Xiangbin Zhao

Drawing on sedimentation field dynamics, this paper redefines public opinion from an aggregation of views to a phase-transition structure of continuation flows on topic paths within the social field. The central claim is that when the opinion flow concentration intensity (OpinionFlow) of a topic path exceeds the critical threshold θ_opinion, a positive feedback mechanism is triggered and continuation flows accelerate their convergence to form a self-organizing opinion structure; θ_opinion ∝ φ_{F_S} / K_{F_S}, so in solidified social fields the concentration threshold is lower and public opinion more easily erupts. The paper derives the complete dynamic equation for concentration (incorporating the concentration seed Seed, saturation constraint, and threshold-activated suppression effect), identifies three forms of concentration (event-driven, accumulative, suppression-induced), and establishes three theorems: (1) Opinion Concentration Formation Tendency Theorem — under conditions of Familiarity asymmetry and non-zero Seed, the system systematically tends toward concentration formation; (2) Concentration Argument-Resistance Theorem — a single individual field’s logical argument cannot break an established concentration; an alternative topic requires Shock exceeding T_replace(T) to trigger genuine topic replacement; (3) Suppression Rebound Theorem — suppression below the replacement threshold triggers rejection and concentration returns in stronger form after suppression (the dynamical formalization of the Streisand Effect). The fundamental path to changing public opinion is not providing better arguments but changing the social field’s structural parameters or introducing a new topic event exceeding the replacement threshold.

Drawing on sedimentation field dynamics, this paper advances the relationship between the individual and society from descriptive accounts of socialization or agency to the level of dynamic equations. The central claim is that individual fields and the social field are engaged in a continuous contest under tension — the social field exerts assimilation pressure (AssimPress ∝ Cpl · K_{F_S} · FamOverlap) that tends to absorb individual fields, while individual fields resist absorption through differential-generative pressure (P_Δ). The paper derives the complete dynamic equation for coupling tension (CplTension = P_Δ − AssimPress), identifies three states (assimilation dominance, tension equilibrium, differentiation dominance), and establishes three theorems: (1) Tension Equilibrium Instability — trending increase in K_{F_S} systematically drifts the equilibrium point toward assimilation dominance; (2) Forced Assimilation Rejection — assimilation pressure exceeding the tolerance threshold triggers a rejection mechanism that reduces actual assimilation effect; (3) Innovation Concentrated in the Tension-Equilibrium Band — genuine structural social innovation systematically originates from individual fields in the equilibrium state that remain coupled while retaining differential-generative margin. A corollary establishes the Innovation Equilibrium Band Compression Effect: the tension-equilibrium band systematically narrows in mature social fields, providing a unified dynamic source for bureaucratization, ideological homogenization, and algorithmic domestication.

Drawing on sedimentation field dynamics, this paper defines social strata as continuation-bias structures generated by the solidification of Familiar Route depth differentials (ΔStratum) among individual fields within the social field — rather than as descriptive consequences of unequal resource distribution. The central claim is that the root of strata is FamOverlap differential, not resource quantity: pure resource equalization that does not simultaneously change the structural overlap (FamOverlap) between individual fields and the social field’s high-Familiarity paths is insufficient to eliminate stratum solidification. The paper derives the Stratum Familiar Route operator (SFR, FlowShare-weighted and normalized), the stratum mobility cost equation (MobCost), the stratum solidification self-reinforcing loop, three observable forms of solidification (cultural capital accumulation, network coupling, capacity occupation), and three theorems (Stratum Solidification Tendency, Stratum Mobility Resistance, Pure Resource Equalization Insufficient to Eliminate Strata). The dynamic equations incorporate a policy correction term (PolicyCorrection) and a path decay term (Decay_SFR), enabling the model to account for both Nordic stratum mobility improvements and historical stratum reconstruction.

Drawing on sedimentation field dynamics, this paper defines institutional lock-in as a dynamic inevitability that emerges once an institution’s Familiar Route depth (Familiarity) and flow-share proportion (FlowShare) jointly exceed their respective lock-in thresholds — at which point the institution actively suppresses the generation of alternative structures, rather than merely persisting through inertia or interest-group protection. The central claim is: reform that does not change Familiar Routes does not change institutions. Any reform attempt below the replacement threshold (T_replace) will not only fail but trigger rebound, leaving the institution harder to change than before. The paper derives the institutional lock-in operator (Lock), the replacement cost equation (RepCost), the self-reinforcing loop, three levels of lock-in (soft, hard, deep), and three theorems (Lock-in Inevitability, Reform Rebound, Deep Lock-in Directional Constraint). All propositions are accompanied by breakdown conditions.

Drawing on sedimentation field dynamics, this paper defines social inertia as a structural inevitability of high compression-strength (K_{F_S}) social fields — the systematic absorption of new inputs into existing Co-Nuclei — rather than a product of cultural or political choice. The central claim is that reform perception does not imply structural transformation: only inputs that cause K_{F_S} to decline or Co-Nucleus restructuring constitute genuine structural change, while any input below the replacement threshold is absorbed and may trigger an inertia rebound. The paper derives the dynamic equation for social inertia intensity, its self-reinforcing loop, three observable forms, and three theorems (Inertia Inevitability, Reform Absorption, Inertia Scale Law). All propositions are accompanied by breakdown conditions.

This paper proposes a minimal dynamical framework for explaining how stable social structures emerge. Conventional social theories often define society as a collection of individuals, institutions, or shared norms. Such approaches describe social organization but do not explain a more fundamental question: why stable supra-individual structures arise and persist. The framework proposed here argues that social structure is not reducible to individual aggregation. Instead, stable social organization emerges when sustained interactions among individuals generate persistent shared structures whose maintenance no longer depends on any single participant. Three minimal formation conditions are proposed: sustained interaction density, stable shared structural accumulation, and independent structural maintenance. The framework further derives consequences including structural inertia, path dependence, stability constraints, fragmentation dynamics, and long-term structural stabilization under sustained interaction. The framework attempts to explain why institutions persist, why collective norms stabilize, why social fragmentation emerges, and why historical structures constrain future social evolution. Potential applications include cognitive science, artificial intelligence, multi-agent systems, computational social science, complex systems, and large-scale structure formation research.

Why do complex systems tend to move from openness toward consolidation? Why are mature systems often more stable but less capable of renewal? Why do historical structures not simply disappear, but continue to shape later systems through residual constraints? This work proposes a dynamical model of long-term evolution in complex structured systems. The framework argues that system evolution is not random drift, but is shaped by finite capacity, differentiation-maintenance pressure, and path dependence. Under sustained input, a system tends to move from an open growth phase into a compressed consolidation phase, eventually approaching either compressive death or structural reorganization under sufficiently strong perturbation. The work further examines system vitality, paradigm shift, historical residue, structural renewal, and evolutionary closure. It argues that external perturbation is the key mechanism by which path dependence can be broken and a new evolutionary trajectory can emerge. The model aims to provide a unified explanation for cognitive rigidity, paradigm change, organizational decline, civilizational evolution, language change, complex system life cycles, and historical path dependence. This work is the concluding chapter of the Field Chapters of On Self-Manifestation. It synthesizes the dynamical relations developed in the preceding chapters and presents a long-timescale model of field evolution.

Why are some shocks absorbed by a system, while others trigger structural collapse, paradigm shift, or cascading propagation? Why are large-scale systems often more resistant to disturbance, yet capable of releasing more violent secondary effects once their core structures are penetrated? This work proposes a dynamical model of structural perturbation, system recovery, and cascade propagation. The framework argues that perturbation is not ordinary noise, but a structural shock that exceeds a system’s normal processing threshold. Whether a perturbation produces long-term structural effects depends on compression strength, openness, stable differentiation capacity, and coupling relations among systems. The work further distinguishes absorptive perturbation, reconstructive perturbation, and core-splitting perturbation, and examines how shocks may trigger structural reorganization, path-dependent recovery, paradigm shift, system collapse, and cross-system cascade propagation. The model aims to provide a unified explanation for cognitive shock, paradigm revolution, crisis propagation, organizational restructuring, post-traumatic reorganization, complex system resilience, and cascading instability. This work belongs to the Field Chapters of On Self-Manifestation and focuses on perturbation, recovery, and propagation mechanisms in complex structured systems under non-stable conditions.

Why do large-scale systems tend to become more stable but less innovative? Why can small-scale systems generate new structures more easily, while often lacking long-term stability? Why do organizations, languages, cognitive systems, and civilizations become increasingly conservative as their scale grows? This work proposes a dynamical model of the relationship between system scale and structural evolution. The framework argues that scale is not merely a measure of system size. It systematically changes the effective ranges of compression strength, openness, resolution availability, and path dependence. Under sustained input and long-term operation, large-scale systems tend to accumulate deeper historical structures, producing higher compression, lower openness, stronger familiar-path locking, and greater resistance to new structural differentiation. Small-scale systems, by contrast, tend to preserve higher openness and greater capacity for novel differentiation, but with lower structural stability. The work further distinguishes scale from hierarchy: hierarchy refers to vertical structural depth, while scale refers to horizontal capacity. These two dimensions are independent. The model aims to provide a unified explanation for organizational conservatism, cognitive rigidity, linguistic stabilization, civilizational path dependence, innovation difficulty in large systems, and the openness of small-scale adaptive systems. This work belongs to the Field Chapters of On Self-Manifestation and focuses on how system scale modifies structural formation, openness, compression, and innovation capacity.

Why does large-scale information input not automatically generate unified experience? Why can systems selectively prioritize information instead of passively receiving all available signals? Why can multiple processing pathways converge into unified objects rather than remain independent streams? This work proposes a dynamical framework for the emergence of unified experience. The framework argues that unified experience does not emerge from input alone, but requires multiple structural conditions simultaneously, including input acceptance capability, bidirectional maintenance loops, cross-process coordination, and sustained stabilization mechanisms. The framework further distinguishes between information entering a system and information becoming part of unified experience. Input dynamics, active regulation, circuit coordination, and long-term maintenance jointly determine whether unified experience can emerge. The model establishes dynamical relationships among unified experience formation, circuit coordination, input selection, structural alignment, and long-term stabilization. The framework aims to provide a unified explanation for consciousness formation, attention mechanisms, multimodal integration, active regulation, unified experience generation, and long-timescale cognitive stability. This work belongs to the Field Chapters of On Self-Manifestation and focuses on mechanisms by which organized cognitive systems generate unified experiential structures.

Why do hierarchical systems emerge? Why can low-level details gradually give rise to high-level abstraction? Why are higher-level structures more stable while becoming increasingly difficult to modify? This work proposes a unified dynamical framework for hierarchical system organization and abstraction formation. The framework argues that abstraction is not primarily the result of deliberate induction, but emerges as a structural consequence of long-term compression and transfer loss across system layers. Different organizational layers exhibit systematic differences in compression strength, resolution capacity, and structural stability. Lower layers preserve more detail, while higher layers preserve increasingly stable relational structures. The framework further develops mechanisms governing hierarchical organization, cross-layer transfer, transfer loss, cascading instability from lower-layer collapse, and long-timescale relations between structural depth and stability. The model aims to provide a unified explanation for abstraction formation, concept emergence, language compression, hierarchical neural processing, complex system organization, and cross-scale stabilization dynamics. This work belongs to the Field Chapters of On Self-Manifestation and focuses on long-timescale hierarchical dynamics in organized systems.

How do complex systems emerge? Why do some structures persist over long periods while others disappear completely? What determines whether a system leaves durable historical constraints or fades without lasting influence? This work proposes a unified dynamical framework for system formation and system termination. The framework argues that organized systems are not pre-given entities but gradually emerge through sustained input, structural accumulation, and long-term maintenance dynamics. Two distinct termination pathways are further proposed: one preserving highly compressed core structures, and another producing gradual forgetting and structural disappearance. These different termination pathways generate different historical residual conditions, which subsequently shape future system formation. The framework establishes relationships among system emergence, structural stabilization, forgetting dynamics, residual structure persistence, and long-term regeneration processes. The model aims to provide a unified explanation for learning formation, memory persistence, skill loss, cognitive path dependence, cultural evolution, and long-timescale dynamics in complex structured systems. This work belongs to the Field Chapters of On Self-Manifestation and focuses on emergence, stabilization, collapse, forgetting, and regeneration mechanisms in organized systems.

Why can some knowledge transfer successfully while repeated input fails to enter other cognitive systems? Why can language shape intention, emotion influence cognition, social consensus emerge, and cultural structures persist across generations? Conventional approaches often interpret system interaction primarily as signal transmission, information exchange, or connection strength. This work proposes an alternative framework: stable interaction requires not merely transmission, but the receiving system’s ability to recognize, accommodate, and maintain incoming structural patterns over time. A dynamical model of cross-system structure transfer is developed, identifying necessary conditions for stable coupling across structured systems, including output capability, structural compatibility, resolution constraints, anchoring mechanisms, and long-term maintenance dynamics. The framework further derives directional asymmetry of coupling, positive feedback under strong coupling, coupling decay, structural rejection, and coupling collapse. The model aims to provide a unified dynamical explanation for learning transfer, skill formation, language influence, social consensus, cultural transmission, and long-term coordination across complex systems. This work belongs to the Field Chapters of On Self-Manifestation and focuses on mechanisms governing long-term structural interaction among multiple organized systems.

Large language models are commonly understood as systems driven primarily by real-time computation. This paper proposes an alternative explanatory framework. It argues that what truly participates in GPT’s core question-answer capability is not primarily real-time computation itself, but structural sedimentation gradually formed during training. The paper distinguishes two functionally different categories of computation inside large language models. The first contributes to training through parameter updates, error backpropagation, and repeated historical accumulation, gradually forming stable structure, historical bias, and long-term sedimentation. The second contributes during inference, where Attention mechanisms determine which historical structures enter the present receptive scope. The paper further argues that Attention operates more closely as receptive-field selection rather than the central mechanism responsible for question-answer capability. Question-answer capability is proposed to arise primarily from accumulated historical structure, together with familiar paths, common structures, and law-continuation already formed inside the Sedimentation-Field. The framework is summarized in one proposition: “Look there — sediment there.” The paper further discusses possible relations among training structure, historical influence, receptive selection, and language question-answer capability.

This paper investigates one central question: Why does flow within a system not remain forever omnidirectionally co-flowing, randomly scattering, completely solidified, or completely collapsing, but instead form river channels, familiar paths, electric currents, desire-orientations, current continuity, and historical inertia? The paper proposes that what is called “potential” is not a result-level probabilistic tendency, result preference, or optimal path, but the unclosed continuation tension in which a system stands after old sustaining can no longer continue original continuation, while new continuation has not yet re-formed sustainable original continuation. Through stepwise interrogation, the paper argues that as long as a system contains continuing flow, continuation-position exclusion, existing sustaining flow, new continuing flow continuously pressing into the same continuation-position, and cross-temporal continuation, any system capable of forming and sustaining continuation-dynamics must simultaneously possess: * a continuing-flow structure, * a continuation-position exclusion structure, * an original-continuation structure, * a forced-bias structure, * a tuning structure, * and a re-continuation structure. The paper further formulates: Continuation-Dynamics = (F, O, L, P, T, K) and, through affirmative proof, reverse proof, breakdown arguments, implementation correspondence, potential-state definition, limit forms, and dissolution forms, argues that: law is not abstract regularity, but the maintenance of original continuation by continuing flow itself; principle is not an externally imposed rule, but the forced bias that makes sustaining unable to continue original continuation; potential is not result tendency, but the continuation tension between the failure of original continuation and the unclosedness of re-continuation.