Xiangbin Zhao

This paper investigates one central question: Why are some fields able to sustain high resolution and complex continuation over long durations, while others gradually move toward compression, solidification, familiar-path locking, and reality rigidity? The paper argues that fields are not infinitely open empty domains. Within fields: * familiar paths, * shared cores, * infiltration, * compression, * and deep sedimentation continuously occupy the effective domains available for the formation of new continuation. Thus: the decisive factor of a field is not its total size, but the proportion of effective continuation volume that still remains open for new continuation. The paper proposes that rigidity, solidification, declining creativity, and structural lock-in within reality are not merely psychological phenomena, but structural consequences of long-term decline in field-volume ratio. As familiar paths deepen, infiltration increases, compression strengthens, and tuning solidifies, fields become increasingly inclined to: * interpret new input through old structures, * reuse existing familiar paths, * compress newly emerging differentiations, * and reinforce reality lock-in. As a result: new continuation becomes increasingly difficult to stabilize. When effective continuation volume continuously declines while new continuation still enters the field, edge-penetration begins occurring, allowing new structures to rupture outward once again. The paper further establishes field-dynamical relations among: * field volume, * effective continuation domains, * field-volume ratio, * infiltration occupation, * familiar-path locking, * and reality solidification, while proposing a structural account of why conservatism, rigidity, declining creativity, and structural lock-in within reality continuously intensify through historical sedimentation.

This paper investigates one central question: Why do continuation-potentials within sedimentation-fields fail to remain permanently separated, instead gradually forming infiltration, shared cores, compression, and stable reality structures? The paper argues that infiltration is neither noise nor erroneous mixing. Rather, infiltration denotes: the condition in which multiple continuation-potentials, after long-term continuation within the same finite field, become increasingly unable to remain fully separated, gradually forming partial shared continuation. Thus: infiltration is neither complete independence nor total collapse, but a stable mutual penetration gradually emerging among continuation-potentials. The paper proposes that as long as multiple continuation-potentials coexist within the same finite field over long durations, they inevitably develop varying degrees of infiltration through: * familiar paths, * deep sedimentation, * tuning, * reentry, * compression, * and boundaries. As infiltration quantity and infiltration complexity continuously increase, continuation pressure within the field progressively rises. Moderate infiltration contributes to: * shared-core formation, * familiar-path reuse, * and stable sedimentation. Excessive infiltration, however, leads to: * increased compression, * declining resolution, * growing boundary-convergence pressure, * and edge-penetration. The paper further establishes field-dynamical relations among: * infiltration, * infiltration complexity, * continuation pressure, * shared cores, * compression, * and edge-penetration, while proposing a structural account of why stable structures within reality are not naturally formed from isolated differentiations, but gradually stabilize through long-term infiltration, sedimentation, compression, and rupture.

This paper investigates one central question: Why do differentiations within reality fail to remain indefinitely independent, instead continuously tending toward compression, shared cores, and stable structures? The paper argues that compression is neither artificial classification nor observational simplification. Rather, compression denotes: the process by which multiple differentiations that previously required independent stabilization begin sharing stable maintenance relations. Thus: as long as differentiations continuously increase while the field possesses only finite stabilization capacity, the field must inevitably begin compressing differentiations. The paper proposes that compression is not merely a secondary consequence, but a necessary dynamical process within finite fields. As differentiation overlap, stabilization complexity, and maintenance pressure continuously increase, the field gradually forms: * familiar-path flow absorption, * shared-core compression, * stable reuse, * structural conservatism, * and compression limits. Meanwhile: when old compression structures can no longer stably sustain newly entering differentiations, edge-penetration and structural dissolution begin occurring, allowing new structures to emerge again. The paper further establishes field-dynamical relations among: * stabilization pressure, * independent maintenance capacity, * compression intensity, * shared-core formation, * compression collapse, * and compression dissolution, while proposing a structural account of why categories, familiar paths, shared cores, and stable structures within reality continuously evolve through cycles of compression, stabilization, and rupture.

This paper investigates one central question: Why can reality not indefinitely sustain newly generated differentiations, and why do fields eventually reach resolution limits? The paper argues that whether differences can stably persist depends not merely on whether incoming impacts differ, but on whether the field still retains the capacity to stably sustain newly generated differentiations. The paper proposes that resolution is neither the amount of information nor the fineness of observation itself. Rather, resolution denotes: the degree to which a domain, under existing sedimentation, overlap, and tuning conditions, can continue stably sustaining newly generated differentiations. As familiar-path solidification, compression saturation, shared-core deepening, and boundary loading continuously increase, the resolution margin of the field gradually declines. As a result: new differentiations become increasingly unable to form stable subdivisions and are gradually compressed back into existing domains. When the resolution margin becomes exhausted while new differentiations continue entering, boundary pressure begins to rupture outward, eventually producing edge-penetration and the formation of new structures. The paper further establishes field-dynamical relations among: * resolution margins, * compression saturation, * domain saturation, * edge-penetration, * resolution collapse, * and resolution recovery, while proposing a structural account of why boundaries, categories, and new structures within reality continuously undergo stabilization, compression, rupture, and reorganization.

This paper investigates one central question: Why do certain paths become extremely easy to continue, while certain structures become extraordinarily difficult to break? The paper argues that stable structures within reality persist not merely because their sedimentation is deeper, but because they have formed sustained continuation advantages over subsequent flow. The paper proposes that “familiarity” is not static depth itself, but the degree to which a path regains priority for continuation within the field. As historical deepening, reentry frequency, low-resistance continuation, and flow occupation advantages continuously reinforce one another, certain paths gradually form stable familiar paths that continue receiving priority access to subsequent flow. As a result, reality begins to exhibit: * path dependence, * historical inertia, * familiar-path bias, * and anti-mutation stability. The paper further establishes field-dynamical relations among: * familiarity, * reentry, * flow occupation, * familiar-path degradation, * familiarity migration, * and familiarity differentials, while proposing a structural account of why dominant structures within reality can remain stable over long durations, yet gradually migrate through historical continuation.

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.