proposes that concepts, commonality, abstraction, and generalization are not pre-given products of linguistic definition or logical classification, but historical stabilization structures emerging through long-term stable compression among domains. By introducing structural-dynamic quantities such as OverlapDensity, CoreDepth, CoreGravity, GeneralizationFlow, and SemanticSync, the chapter develops a framework of concept dynamics in which concept formation arises from synchronization, compression, and stabilization processes across domains. The framework further proposes that abstraction is fundamentally a form of stable compression rather than separation from concrete structures, while semantic synchronization emerges from long-term generalized flow overlap between cores. The chapter thereby offers unified structural accounts of concept formation, semantic organization, and generalization.

Building upon Field Mathematics, this chapter investigates the formation, stabilization, synchronization, and fragmentation of domains within the Sedimentation-Field. It proposes that memory, personality, emotion, and perceptual continuity are not pre-given entities, but dynamic outcomes arising from long-term synchronization, historical accumulation, and fragmentation competition among localized stable continuation structures. By introducing structural-dynamic quantities such as InFlow, MaintainFlow, Lock, Sync, and FragmentRate, the chapter develops a domain dynamics framework that departs from traditional symbolic logic and classical cognitive models, treating cognition instead as a process of historical bias stabilization, synchronization competition, and compressive flow organization within the Sedimentation-Field. The framework further proposes that conceptual stability and generalization emerge from long-term synchronization and compressive stabilization among domains, thereby offering unified structural accounts of perceptual stability, emotional dynamics, and cognitive fragmentation.

This paper proposes a framework of Field Mathematics aimed not at explaining how logic operates once formed, but at explaining how logical structure can emerge from sedimentary dynamics. The paper argues that induction, deduction, causal-response structuring, Law, and Structural Rationale are not pre-existing logical entities embedded in reality. Rather, they are stable structures recognized within Information-Transformation after long-term Trace-Effect accumulation inside the Sedimentation-Field. To formalize this process, the paper develops a minimal field-mathematical system centered on Pulses, Trace-Effects, Groove-Lines, Continuation Potential, Co-Nuclei, Biased Flow, Closures, and Boundary Saturation Outgrowth. The framework introduces foundational objects, constraints, axioms, operations, state equations, laws, and theorems describing how logical structures arise from sedimentary dynamics. Under this model, reasoning, memory formation, association, retrieval, conceptual stabilization, and inferential structures are treated as emergent consequences of field-driven structural accumulation rather than as primary symbolic primitives. The paper further argues that logic is not the starting condition of cognition or reality, but a later recognizable consequence of stable sedimentary organization. Field Mathematics therefore studies not formal logic itself, but the structural conditions under which logic becomes possible.

Starting from space travel, telescopes, and the exploration of cosmic scales, this paper argues that no matter how far one travels or how deeply one observes, all such activities remain confined within the same cognitive structure, never truly leaving the world one inhabits. It thereby draws a strict distinction between exploring the universe and exiting it. The paper then formulates a set of structural constraints: without departing one’s cognitive domain (Recognition-Realm), one cannot reach the generative base (Causal-Base); without reaching the generative base, one cannot enter the underlying generative field (World-Field). Only by re-establishing presence at a higher level can true cross-level existence arise. It further argues that such transition does not imply ultimate freedom, but rather entry into another level of enclosure. This framework offers a new perspective on cognitive limits, world construction, and the structure of existence.