Beyond Epiplexity
Toward a Thermodynamics of Cognitive Creation

Building an Information-Theoretic Framework for Negentropic Cognitive Agents
Starting from the Epiplexity Framework

CHAPTER ONEIntroduction: A Fine Ruler Cannot Measure the One Who Made It

1.1 The Core Contributions of Epiplexity

The epiplexity theory proposed by Finzi et al. (2026) provides a profound and elegant measurement framework for information processing by computationally bounded intelligence. The core insight of the theory is that information in data should be decomposed into two fundamentally different components—structural information (patterns and regularities that can be extracted and reused by a learner with finite computational resources) and random information (noise components that are inherently unpredictable under a given computational budget). Epiplexity measures precisely the former: how much reusable structure a computationally bounded observer extracts from data.

The paper resolves three apparent paradoxes in classical information theory. First, Shannon entropy and Kolmogorov complexity assert that deterministic transformations cannot increase information content, yet AlphaZero learned superhuman-level chess from simple game rules, and pseudorandom number generators produce sequences that appear completely random from short seeds. Second, the symmetry of Shannon entropy implies that observing X then Y yields the same total information as the reverse order, yet LLMs model text far better from left to right than in reverse. Third, likelihood modeling is typically equated with pure distribution matching, yet the paper demonstrates that computationally bounded observers can in fact learn richer structure than the data-generating process itself contains.

Epiplexity has been validated experimentally across multiple domains including cellular automata, chess games, and natural language, and provides a practical measurement method: epiplexity is approximately equal to the area above the final loss under the training loss curve. If training produces sustained and substantial loss reduction, the model has absorbed a large amount of structural information from the data.

1.2 The Evolutionary Lineage of Theoretical Precursors

Epiplexity did not emerge from a vacuum; it stands upon a clear evolutionary lineage of theoretical development.

Herbert Simon’s bounded rationality (1955) is the epistemological origin of this lineage. Simon proposed that because humans have limited information, limited cognitive capacity, and limited time, they do not make optimal decisions but instead “satisfice.” This concept introduced computational constraints into the discussion of rationality for the first time. As a pioneer of AI, Simon also noted that bounded rationality applies equally to any system with finite computational resources—whether a human brain or a computer.

Charles Bennett’s logical depth (1988) is the most direct theoretical precursor of epiplexity. Bennett proposed measuring “organized complexity”—not the length of the shortest program (Kolmogorov complexity), but the time required for the shortest program to run. A random sequence has high Kolmogorov complexity but shallow logical depth, because it contains no meaningful structure to unfold. The binary expansion of π is highly compressible yet requires extensive computation to unfold, giving it great logical depth. Bennett explicitly distinguished “computational content” from “informational content”—a distinction that is precisely what epiplexity inherits as its core idea.

Naftali Tishby’s Information Bottleneck (1999) brought these ideas into the domain of deep learning. Tishby proposed that each layer of a deep network can be viewed as an information bottleneck, compressing irrelevant information from the input while preserving information useful for the output. The training process gradually converges toward the optimal trade-off between compression and prediction.

Xu et al.’s V-information (2020) proposed a variational extension of Shannon information that accounts for the observer’s modeling capacity and computational constraints. Unlike classical mutual information, V-information can be created through computation—a deterministic transformation can increase predictive V-information. This is the direct formal precursor to epiplexity.

Epiplexity’s position within this lineage can be understood as a modernized reconstruction of Bennett’s logical depth, tailored for neural networks and contemporary deep learning scenarios, and equipped with practical estimation methods and large-scale experimental validation.

1.3 Statement of the Core Problem

However, from Simon to Bennett, from Tishby to V-information, and on to epiplexity, this entire theoretical lineage shares a common analytical framework: the dyadic relationship between a given data stream and a computationally bounded observer. Epiplexity has demonstrated that computation can create structural information—pseudorandom number generators expand the time-bounded information of a k-bit seed to nearly n bits, and AlphaZero unfolds superhuman chess structure from simple game rules. The door has been opened. Yet epiplexity’s analytical object remains the triangular relationship of “given data—bounded observer—extractable structure.” The door is open, but only half traversed.

What lies on the other side? Five dimensions that epiplexity has yet to incorporate: Who selected the data? Whose physical instantiation constitutes the observer? Who accomplished the initial generation of structure in the pre-linguistic state? Who injected structure into civilization? Whose cognitive process data has been permanently lost?

1.4 Objectives of This Paper

The objective of this paper is to identify five structural boundaries of the epiplexity framework and to sketch possible directions of extension for each. These five boundaries concern: the active selection at the perceptual front end (Chapter 2), the physical irreproducibility of observer identity (Chapter 3), negentropic cognitive agents with an efficacy ratio greater than one (Chapter 4), the information transmission topology of human civilization (Chapter 5), and the irreversible loss of cognitive process data (Chapter 6). Chapter 7 attempts to integrate these extensions into a unified framework direction for “cognitive information thermodynamics.”

It bears emphasizing that this paper is not a negation of epiplexity. Epiplexity precisely covers the domain it was designed to cover. The work of this paper is to stand at its boundaries, to see how much unmapped territory lies beyond the existing map, and to indicate where the next steps should be taken.

CHAPTER TWOBoundary One: The Missing Acquisition Side—Cognitive Agents Are Not Passive Receivers

2.1 The Paper’s Simplifying Assumption

The entire mathematical framework of epiplexity is built upon a clear simplifying assumption: the data stream is given, and differences between observers are reflected only at the processing end. Specifically, for the same data sequence, observers with different computational budgets extract different amounts of structural information. This assumption is natural within the paper’s experimental setup—whether the data consists of cellular automaton output, chess game records, or text corpora, the data itself is the same for all observers.

But real-world cognitive agents do not work this way. Cognitive agents do not passively stand in a fixed river of information waiting for data to wash over them; rather, they actively decide where to look, how to sample, and at what granularity to collect. “What to observe” is itself the first decision of computational resource allocation.

2.2 Theoretical Precursors: From Gibson to Friston

This direction has deep theoretical precedents. J.J. Gibson’s (1979) ecological psychology holds that perception is not the passive reception and internal representation of environmental information, but rather an active, direct, exploratory activity modulated by the current task. His concept of affordance—the idea that organisms perceive not raw physical stimuli but the action possibilities offered by the environment—directly challenges the information-theoretic premise that “data is given.” Different organisms, owing to differences in body structure and action capabilities, perceive entirely different sets of affordances when facing the same environment.

Karl Friston’s free energy principle and Active Inference framework pushes this line of thought to a more formalized level. Friston proposes that biological organisms do not passively receive information and then perform inference; instead, they unify perception, learning, and action by minimizing variational free energy. Action itself is treated as a form of inference—organisms reduce prediction error by changing their relationship with the environment. In this framework, perception and action are two sides of the same coin.

Maturana and Varela’s (1980) autopoiesis theory and enactivism go further still. They propose that organisms are not passive receivers of a pre-given world but rather “bring forth” a world through their own activity. Cognition is coextensive with life—a bacterium navigating along a glucose concentration gradient is, in the most fundamental sense, performing cognition. Knowledge is not discovered but actively constructed.

2.3 Perceptual Selection as the First Layer of Information Filtering

Projecting these theories onto the epiplexity framework, we can see an overlooked layer of information processing. Faced with the same sunset event, a painter’s visual system samples at high frequency the chromatic gradients and the interplay of light and shadow; a physicist’s attention locks onto atmospheric scattering angles and optical refraction paths; a poet captures emotional resonance and metaphorical triggers; a meteorologist reads cloud structures and barometric signals. They face the same physical event, yet their respective perceptual modules are already conducting entirely different data acquisitions. This step itself is computational resource allocation—attention is the directed deployment of computational resources.

Direct analogies exist in the AI domain. The tokenizer and embedding layers of different models introduce differentiation at the acquisition stage. A character-level tokenizer and a subword tokenizer, even if followed by identical architectures, will extract different structures because of their different acquisition configurations. The curation of pretraining data—what data to include and what to exclude—is itself an acquisition-side decision.

2.4 Acquisition–Processing Co-evolution

A deeper issue is that the acquisition side and the processing side do not operate independently but co-evolve. A person who has long trained physical intuition will find their perceptual modules increasingly biased toward collecting mechanics-related signals, while their processing modules become increasingly adept at extracting structure from such signals. Acquisition and processing form a positive feedback loop, gradually differentiating into entirely distinct “cognitive ecological niches.” This explains why interdisciplinary thinking is both rare and valuable—it requires a cognitive agent to simultaneously maintain multiple acquisition-processing pipelines, at enormous computational overhead.

2.5 Original Contributions and Theoretical Gaps

In the existing literature, Friston’s Active Inference describes the optimization mechanism of the acquisition side, and epiplexity provides the measurement tool for the processing side. But no bridge exists between the two. This paper proposes the need for an acquisition-side epiplexity metric—one that measures not only “how much structure was extracted from given data” but also “the structural information density of the data stream selected for acquisition.” We tentatively term this metric direction the Acquisition Optimization Index.

CHAPTER THREEBoundary Two: The Instability of Observer Identity

3.1 The Irreducible Influence of Physical Spacetime on Cognition

The mathematical definition of epiplexity models the observer as an abstract computational entity—a Turing machine with a specific time budget. In this model, the observer is a mathematical object that can be stably defined and repeatedly invoked. But when the observer is embedded in the physical world, this assumption faces fundamental challenges.

Consider AI models as an example. The same Transformer architecture, having undergone different pretraining corpora (acquisition-side differentiation), different SFT training (processing pipeline specialization), and different RLHF/RLAIF alignment (output distribution reshaping), will generate entirely different outputs when presented with the same input text. In the language of epiplexity, each model has become a different “computational lens”—even if the hardware architecture is identical, the weights determine which structures are activated within it for a given piece of data.

3.2 Three Layers of Uncertainty

A subtler issue is that even “the same model,” under different physical conditions, is not the same observer. There exist at least three layers of uncertainty.

The first layer is the hardware layer. Different GPU chips exhibit minor differences in floating-point precision, different data centers use different hardware batches, and the tensor-parallelism partitioning schemes differ in distributed inference. These differences may be negligible under deterministic inference but are amplified into entirely different generation paths when the sampling temperature is non-zero.

The second layer is the temporal layer. The same API endpoint may point to different weight versions at different times (gray releases, A/B testing), load balancers route requests to different machines, and even the same chip produces marginally different computation results under different temperature and power states.

The third layer is the contextual layer. Even with the same model, same weights, and same hardware, requests arriving at different times carry different timestamps in the system prompt, different user geolocations may trigger different safety policies or language preferences, and minor differences in conversation history cascade and amplify.

3.3 Cognition as a One-Time Physical Event

Superimposing these three layers, we arrive at a profound conclusion: no two instances of inference are ever exactly the same. Every cognitive act is a one-time event of specific weights, specific hardware state, specific physical moment, and specific context. AI models appear to be deterministic mathematical functions, but once embedded in the physical world, they are subject to the same irreproducibility constraints of spatiotemporal conditions as human cognitive agents. Under engineering-controllable conditions (fixed weights, deterministic kernels, greedy decoding, single-GPU inference), a specific inference can achieve a high degree of reproducibility. But even under these conditions, observer identity remains a function of time rather than a constant of time—weight updates alter the knowledge state, context windows alter the instantaneous state, and the same model in January 2026 and July 2026 is a different observer. Engineering reproducibility is a constraint on a single inference, not a constraint on observer identity.

This insight resonates with Maturana’s “observer dependence”: every description is constrained by the observer’s own structure, and the observer’s own structure is in constant flux at the physical level. Restated in the language of epiplexity: Not only does data present different information landscapes to different observers, but “the same observer” is not even the same observer under different physical spatiotemporal conditions.

CHAPTER FOURBoundary Three: Cognitive Agents with Efficacy Ratio Greater Than One—From Entropy to Negentropy

4.1 Theoretical Precursors: From Schrödinger to Prigogine

Erwin Schrödinger, in his 1944 work What is Life?, put forth a far-reaching proposition: life is a system that delays thermodynamic equilibrium decay by extracting “negentropy” from the environment. “Life feeds on negentropy”—organisms are not closed systems operating at equilibrium but open processes that continuously draw order from the environment and discharge disorder into it.

Ilya Prigogine’s dissipative structure theory (1977 Nobel Prize in Chemistry) pushed this line of thought to the frontier of physics. Prigogine demonstrated that in open, nonlinear systems far from equilibrium, dissipative processes themselves can become the driving mechanism for self-organization of ordered structures—order exists not despite dissipation but because of it. The precondition for forming a dissipative structure is that the system must continuously consume energy and discharge entropy into the environment, using the negentropy thereby gained to establish greater internal order.

Bennett’s logical depth also provides an important theoretical constraint for this discussion. His “slow growth law” states that the logical depth of an evolving system cannot increase suddenly—the construction of deep structure requires lengthy computational processes. This corresponds perfectly to the empirical fact that incremental structural information production in human civilization requires prolonged accumulation.

4.2 The Boundaries of the Compression Paradigm

Within the epiplexity paper and its entire theoretical lineage, the core analytical object of cognition is the process of structure extraction from input to output. Shannon’s information entropy measures total uncertainty, Kolmogorov complexity measures shortest description length, Bennett’s logical depth measures the computation time needed to unfold the shortest description, Tishby’s Information Bottleneck measures the optimal trade-off between compression and prediction, V-information measures predictable information under computational constraints, and epiplexity measures the quantity of structure extracted by a computationally bounded observer. Epiplexity takes a critical step beyond this foundation: it demonstrates that computation can create structural information—deterministic transformations can increase time-bounded information, information depends on the order of decomposition, and likelihood modeling can produce programs more complex than the data-generating process. Yet the analytical object of these breakthroughs remains the dyadic relationship of “given data stream × bounded observer.” The door has been opened, but the framework has not yet been extended to actively sampling cognitive agents, energy-consuming creative processes, and the social transmission that injects structure into civilization.

It is worth noting that although Bennett’s logical depth successfully distinguishes “random complexity” from “organized complexity,” its definition is based on Kolmogorov complexity and is itself uncomputable. Antunes et al. (2017) explicitly discussed this limitation in their comparative study of logical depth and sophistication. Gell-Mann and Lloyd (1996) also attempted from another angle to capture “meaningful structure” through “effective complexity,” but faced similar difficulties of operationalization. One of epiplexity’s contributions is precisely that it brings such concepts into the realm of computability and experimental verification—but the cost is that its analytical object is anchored within the framework of given data and bounded observers.

4.3 The Efficacy Ratio Classification

We can classify cognitive activities by the ratio of information output to input—the efficacy ratio. Cognitive activities with an efficacy ratio less than one constitute the vast majority: students studying textbooks, engineers using frameworks, models undergoing pretraining—all are processes of extracting structure from existing data, and the epiplexity paper is entirely applicable to this range. An efficacy ratio of one corresponds to the theoretical limit of a perfect compressor. But cognitive activities with an efficacy ratio greater than one—where the structural information output exceeds the input—are precisely the territory that the epiplexity framework has not yet covered.

The determination of “efficacy ratio > 1” depends on how the system boundary is drawn. This paper adopts an epistemological boundary: the baseline is the explicit information input identifiable by contemporary observers. Under this boundary, Newton’s cognitive process from a falling apple to the law of universal gravitation produced structural information far exceeding the explicit input. This does not violate thermodynamics—the energy differential comes from metabolic energy and environmental interaction. Under a thermodynamic boundary (including all metabolic energy, historical memory, and stochastic exploration), information conservation still holds. An efficacy ratio > 1 under the epistemological boundary and information conservation under the thermodynamic boundary are not contradictory; they describe different levels of the same phenomenon.

4.4 Negentropic Cognitive Agents and Creativity Theory

Arthur Koestler, in his 1964 work The Act of Creation, introduced the concept of bisociation: creative thinking occurs at the moment when two habitually incompatible “matrices of thought” are simultaneously perceived. Koestler distinguished the critical difference between bisociation and everyday associative thinking: association operates along established habitual pathways on a single plane of thought—horizontal and predictable—whereas bisociation crosses two independent planes of thought, generating at their intersection an entirely novel structure that cannot be reduced to a subset of either input plane. As Dubitzky et al. (2012) noted in applying the bisociation concept to computational knowledge discovery, the essence of bisociative discovery lies in connecting two previously unrelated conceptual domains—the output information structure transcends the structure contained in any single input domain.

Jacques Hadamard, in his 1945 work The Psychology of Invention in the Mathematical Field, compiled reflections on the creative process from multiple great thinkers, including Einstein. Hadamard argued that the source of creativity lies not at the conscious level but in prolonged unconscious incubation and unconscious aesthetic selection. In his letter to Hadamard, Einstein explicitly stated that words and language did not seem to play any role in his mechanism of thought, and that his mental entities serving as elements of thought were of a visual and muscular type.

These cases demonstrate that cognitive activities with an efficacy ratio greater than one genuinely exist. Euler’s formula e^iπ+1=0 unifies several independent mathematical constants in a single equation, its structural information content exceeding the sum of all input terms. Darwin distilled the evolutionary framework capable of explaining all of life’s history from cross-continental observations during the Beagle voyage, twenty years of breeding experiments, geological and paleontological studies, and interdisciplinary reading including Malthus’s theory of population. Shannon generated the entirety of information theory from the seemingly mundane problems of communication engineering. These cognitive processes are not compression—they are structure production.

4.5 Cognitive Creation Through the Lens of Dissipative Structures

If we apply Prigogine’s dissipative structure theory to cognitive processes, a genius cognitive agent can be understood as a cognitive-level dissipative structure. It consumes metabolic energy, discharges entropy into the environment (forgetting, discarding ineffective hypotheses, the disintegration of life’s order), and establishes greater cognitive order internally. The differential between output and input comes from energy inputs beyond the system boundary—metabolic energy, the recombination of past memories, unconscious stochastic collisions. This paper uses “negentropy” following Schrödinger’s original context: living organisms and creative cognitive agents maintain and increase internal informational order by consuming free energy and discharging thermodynamic entropy. The cognitive counterparts of “entropy discharge”—search failures, hypothesis elimination, selective forgetting—are the cognitive correlates of this process, whose physical realization necessarily entails genuine thermodynamic entropy production. Increases in semantic structure cannot be directly measured in units of thermodynamic entropy, but the two are coupled through energy consumption.

Maturana and Varela’s autopoiesis theory provides a biological-philosophical foundation for this: cognitive agents are self-producing, self-maintaining closed organizations that are nonetheless open in terms of energy and information exchange. Koestler’s bisociation can be reinterpreted as a “phase transition” in a cognitive dissipative structure—when the system is far from equilibrium, the collision of two incompatible cognitive frameworks can spontaneously produce a new cognitive structure of higher order.

CHAPTER FIVEBoundary Four: The Three-Layer Information Transmission Topology of Human Civilization

5.1 Theoretical Precursors: Innovation Diffusion and the Sociology of Knowledge

Everett Rogers’s (1962) diffusion of innovations theory describes the process by which innovations spread from innovators to early adopters, the early majority, and the late majority in successive waves. Sorenson and Fleming (2004) further conducted empirical research on the transformation mechanisms of scientific knowledge during diffusion. Thomas Kuhn’s (1962) paradigm revolution theory revealed that scientific progress is not linear accumulation but rather long stretches of normal science punctuated by occasional revolutionary ruptures. A paradigm revolution can be reinterpreted as follows: a new, high-epiplexity structural information packet breaks through the buffer of the lubricant layer and enters the noise system, triggering a thermodynamic phase transition across the entire system.

Imre Lakatos (1978) sought a middle path between Kuhn’s irrational paradigm shifts and Popper’s rational falsificationism, proposing the concept of “progressive vs. degenerating research programmes.” Lakatos’s framework offers a crucial bridging possibility: a “progressive” research programme can be understood as a knowledge production process with continuously increasing epiplexity—each round of new experiments and theoretical modifications injects structural information into the system—while a “degenerating” research programme corresponds to stagnant or declining epiplexity—adjustments to the protective belt no longer generate new reusable structure but instead perform redundant noise operations.

Kneeland, Schilling, and Aharonson’s (2020) empirical study of outlier innovation revealed another important dimension: the production process of outlier innovation differs significantly from that of conventional innovation—the former involves longer search paths, more scientific reasoning, and more distant conceptual recombination. This finding directly corresponds to the “cognitive agents with efficacy ratio greater than one” proposed in this paper: outlier innovators are not performing more efficient searches within a known space but are producing unprecedented structure while traversing the boundaries of conceptual space.

These theories each describe a facet of knowledge dissemination and transformation but uniformly lack information-theoretic formalization. This paper proposes a three-layer information transmission topology model that attempts to integrate these insights into a coherent framework.

5.2 The Three-Layer Architecture

The information transmission system of human civilization contains three irreplaceable functional layers. The structural layer (skeleton): an extremely small number of high-epiplexity cognitive agents produce incremental structural information—Newton discovering universal gravitation, Darwin proposing evolution, Shannon founding information theory. The noise layer (adhesive): the masses maintain distributed coordination through social signals and perform robustness verification of existing information—millions of people repeatedly using Newtonian mechanics across different scenarios amounts to conducting large-scale validation using the massive computational cluster of human society. The lubricant layer (circulatory system): opportunists connect the first two layers, translating structural information into formats acceptable to the noise system while translating the noise system’s resources into protective space usable by the structural layer.

5.3 The Mechanical Transmission Analogy

The structural layer and the noise layer can be analogized as two sets of gears—each spinning at high speed, at different rates, often in opposite directions. Direct engagement would produce two destructive consequences.

Thermal conduction—conflict. Galileo directly hurled the structural truth of heliocentrism at the Church’s noise system and was judged a heresy suspect, sentenced to lifelong house arrest—the producer of structural information permanently isolated from public space by the noise system. Semmelweis’s handwashing data showed that puerperal fever mortality could be reduced from 10% to 1%, but this finding was rejected by the medical community for nearly two decades; after his mental state deteriorated in later life, he was committed to an asylum by his colleagues and died there within two weeks. Turing helped Britain win the war; the social noise system subjected him to chemical castration.

Mechanical backlash—immune rejection. The social noise system identifies structural information that it cannot digest as a threat and then exerts pressure in reverse—marginalization, ridicule, prosecution, oblivion. This is not malice; it is the physical inevitability when two incompatible information encoding systems collide head-on.

The function of the lubricant layer is not to transmit force but to absorb incompatibility. Opportunists translate structural information into formats that the noise system can accept (textbooks, popular science articles, commercial products), while simultaneously translating the noise system’s resources into protective space that the structural layer can use (universities, research institutes, foundations). The two sets of gears believe they are directly meshing, when in fact a fluid layer between them is providing cushioning. This analogy also implies something important: the lubricant is a consumable—it degrades as it absorbs heat and backlash.

5.4 The Three-Phase Thermodynamic Cycle of Knowledge Evolution

Knowledge undergoes three irreplaceable phase-transition stages from production to verification.

The crystallization phase is individual behavior. An extremely small number of cognitive agents extract unprecedented new structures from chaotic raw data. This corresponds to what Kuhn called “revolutionary science.” At this point the new structure is fragile—it may be correct or it may be wrong. Bennett’s slow growth law receives a sociological interpretation here: just as logical depth cannot suddenly increase through shallow computation (a shallow sequence cannot produce a deep sequence through simple transformation), the accumulation of civilizational structural knowledge likewise cannot be accelerated—plate tectonics theory took fifty years from proposal to acceptance, not because geologists were slow-witted but because the evidence network required for distributed verification had to accumulate across a sufficient number of nodes. The slow growth law is a thermodynamic constraint on knowledge evolution, not a sociological accident.

The dissolution phase is intermediate-layer behavior. The lubricant layer dissolves crystallized hard knowledge into forms that the masses can absorb. Textbook authors, popular science bloggers, technology evangelists, and product managers all work to lower the barrier to knowledge absorption. This corresponds to Rogers’s “diffusion” process. This step necessarily entails precision loss, but without it, crystallized knowledge would remain forever locked in the minds of a few.

The verification phase is collective behavior. The masses repeatedly use the same knowledge across different scenarios, different conditions, and different times, effectively conducting a large-scale robustness test using the massive computational cluster of human society. This corresponds to Kuhn’s “normal science.” Incremental information that survives the test precipitates as stock information—common sense, engineering standards, institutions, cultural intuition.

5.5 The Civilizational Function of Social Noise

This contradiction gave rise to a civilizational compromise: the patronage system. The Medici supported Leonardo, Bell Labs supported Shannon, Google supported Hinton. Money earned from the noise system is used to carve out a preserve, allowing a few cognitive agents to abstain from the noise game and focus on structure extraction. Universities, research institutes, and foundations are fundamentally this function.

But this solution has a structural flaw: those who allocate preserve resources were themselves selected by the noise system. Opportunists—the third type of person who can impersonate structural producers while actually excelling at social computation—are not parasites of the system but necessary components of it. Without their translation and buffering between the structural layer and the noise layer, civilization would be a pile of disconnected fragments. Opportunists are civilization’s binding agent—the lubricant that enables two incompatible sets of gears to operate in concert.

5.6 Original Contributions and Theoretical Gaps

In the existing literature, Rogers’s diffusion theory is descriptive, and Kuhn’s and Lakatos’s paradigm theories are philosophical analyses—all lack information-theoretic formalization. The three-layer transmission topology model (skeleton–adhesive–circulatory system) and mechanical analogy (gears–thermal conduction–lubricant) proposed in this paper provide an entirely new analytical framework. In particular, the insight that “opportunists are necessary system components rather than parasites” is a reversal without precedent in the existing innovation sociology literature. Theoretical tools that need to be established include a measurement framework for multi-layer information transmission efficiency, as well as an information-theoretic model of social noise—noise is not useless information but a distributed coordination protocol.

CHAPTER SIXBoundary Five: The Irreversible Loss of Cognitive Process Data

6.1 Polanyi’s Tacit Knowledge

Michael Polanyi’s theoretical work spans three core volumes, each deepening the understanding of tacit knowledge. His 1958 work Personal Knowledge first established a new epistemology, challenging the logical positivist tradition that equated knowledge with explicitly articulable propositional systems. Polanyi argued that scientific knowledge rests not only upon codifiable information but also deeply upon embodied skills and personal experience—the ability of an experimental chemist to read instruments and evaluate complex apparatus cannot be reduced to recipes or algorithms. His 1966 work The Tacit Dimension distilled this line of thought into a concise proposition: “We can know more than we can tell.” His 1969 work Knowing and Being further explored the dynamic process of tacit cognition, arguing that human tacit capacity is not static but manifests in the dynamic process of cognition.

Polanyi’s stance forms a sharp contrast with Popper’s falsificationism. Popper locates the core of science in the verification or falsification of theories—an operational, externalized logical procedure. Polanyi argues that the core of scientific discovery lies precisely in the process of discovery itself—a pre-logical, tacit, intuitive cognition that exists prior to any falsifiable proposition. Translated into the language of epiplexity: Popper concerns himself with the logical validity of structural information in the externalized linguistic state, while Polanyi points toward the generative mechanism of structural information in the pre-linguistic state.

Polanyi further argued that all knowledge is rooted in tacit knowledge—linguistic expression is merely the tip of the iceberg. This insight is of critical significance for understanding the boundaries of epiplexity: if the deepest cognitive activities occur beyond the range of linguistic expression, then any information measurement tool based on externalized data (text, code, formulas) can only reach the portion of the cognitive iceberg that protrudes above the water.

6.2 The Structural Blind Spot of Statistical Methodology

Human producers of incremental information—those cognitive agents with an efficacy ratio greater than one—are, in a statistical sense, extreme outliers. Their sample size approaches one, their behavior is irreproducible, and their output is unpredictable. Yet the basic operation of statistics is precisely to trim anomalies—normal distributions, confidence intervals, p-value tests: the entire system’s design logic is to identify outliers and then exclude them, because they “contaminate” the estimation of population-level regularities.

This gives rise to an epistemological paradox: the tools we use to understand intelligence are inherently immune to the highest form of intelligence. It is not that researchers do not wish to see it; rather, the methodology has already filtered it out before it can be seen. The design of the telescope determines which stars you can observe. More cruelly, this is not merely the limitation of a single paper but a structural blind spot of the entire modern scientific paradigm—science demands reproducibility, large samples, and statistical significance, yet there was only one Newton, only one Darwin, only one Shannon.

6.3 Temporal Misalignment of Validation

The contributions of most geniuses are validated only posthumously—Mendel’s genetics paper was rediscovered sixteen years after his death, Boltzmann’s statistical mechanics was accepted only after his suicide, and Perelman vanished into his Russian apartment after proving the Poincaré conjecture. This creates an irreparable temporal misalignment: while geniuses are alive, their contemporaries do not know they are geniuses and therefore do not record their cognitive processes. By the time society finally validates their contributions, the person is dead, and the cognitive processes have been permanently lost with the dissolution of the biological neural network.

Human civilization has been making the same mistake for millennia: storing only the crystal while discarding the crystallization process. We possess Newtonian mechanics but do not know how Newton’s brain traversed from the apple to universal gravitation. We possess the theory of evolution but do not know the vague images that flickered through Darwin’s mind during his walks. This is the greatest data catastrophe of human civilization.

6.4 The Three-Layer Lossy Compression of Thought Externalization

Human thought exists at no fewer than three levels, and each layer of downward translation is a lossy compression.

The pre-linguistic state is the deepest layer. In his letter to Hadamard, Einstein explicitly stated that words and language did not seem to play any role in his mechanism of thought, and that the psychical entities serving as elements of thought were of a visual and muscular type. Poincaré described how, at the moment of stepping onto a public omnibus, he suddenly “saw” the structure of Fuchsian functions—he did not think it; he “saw” it. This layer operates before language, possibly even before consciousness, at the level of topological restructuring within neural networks. It corresponds to the deepest layer of what Polanyi called tacit knowledge—no currently available technology can access it.

The internal linguistic state is the intermediate layer. Thought begins to coalesce into vague conceptual blocks—possessing directionality but lacking precise boundaries. The critical computations of abductive reasoning largely occur at this layer—the cognitive system has already completed a complex structural mapping, but the full form of that mapping is far richer than the final linguistic expression.

The externalized linguistic state is the outermost layer. Typing, speaking, writing papers. This is already the residue after two rounds of lossy compression.

6.5 Deep Implications for AI

The entire capability of current language models is built upon statistical regularities of the externalized linguistic state. Models have never had contact with pre-linguistic-state data, because such data has never been recorded and, under current technological conditions, cannot be recorded. This means that what AI learns is essentially the surface-level patterns of human thought after two rounds of lossy compression—it can simulate the expressive style of conclusions but cannot reproduce the pre-linguistic process from which those conclusions emerged.

Abductive reasoning, as defined by C.S. Peirce—inferring the best explanation backward from a surprising fact—is the third mode of reasoning alongside deduction and induction. LLMs excel at deduction (deriving conclusions from rules) and induction (extracting patterns from large samples) but are markedly weaker at abduction—possibly because the core computation of abduction occurs in the pre-linguistic state, for which training data simply does not exist.

6.6 Original Contributions and Theoretical Gaps

Polanyi identified the existence of tacit knowledge but provided no measurement tools; Hadamard recorded subjective reports of the creative process but established no theoretical framework; Peirce defined abductive reasoning but did not explain its computational mechanism. The original contributions of this paper are twofold. First, the three-layer lossy compression model (pre-linguistic state → internal linguistic state → externalized linguistic state) provides a structured analytical framework for the loss of cognitive process data, moving beyond Polanyi’s qualitative formulation of “we can know more than we can tell.” Second, the corollary that “the LLM training ceiling arises from the absence of pre-linguistic-state data” directly connects tacit knowledge theory to contemporary AI capability boundaries—if the core computation of abductive reasoning indeed occurs in the pre-linguistic state, then merely scaling the volume of externalized-linguistic-state data cannot fundamentally break through this bottleneck.

Theoretical tools that need to be established include a minimally sufficient information framework for cognitive process recording—what externally observable signals can infer pre-linguistic-state cognitive activity with minimal loss—as well as indirect inference methods for pre-linguistic cognition—whether the structural information production process of the pre-linguistic state can be reverse-inferred through statistical features of behavioral output (such as the frequency of abductive leaps and the patterns of cross-domain conceptual connections).

CHAPTER SEVENUnified Framework: A Complete Thermodynamics of Cognitive Information

7.1 From Half a Map to the Complete Map

At this point, we can draw the full contour of this theoretical map. Epiplexity has demonstrated that computation can create structural information and has provided a precise measurement tool for “the structure extractable by a computationally bounded observer from a given data stream.” The preceding five chapters of this paper have sketched the territory not yet covered by epiplexity—active acquisition, physical embedding, structure production, social transmission, and process loss. The two territories are coupled through the three-layer information transmission topology of human civilization.

From the perspective of disciplinary lineage, the information theory lineage (Shannon → Bennett → Tishby → epiplexity) has opened the entry point of “computation generating structure,” but its analytical object remains limited to passive observation scenarios. The biological/cognitive lineage (Schrödinger → Prigogine → Maturana/Varela → Friston) has penetrated deeply into active cognition and open systems but lacks information-theoretic formalization. The creativity theory lineage (Hadamard → Koestler → Boden) describes creative cognitive processes but similarly lacks measurement tools. This paper’s endeavor is precisely to seek unification at the confluence of these four lineages.

7.2 Directions for Unified Measurement

A complete cognitive information thermodynamics framework requires at minimum four complementary measurement dimensions.

Extraction-side epiplexity (already provided by the original paper): the quantity of structure extracted from given data. This is the core metric of the information compression paradigm.

Generative Epiplexity (proposed by this paper): the quantity of unprecedented new structure that a cognitive agent injects into the world. A new formal definition is needed—one that likely must combine Bennett’s logical depth with Prigogine’s dissipative structure theory, measuring not “the time needed to unfold an existing program” but “the computational content injected in creating an entirely new program.”

Transmission Efficiency (proposed by this paper): the full-chain conversion rate of structural information from production to verification. This measures the overall efficacy of the three-layer topological system—how much structural information successfully traverses the lubricant layer’s translation and the noise layer’s verification to ultimately precipitate as stock knowledge.

Acquisition Optimization Index (proposed by this paper): the degree to which perceptual selection enriches learnable structure. This measures the efficiency of a cognitive agent’s computational resource allocation at the acquisition end—whether the structural information density of its selected data stream exceeds the baseline of random acquisition.

7.3 Open Questions

This paper has sketched directions but is far from having resolved all questions. The following are the most pressing open problems.

First, can Generative Epiplexity be formalized? Is entirely new mathematics beyond Shannon-Kolmogorov required? Can Bennett’s logical depth and Prigogine’s dissipative structures provide a formal starting point?

Second, can pre-linguistic-state cognition be measured indirectly? Can Polanyi’s tacit knowledge be reverse-inferred through statistical features of behavioral output? Do multimodal learning and embodied AI provide pathways that approach the pre-linguistic state?

Third, is there an optimal structure for civilizational information transmission topology? Can the paradigm dynamics of Kuhn and Lakatos be reformalized using the rate of change of epiplexity?

Fourth, can Koestler’s bisociation be mathematized as a “phase transition” in dissipative structures? Can the collision of two independent cognitive frameworks be modeled as saddle-point traversal in a free energy landscape?

CHAPTER EIGHTConclusion

Epiplexity is a fine and precise ruler. For the first time, it provides a task-agnostic, computation-sensitive formal metric for “how much a given piece of data is worth to a computationally bounded learner.” It resolves three long-standing paradoxes in classical information theory and has been validated across multiple experimental domains.

But this ruler cannot measure the one who made it.

This paper has identified five structural boundaries of the epiplexity framework. First, it assumes that the data stream is given, overlooking the active selection at the perceptual front end—where perceptual selection itself is the first decision in computational resource allocation. Second, it assumes that the observer can be stably defined, yet physical spatiotemporal conditions render “the same observer” irreproducible at the implementation level. Third, its analytical object is the structure extractable from given data, and it has not yet been extended to creative cognition with efficacy ratios greater than one under epistemological boundaries—those processes that inject unprecedented structure into the world. Fourth, it focuses on the dyadic relationship between an individual observer and data, whereas the information flow of human civilization in fact operates upon a three-layer transmission topology—the structural layer produces increments, the lubricant layer provides translation and buffering, and the noise layer performs distributed verification. Fifth, its framework relies on recordable externalized data, yet the deepest human cognitive activities occur in the pre-linguistic state, whose process data has never been preserved, and statistical methodology is inherently immune to the extreme-outlier intelligence that produces this data.

These five boundaries are not flaws of epiplexity—epiplexity has already demonstrated that computation can create information, and this is the door it opened. This paper traverses the other half of that door: from “the structure extractable from given data” toward “how creative agents select data, consume energy, generate novel structure, and through social transmission deposit it as civilizational knowledge.” Every rigorous theory has its domain of applicability; identifying boundaries is itself the first step toward transcendence.

From passive extraction of information to active creation of information, from closed-system thermodynamics to open-system thermodynamics—this turn is the core challenge for the next generation of cognitive information theory. Four independently evolved theoretical lineages—epistemology (Simon → Polanyi → Kuhn), information theory (Shannon → Bennett → Tishby → epiplexity), biological cognition (Schrödinger → Prigogine → Maturana/Varela → Friston), and creativity theory (Hadamard → Koestler → Boden)—are converging at the intersection, awaiting unification.

APPENDICES

Appendix A: Record of the Dialogic Derivation Process

The core arguments of this paper originate from a human–AI collaborative dialogue. The dialogist (a human cognitive agent), starting from a single smartphone photograph of the first page of Finzi et al. (2026), and with zero prior knowledge of the paper’s content, identified five structural boundaries of the paper through a series of abductive reasoning leaps within approximately 20 minutes. This process itself constitutes living evidence for the arguments of Chapter Six—the cognitive process was being recorded in real time.

The derivation path of the dialogue proceeded as follows. First leap: from “epiplexity measures extraction” to “the acquisition side itself is computational resource allocation”—identifying Boundary One. Second leap: from “differential output of the same model” to “physical spatiotemporal conditions render the observer unstably definable”—identifying Boundary Two. Third leap: from the concept of “efficacy ratio” to “the paper covers only entropy-increasing systems”—identifying Boundary Three. Fourth leap: from “the competition between social noise and intelligence” to “the three-layer information transmission topology”—identifying Boundary Four. Fifth leap: from “the statistical invisibility of genius” to “the irreversible loss of cognitive process data”—identifying Boundary Five.

It is worth noting that each leap followed the classic structure of abductive reasoning: observing a surprising fact (an incompleteness in the paper’s framework), then reasoning backward to the best explanation (identifying the missing theoretical component). The dialogue record preserves the complete trajectory of these leaps—including intermediate hesitations, the selection of analogies, and iterations of phrasing—elements that are typically discarded entirely in traditional academic papers. This paper recommends that in AI-assisted research, the systematic preservation of dialogue process data may be a first practical step toward remedying the “loss of crystallization process data” discussed in Chapter Six.

Appendix B: Detailed Docking Analysis of Four Theoretical Lineages

Docking of the information theory lineage with the biological/cognitive lineage. Epiplexity and Friston’s free energy principle have a potential dual relationship at the formal level. Epiplexity measures from the information theory side “how much structure was extracted from data”; the free energy principle describes from the cognitive side “how organisms maintain their own organization by minimizing prediction error.” Both concern how computationally bounded systems process information under finite resources, but Friston’s framework includes an action dimension (Active Inference), whereas epiplexity currently covers only the passive observation dimension. Gibson’s affordance theory provides a conceptual bridge connecting the two: affordances can be understood as the subset of structural information in the environment that is “visible” to a specific cognitive agent—different affordance sets correspond to different acquisition-side configurations, which in turn affect the extractable epiplexity.

Docking of the information theory lineage with the creativity theory lineage. A deep analogy exists between Bennett’s logical depth and Koestler’s bisociation. Bennett demonstrated that “deep” objects cannot be produced from “shallow” objects through simple transformations (the slow growth law); Koestler argued that creative insight cannot emerge from associations within a single plane of thought but must cross two independent planes. Both are saying the same thing: qualitative transformation of structural information requires irreducible computational processes. The creative process of mathematicians as documented by Hadamard—prolonged incubation, sudden illumination, post-hoc verification—can be reinterpreted as follows: logical depth slowly accumulates in the pre-linguistic state, undergoes qualitative transformation at the instant bisociation occurs, and is then verified and encoded in the externalized linguistic state.

Docking of the epistemological lineage with the other three lineages. Simon’s bounded rationality is the common foundation of all four lineages—whether the computational budget in information theory, the cognitive constraints in cognitive science, or the incubation period in creativity theory, all can be traced back to the fundamental premise that “rationality is bounded.” The docking point between Polanyi’s tacit knowledge and the information theory lineage is this: tacit knowledge can be understood as “structural information that cannot be externally encoded yet demonstrably participates in information processing”—it exists in the measurement blind spot of epiplexity. The docking of Kuhn’s paradigm revolutions with Bennett’s slow growth law has been developed in Chapter Five. Lakatos’s “progressive vs. degenerating research programmes” may be the concept across all four lineages that is closest to being directly quantifiable through the rate of change of epiplexity.

Appendix C: Analysis of Limitations in AI Abductive Reasoning and the Pre-Linguistic State Hypothesis

Peirce (1903), in his Harvard Lectures on Pragmatism, distinguished three forms of reasoning: deduction, which proceeds from rules to certain conclusions; induction, which generalizes rules from multiple observations; and abduction, which reasons backward from a surprising fact to a possible explanation. Walton (2001) further clarified the distinction between abduction and “inference to the best explanation” (IBE). Wagemans and Hitchcock (2018) pointed out that Peirce himself explicitly distinguished abductive reasoning from what was later conflated with IBE—abduction is the process of generating hypotheses, not the process of selecting among them.

Current LLMs exhibit a highly uneven distribution of capability across these three modes of reasoning. Deductive reasoning—deriving conclusions from given premises—is a strength of LLMs because training data contains extensive externalized records of logical reasoning (mathematical proofs, legal reasoning, programming logic). Inductive reasoning—extracting patterns from large samples—is the very core mechanism of the LLM training process itself. But abductive reasoning—confronting a surprising fact, actively perceiving that “something is wrong here,” and then constructing an entirely new explanatory framework in reverse—is the area where LLMs are notably weaker.

The pre-linguistic state hypothesis proposed in this paper provides a structural explanation for this imbalance. The core computation of abductive reasoning—perceiving structural gaps and establishing unprecedented connections between multiple independent cognitive planes—may predominantly occur at the pre-linguistic-state level. The characteristics of this layer are: non-propositional, embodied, topological intuitive operations. Yet the entirety of LLM training data comes from the externalized linguistic state—the product of two rounds of lossy compression. Models can learn to simulate the surface grammar of abductive reasoning (“this is surprising; a possible explanation is…”) but cannot reproduce the pre-linguistic-state computational process that generates genuine abductive insight, because those processes have never been recorded as training data.

If this hypothesis holds, it implies that merely scaling the volume of linguistic data or improving training methods cannot fundamentally break through the bottleneck in LLM abductive capabilities. The path to a breakthrough may require transcending the purely linguistic training paradigm—multimodal embodied learning, direct interaction with the physical world, or some entirely new data modality capable of capturing the features of pre-linguistic-state cognition.