\section{Markov Blankets as Scale-Relative Models}

The formal center of Volume 2 is the conditional independence of internal and external states given blanket states. In a Gaussian setting, this independence can be represented by a block-sparse precision matrix. Let \(x=(c,s,a,\lambda)\) denote the state vector and let \(\Sigma\) be its stationary covariance. If the relevant off-diagonal block of \(\Sigma^{-1}\) vanishes, then internal and external variables are conditionally independent given the remaining variables. This is a powerful result because it translates a graphical separation into an estimable algebraic property. It also makes clear that a blanket is a property of a joint distribution, not merely a visible physical surface.

Volume 2 derives the stationary covariance from linearized stochastic dynamics. Around a non-equilibrium steady state, the drift is approximated by a Jacobian \(A\), and the covariance satisfies a Lyapunov equation of the form

\[
A\Sigma+\Sigma A^\top+2D=0,
\]

where \(D\) is a diffusion tensor. A Helmholtz-style decomposition expresses the flow in terms of dissipative and solenoidal components. Under conditions preserving the proposed boundary topology, the precision matrix remains block sparse. The derivation gives the blanket claim mathematical substance, but each step introduces assumptions whose philosophical importance must be made explicit.

First, linearization is local. It describes dynamics near a selected steady state. Neural systems routinely undergo transitions, oscillations, metastable itinerancy, and context-sensitive reconfiguration. A blanket identified around one regime may dissolve or relocate in another. If the intellecton is meant to be a persistent agent, its identity cannot depend only on a single linear neighborhood. It must survive, or transform coherently across, multiple dynamical regimes.

Second, stationarity is an explanatory idealization. Biological systems maintain themselves far from equilibrium, but their empirical distributions may only be approximately stationary over selected windows. The relevant window is not given by the mathematics alone. At a short timescale, fast synaptic variables may define one partition. At a longer timescale, plasticity and neuromodulation alter the coupling structure. Over development, even the set of relevant variables changes. A blanket is therefore relative to temporal grain.

Third, conditional independence is relative to a variable set. Omitting a common cause can produce an apparent dependence; conditioning on a collider can create one; coarse-graining can eliminate or generate dependencies. The master key correctly worries about the sensory state becoming a collider and specifies an asymmetric dependency structure to avoid that problem. But the correctness of this structure is an empirical claim about the selected neural variables. Real cortical circuits include feedback, recurrent lateral coupling, diffuse neuromodulation, and common inputs. The graph must be tested rather than inferred from canonical labels.

These considerations motivate a scale-relative blanket measure. For a coarse-graining level \(\ell\), define

\[
\mathcal{B}_{\ell}
=I(C_{\ell};\Lambda_{\ell}\mid S_{\ell},A_{\ell}),
\]

where \(I\) is conditional mutual information. An exact Markov blanket has \(\mathcal{B}_{\ell}=0\). Empirical systems will generally yield a small but nonzero value. The relevant question is not simply whether a blanket exists, but how \(\mathcal{B}_{\ell}\) changes across scales, timescales, tasks, and perturbations.

This formulation has three advantages. It permits approximate blankets, which are more realistic than exact independencies. It makes scale explicit, preventing a boundary discovered at one resolution from being treated as an absolute metaphysical division. And it supports comparative analysis: candidate agent boundaries can be ranked by the degree and robustness of mediation they provide.

Scale relativity does not imply arbitrariness. A mountain has different boundaries in geological, ecological, and political descriptions, yet some boundaries are more explanatory than others. Likewise, a biological agent may admit multiple blankets, but some partitions better predict intervention outcomes, preserve identity across perturbations, or compress the system's dynamics. The problem is to articulate these standards.

One standard is predictive adequacy. A useful blanket partition should allow internal and blanket states to predict future system behavior without direct access to external states. Another is intervention stability. The partition should remain informative when external variables are perturbed. A third is dynamical persistence. The boundary should recur across time rather than appearing as a transient statistical accident. A fourth is explanatory compression. The blanket should support a simpler yet accurate model of the system's coupling to its environment.

These standards transform the Markov blanket from a binary property into a research program. Suppose several partitions satisfy approximately low conditional mutual information. One may correspond to a cortical microcircuit, another to a brain network, and another to the whole organism. Rather than asking which is the "real" blanket in isolation, investigators can ask which partition exhibits the greatest stability, autonomy, integration, and predictive utility for the target phenomenon. The answer may be plural.

This pluralism challenges a common reading of the free energy principle in which every system with a Markov blanket is thereby interpreted as engaging in inference. The mathematical equivalence between certain flows and gradient descent on a variational quantity is not automatically an account of representation or cognition. A system may be describable as minimizing a functional without literally estimating hidden causes. Interpretive restraint is essential. The intentional vocabulary of beliefs, predictions, and evidence should be earned by additional behavioral and causal criteria.

The same restraint applies to cortical grounding. The canonical microcircuit provides a plausible architecture for predictive processing, with superficial populations conveying prediction errors and deep populations conveying predictions. Yet canonical circuitry is an idealized motif, not a complete description of every cortical region. If the proposed blanket relies on the absence of direct couplings that are present in vivo, the proof applies to the model rather than the tissue. This does not invalidate the theory; it identifies the empirical burden.

The solenoidal flow assumption deserves particular attention. Non-dissipative flows can circulate probability around steady-state contours. If such flows cross the proposed boundary in ways that couple internal and external states, blanket sparsity may fail. Requiring the flow to preserve boundary topology is therefore substantial. It may encode the very autonomy that the blanket is later used to explain. If so, the derivation risks circularity: the system has an agent-like boundary because its flows are assumed to respect an agent-like boundary.

Avoiding circularity requires an independent account of why the relevant flow constraints arise. In biological systems, they may arise through evolved morphology, cellular membranes, synaptic architecture, and active regulation. In artificial systems, they may arise through design. In both cases, the boundary is historically and dynamically produced. The precision matrix records the consequence of this production; it does not explain it by itself.

A process-oriented account therefore treats a low \(\mathcal{B}_{\ell}\) as a snapshot of an ongoing organization. The snapshot is informative, just as a metabolic profile is informative, but the agent consists in the mechanisms that sustain the profile. This view integrates the statistical strength of Markov blankets with the biological insight that living boundaries are made and repaired.

The scale-relative interpretation also protects Volume 2 from two opposing errors. The first is blanket inflation, in which every conditional independence becomes an agent. The second is blanket eliminativism, in which scale dependence is mistaken for unreality. Between them lies a disciplined realism: blankets are real patterns when they support robust prediction, intervention, and compression across relevant conditions. Their reality is relational and processual rather than absolute.

On this view, the Markovian boundary is not a final answer to individuation. It is a formal instrument for locating candidate units whose autonomy can then be tested. The next step is to specify what autonomy adds to statistical separation and why that addition matters for the Intellecton project.

\subsection{Methodological Constraints}

The scale-relative account raises a concern: could investigators always choose a grain that produces the blanket they expect? This danger is real. It can be controlled through preregistration, held-out prediction, intervention, and comparison with null models. A proposed partition should outperform alternatives on data not used to construct it. Its advantage should persist when variables are measured differently and when plausible latent causes are introduced. Scale relativity becomes productive only when scale selection is constrained by performance.

There is also a distinction between epistemic and ontic scale relativity. Epistemic relativity concerns limits of measurement. Ontic relativity concerns the possibility that causal organization itself is genuinely layered. A cortical population can exert causal influence as a population even though it consists of neurons. Higher-level regularities are real when interventions on higher-level variables support stable generalizations. The present account therefore does not reduce every blanket to an observer's convenience; it asks whether a partition identifies a robust pattern.

This provides a route to adjudicating competing boundaries. If organism-level active states preserve viability under intervention while a microcircuit's proposed active states do not preserve the circuit as a unit, the organism boundary has stronger autonomy credentials. The microcircuit blanket remains useful, but for a different explanatory purpose. Blanket landscapes may also migrate during anesthesia, learning, or social coordination, revealing the dynamic assembly of functional units.

The immediate implication is that blanket discovery should be treated like model selection, not metaphysical detection. Candidate partitions should be compared by their predictive accuracy, stability under perturbation, compression, and capacity to support causal generalization. A partition that performs well only in one dataset is a local convenience. A partition that survives changes in measurement and intervention is evidence of a real organizational level. This criterion gives the Canon a disciplined realism: the boundary is neither an absolute line nor a free choice, but a robust relation discovered through constrained inquiry.