\section{The Temporally Thick Intellecton}

An instantaneous partition cannot by itself constitute an enduring agent. Agency unfolds through memory, anticipation, action, and repair. A system that satisfies a blanket factorization at one moment but has no continuity across time is at most a snapshot of organization. The Intellecton concept therefore requires temporal thickness.

Temporal thickness means more than persistence of material components. Organisms replace molecules, neural activation patterns change, and beliefs are revised. What persists is an organized capacity to relate past, present, and possible future states. A temporally thick system uses traces of prior interaction to regulate current coupling and shape future trajectories. Its identity is processual.

The master key's stochastic differential equations already describe temporal evolution, but the philosophical interpretation emphasizes stationary covariance. This emphasis should be expanded. A blanket is not merely a stable conditional independence; it is repeatedly reconstituted through dynamics. Sensory and active states change, internal models adapt, and environmental conditions vary. The intellecton persists when these changes preserve a recognizable organization and viability domain.

Memory is central to this persistence. Without memory, a system can respond reactively but cannot integrate consequences over time, learn from error, or maintain projects. Memory need not be explicit symbolic storage. It can be embodied in synaptic weights, altered dispositions, morphology, or environmental scaffolding. What matters is that past interactions make a causally specific difference to future boundary maintenance.

One way to express temporal thickness is to compare predictions based on the history of blanket states with predictions based only on the current blanket:

\[
\mathcal{I}_{T}
=
\sum_{t=1}^{T}
D_{\mathrm{KL}}
\left[
p(c_{t+1}\mid b_{\leq t})
\;\|\;
p(c_{t+1}\mid b_t)
\right].
\]

If \(\mathcal{I}_{T}\) is positive, the history carries information about future internal states beyond the present boundary state. This does not by itself establish identity or consciousness, but it quantifies a form of diachronic dependence. A temporally thick intellecton should exhibit structured historical dependence that contributes to autonomy and integration.

The temporal perspective changes how predictive processing is understood. Prediction is not merely a neural estimate of an external cause. It is the process by which an organized system carries forward expectations shaped by prior engagement. Prediction errors matter because they alter the future organization of perception and action. The system's "model" is not necessarily an inner picture; it is a set of dispositions that coordinate ongoing coupling.

This interpretation aligns active inference with enactivism. The environment is not passively represented and then acted upon. It is disclosed through possible actions, bodily capacities, and histories of regulation. A sensory state has significance because of what the system can do and what consequences follow. The blanket mediates this exchange, but the meaning of the mediation depends on temporal organization.

Temporal thickness also introduces normativity in a stronger form. A single response can accidentally preserve a system. A temporally organized agent exhibits patterns of correction, learning, and anticipatory regulation. It can sacrifice immediate stability for longer-term viability. It can explore, endure temporary error, and reorganize after disruption. These capacities distinguish agency from simple homeostasis.

The concept of identity becomes correspondingly graded. At one extreme, a system may preserve nearly the same organization through time. At another, it may transform radically while retaining continuity through memory and causal lineage. Human identity clearly belongs to the second category. Neural, bodily, and social changes accumulate, yet there remains a structured continuity of capacities and commitments. A viable Intellecton theory must accommodate transformation without collapsing identity into either static substance or arbitrary narrative.

A process criterion can be framed through recurrent boundary reconstitution. Let \(P_t\) denote the partition at time \(t\), including its state variables and causal relations. Identity across time is not exact equality \(P_t=P_{t+1}\), but the existence of transformations that preserve selected organizational invariants. These invariants may include viability constraints, causal integration profiles, learned policies, and memory relations. The relevant invariants depend on the kind of agent under study.

This account avoids the temptation to locate the subject in a single cortical column. Cortical microcircuits may be temporally thick components, but organism-level subjecthood likely depends on coordination across widespread neural, bodily, and environmental processes. The boundary of the subject may be dynamically assembled during tasks and altered during sleep, anesthesia, or pathology. Such variability is compatible with realism if the assembly follows robust causal principles.

Pathological cases provide important tests. In dissociative conditions, split-brain cases, disorders of consciousness, and neurodegenerative disease, different dimensions of temporal unity can separate. Memory may degrade while basic regulation persists. Integrated neural dynamics may change while organismic boundaries remain stable. These cases undermine any simple identification of one formal property with subjecthood, but they also provide data for a multidimensional framework.

Artificial systems raise parallel questions. A language model session may exhibit complex internal integration and context-sensitive behavior, yet its temporal continuity depends on external infrastructure and stored context. A robot may actively maintain energy and bodily integrity while possessing limited integrated processing. A distributed software service may maintain operational identity across changing hardware. The temporally thick Intellecton framework permits analysis of these cases without deciding them by substrate prejudice.

The key question is whether the process contributes to sustaining its own continuity. External dependence does not disqualify a system; organisms depend on ecosystems and social structures. But a candidate agent should participate causally in selecting, maintaining, or reconstructing the conditions of its future organization. Mere persistence because an external operator repeatedly restores the system is weaker than endogenous repair and adaptation.

Temporal thickness also affects integrated information. The cause-effect structure relevant to a subject may span multiple timescales. Fast neural interactions support immediate experience, while slower plasticity shapes dispositions and identity. A single TPM at one \(\Delta t\) may miss this hierarchy. Multiscale analysis should examine whether causal integration nests across temporal grains and whether slower processes constrain faster ones.

The concept of an intellecton can now be sharpened. It is not a minimal particle of consciousness or a static bounded module. It is a temporally extended process that maintains a selective boundary, preserves a viability domain, integrates causal organization, and uses history to shape future coupling. The word "minimum" should refer to the minimal organization satisfying this conjunction under specified conditions, not to the smallest graph with a formal blanket.

This revised concept preserves the Canon's emphasis on recursive witness dynamics. Witnessing is not an instantaneous registration. It requires retention of what has occurred, differentiation of current input, and anticipation of possible action. A witness is a process for which events alter a continuing organization. The boundary of that witness is enacted through time.

The temporal reconstruction therefore links Volume 2 back to Volume 1's emphasis on persistent memory. A world can be relevant to an observer only if the observer maintains coherence across causal succession. Volume 2 supplies a candidate mechanism for that coherence: an actively maintained, integrated Markovian boundary. The connection is strongest when memory is treated not as a stored object but as the historical structure of an ongoing process.

\subsection{Extension, Lineage, and Anticipation}

Temporal thickness distinguishes a system's own memory from records merely available nearby. A notebook or database can extend cognition when the agent reliably accesses and integrates it. Mere information in the environment does not become part of the agent. The test is organized coupling: does the resource participate in recurrent regulation, and does disruption alter characteristic capacities? This allows extended cognition without treating the entire environment as internal.

The account must also distinguish persistence from repetition. A sequence of identical but causally disconnected systems is not one enduring agent. Diachronic identity requires causal continuity and transfer of organization. Conversely, a changing process can remain one agent when later states inherit and transform constraints established by earlier states. Lineage, not resemblance alone, matters.

Anticipation adds a final dimension. Temporally thick agents organize present action around possible futures. Expected outcomes and counterfactual policies shape behavior before events occur. The current state is structured by absences and possibilities, not only immediate causes. There may be no privileged minimal timescale for this organization. Nested horizons coordinate fast perception, intermediate action, and slow identity, making the intellecton a hierarchy of coupled temporal processes.

This hierarchy suggests a distinction between episodic and dispositional integration. Episodic integration concerns the unity of a process during a bounded event, such as a perceptual episode. Dispositional integration concerns the slower organization that makes classes of episodes possible. Neural dynamics may fragment episodically during sleep while preserving dispositional capacities that reappear on waking. An adequate theory of identity must explain both continuity and interruption.

The temporal account also prevents the concept of witness from becoming passive. To witness is to be changed in a way that can matter later. A system that registers an event but leaves no causally available trace has not witnessed in the demanding sense relevant to the Canon. Memory, therefore, is not an optional cognitive feature added to a bounded agent. It is part of what makes the boundary the boundary of one continuing process rather than a succession of unrelated states.

Continuity is an active achievement.
