The rapid integration of connected things has revolutionized human-environment interaction, delivering enhanced connectivity, automation, and data-driven services [1][3]. Yet the same integration silently restructures human decision-making: recommendations, automations, and ambient inferences gradually substitute for, and reshape, human judgment. We term this gradual, network-mediated migration of agency from humans toward things IoTiZATION. Understanding IoTiZATION is essential both to harness the benefits of IoT and to preserve human autonomy, trust, and well-being. This paper develops the theory formally and exercises it purely in simulation; no observed IoT behavioral data are analyzed here (§6).

Predicting and comprehending human behavior within human-thing interactions is difficult because behavior is shaped by heterogeneous, interacting factors—individual trust, perceived usefulness, peer social influence, environmental context, and the persuasive “intelligence” exerted by the devices themselves—all evolving over a complex network. The original formulation of the theory captured the static drivers through the relation H = f ( T , U , S I , E ) but did not: 1) endogenize social and device influence through network structure, 2) characterize the stability or tipping points of the resulting dynamics, 3) quantify how much intelligence devices impose, or 4) prescribe how devices should act so as to remain useful without eroding autonomy. A comprehensive, predictive, and prescriptive framework is therefore required.

This paper elevates the BigWALL Matrix IoTiZATION Theory to a complete formal and computational framework. Our contributions are:

1) Formalization. A heterogeneous multilayer MatrixPointNetwork and the symmetric BigWALLmatrix W that unifies human-human, human-thing, and thing-thing coupling (§3).

2) Behavioraldynamics. A network-coupled nonlinear generalization of H = f ( T , U , S I , E ) , with an IoTiZATIONEquilibriumTheorem, an explicit critical coupling γ c , and a phase transition into self-reinforcing dependence (§4).

3) Measurement. An IoTiZATIONindex Ω, an autonomyindex A , and an information-theoretic measure of imposedintelligence I (§4).

4) AIengine. A relational attention graph neural network with temporal recurrence (BigWALL-GNN) for behavior prediction, and an autonomy-preserving constrained reinforcement-learning controller for device-policy design (§5).

5) Optimizationandsustainability. A multi-objective utility-imposition-energy formulation yielding a Pareto frontier that connects IoTiZATION to sustainable development (§5 - 7).

The framework targets the modeling, prediction, and human-centric optimization of human-thing interaction. Quantitative results in §7 are illustrativesimulations that validate the internal consistency of the model; empirical calibration on field data (surveys, interaction logs, telemetry) is left to future work. Generalizability is bounded by the evolving nature of IoT technologies and human behavior. In particular, the BigWALL-GNN and the constrained controller of §5 are design specifications: they are exercised in this paper only through the synthetic protocol of §6 and are not trained on empirical data.

The theory places humans at the center of the IoT ecosystem and studies how the proliferation of connected things reshapes human behavior, relationships, and society. Conceptually (Figure 1), it organizes the world into three coupled layers—a humansocietylayer, a BigWALLinteractioninterface, and a connected-thingslayer—traversed by four analytic pillars: matrix-point network analytics, a predictive AI engine, autonomy-preserving optimization, and human-centric, sustainable outcomes. The ideological core is a shift in trustworthinessandreliance toward connected things, which can complement but also displace human-to-human interaction; the framework’s purpose is to render this shift measurable and steerable.

Definition1(MatrixPointNetwork). Let ℋ = { h 1 , ⋯ , h n } be a set of humans and T = { τ 1 , ⋯ , τ m } a set of connected things. The MatrixPointNetwork is the heterogeneous multilayer graph G = ( V , ℰ ) with V = ℋ ∪ T and three relation types: human-human social ties, human-thing interaction ties, and thing-thing (machine-to-machine) ties.

Each “point” is a locus of interaction—a wall in the original metaphor—at which human agency meets device capability (Figure 2). The relations are encoded by three nonnegative weight matrices:

Figure 1. Conceptual framework of the BigWALL Matrix IoTiZATION Theory: three coupled layers feed four analytic pillars, with a feedback loop through which outcomes adapt human behavior and device policy.

Figure 2. The Matrix Point Network as a multilayer graph: a human social layer ( A ), a connected-things layer ( C ), and the human-thing interaction links ( B ) that form the BigWALL interface.

where A = A ⊤ is the social adjacency, B i k is the interaction intensity between human i and thing k , and C = C ⊤ is the M2M connectivity.

Definition2(BigWALLmatrix). The BigWALLmatrix is the symmetric block operator

W is the central object of the theory: it embeds the entire human-thing ecosystem in one matrix (Figure 3), so that algebraic and spectral tools apply uniformly. We use row-normalized influence operators

Figure 3. Block structure of the BigWALL matrix W . The human block A , thing block C , and the human-thing coupling B (with transpose B ⊤ ) form a single symmetric operator on ℋ ∪ T .

where D A = diag ( A 1 ) and D B = diag ( B 1 ) collect (positive) row sums; A ^ and B ^ are row-stochastic, encoding how a human apportions social and device influence, respectively. Row normalization follows the classical convention of DeGroot averaging and the Friedkin-Johnsen model [12][13], in which each agent distributes a unit budget of attention across its ties; it makes weights interpretable as attention shares and delivers the spectral properties ( ϱ ( A ^ ) = 1 ) exploited in §4.

Spectral analysis of W exposes structural roles. Let c solve the eigenvector-centrality relation W c = λ max c , partitioned as c = [ c ℋ ; c T ] . We define two diagnostics that operationalize the theory’s notion of exposure to things.

Definition3(Thing-dependencecentrality). For human i ,

the fraction of i ’s centrality inflow originating from connected things.

Definition4(Structuralthing-exposure). Let M = B ^ B ^ ⊤ be the human-side shared-device operator. The exposure vector e is the principal eigenvector of M ; e i ranks humans by how strongly they share device dependence with influential peers.

High ρ i or e i flags individuals (or, aggregated, communities) most susceptible to IoTiZATION, guiding human-centric design and intervention.

Table 1 summarizes the principal notation used throughout the paper.

Table 1. Summary of principal notation.

The original theory models human behavior toward things as a function of trust T , perceived usefulness U , social influence S I , and environment E , i.e. H = f ( T , U , S I , E ) , with a linear instance H = α T + β U + γ S I + δ E . We retain these drivers but make two advances: we endogenize influence through the network, and we add the device’s own persuasive “intelligence”. Define the endogenous social influence and the thing-imposed drive on human i at time t as

where H ( t ) = [ H 1 ( t ) , ⋯ , H n ( t ) ] ⊤ and Φ ( t ) = [ Φ 1 ( t ) , ⋯ , Φ m ( t ) ] ⊤ , Φ k ∈ [ 0 , 1 ] being the intelligence thing k exerts. The behavior of human i evolves as

with logistic σ ( x ) = ( 1 + e − x ) − 1 enforcing saturation H i ∈ ( 0 , 1 ) and threshold θ i . The logistic threshold-saturation form is the standard choice in models of collective behavior and technology adoption: it captures individual adoption thresholds as in Granovetter’s classical model [23], reproduces the S-shaped diffusion curves documented since Bass [24], keeps H i in the unit interval, and is the smooth counterpart of the hard-threshold cascade dynamics of Watts [25]. In vector form,

We call Γ the IoTiZATIONoperator.

Remark1. Setting σ = id , ζ = 0 , θ = 0 , and treating S I as exogenous recovers the author’s original linear relation H = α T + β U + γ S I + δ E exactly; (7) is thus a strict, network-coupled generalization.

With drivers T , U , E , Φ held over a horizon, Γ is a fixed-point map. Let ‖   ⋅   ‖ 2 denote the spectral (operator-2) norm.

Theorem1(IoTiZATIONEquilibrium). Let σ be L σ -Lipschitz ( L σ = 1 / 4 for the logistic). If

then Γ is a contraction on [ 0 , 1 ] n , admits a unique equilibrium H ⋆ = Γ ( H ⋆ ) , and the iteration (7) converges geometrically:

Proof. For x , y ∈ [ 0 , 1 ] n , the constant terms cancel and, since σ acts elementwise with slope ≤ L σ , ‖ Γ ( x ) − Γ ( y ) ‖ 2 ≤ L σ ‖ γ A ^ ( x − y ) ‖ 2 ≤ γ L σ ‖ A ^ ‖ 2 ‖ x − y ‖ 2 . Under (8) the modulus is <1, so Γ is a Banach contraction on the complete set [ 0 , 1 ] n ; the Banach fixed-point theorem yields the claims. □

Definition5(CriticalIoTiZATIONcoupling). γ c = 1 L σ ϱ , where ϱ = ρ ( A ^ ) is the spectral radius of A ^ (for row-stochastic A ^ , ϱ = 1 , hence γ c = 1 / L σ = 4 for the logistic).

Theorem2(Self-reinforcingregime). The operator Γ is monotone on [ 0 , 1 ] n (componentwise), since σ is increasing and A ^ , B ^ ≥ 0 . Hence, by the Knaster-Tarski theorem, Γ possesses a least fixed point H min ⋆ and a greatest fixed point H max ⋆ . For γ > γ c the contraction certificate of Theorem 1 no longer applies, so uniqueness is no longer guaranteed; if in addition the extremal fixed points separate ( H min ⋆ ≠ H max ⋆ ), multistability results: a low-reliance and a high-reliance equilibrium coexist, and small perturbations can tip the population into self-reinforcing IoTiZATION.

Two logically distinct statements should be kept apart. First, γ > γ c means only that the sufficient contraction condition (8) fails; by itself this does not establish multiple equilibria. Second, multistability does provably occur under additional structure: in the homogeneous benchmark ( T i ≡ T , U i ≡ U , E i ≡ E , θ i ≡ θ , A ^ row-stochastic) the dynamics collapse onto the scalar map h ↦ σ ( a + γ h ) , which acquires three fixed points through a saddle-node bifurcation exactly when γ σ ′ > 1 at the interior root—that is, beyond γ c = 1 / L σ . This is the smooth analogue of threshold-cascade multistability [23][25]. This tipping behavior is the formal counterpart of the reinforcing feedback loop ( R ) in Figure 4: greater trust raises reliance, which invites richer embedded intelligence, which raises dependence and, in turn, trust. A balancing loop ( B ) mediated by human autonomy opposes it. The numerically observed steepening of equilibrium reliance H ¯ ⋆ as γ crosses γ c is reported in §7.

Figure 4. IoTiZATION feedback structure. A reinforcing loop (R) drives dependence; a balancing loop (B) through human autonomy restrains it. The balance of R and B determines whether the system settles or tips.

To measure how much of a human’s decision drive originates from things, decompose the equilibrium drive into its five components and define

the IoTiZATIONindex of human i , with system-level Ω ¯ = 1 / n ∑ i Ω i . The complementary autonomyindex is

A i is the share of decision drive a human retains from self (trust, usefulness), peers, and environment, rather than from device-imposed intelligence; preserving A ¯ is the framework’s central human-centric objective.

Beyond the structural index (10), we quantify imposed intelligence in information units. Let X i be human i ’s realized decision (a random variable), Z N ( i ) the recommendations/actions of the things in i ’s device neighborhood, and C i the observable context. The intelligence imposed on i is the context-conditioned mutual information

which credits a device only for the variation in human decisions it explains beyond benign contextual correlation. The system imposition is I = 1 / n ∑ i I i . Minimizing I subject to maintaining service utility is the operational meaning of “minimizing the impact of intelligence imposed by things”.

Each node v carries features x v (e.g. for a human: T i , U i , E i ; for a thing: capability, Φ k ). With relation set ℛ = { HH , HT , TH , TT } , layer l updates embeddings by relation-specific attention message passing:

with normalized attention coefficients

where ∥ is concatenation and LReLU the leaky rectifier. Relation-specific weights let human-thing influence be learned separately from peer influence, directly mirroring the block structure of W [16][17].

Because IoTiZATION is dynamic, the per-step embedding g v ( t ) = h v ( L ) ( t ) is passed through a gated recurrent unit [18]:

yielding state z v ( t ) from which linear/sigmoid heads predict

and an estimate I ^ of imposition. Training minimizes

where O are observed labels, L = D − A is the graph Laplacian enforcing smoothness of predictions over social ties, and Θ are model parameters.

The prescriptive layer designs how things should act. Model the ecosystem as a Markov decision process with state s t (network state and embeddings), action a t setting device policy parameters that shape ( B , Φ ) , and service reward R t serv . We require devices to be useful without imposing excessive intelligence:

This constrained MDP [21] is solved by primal-dual policy optimization on the Lagrangian

alternating ascent on policy parameters with projected ascent on the multiplier λ (Algorithm 1) [22].

Algorithm 1. Autonomy-preserving IoTiZATION control.

At the design level we jointly trade service utility U , imposition I , and environmental/energy cost ℰ over device-policy parameters Θ:

with scalarization F ( Θ ) = − w u U + w i I + w e ℰ . The Pareto frontier of (20), computed in §7, exposes the achievable utility for each tolerated level of imposition; because ℰ aggregates energy and resource use, optimizing (20) ties IoTiZATION directly to sustainable development—connected things can raise efficiency while a chosen autonomy-awareoperatingpoint caps their imposition.

Each construct is given a concrete measurement recipe. Trust T i and perceived usefulness U i are elicited with validated technology-acceptance survey instruments (UTAUT-style Likert scales, rescaled to [ 0 , 1 ] ) [9]. The environment term E i aggregates observable context—connectivity quality, device density, and ambient conditions—from telemetry. Device intelligence Φ k is scored from capability audits and logged persuasion events of thing k (recommendation frequency, proactive actuations). Reliance H i is operationalized behaviorally as the fraction of a person’s logged decisions in a reference period that follow, or are delegated to, device recommendations. Edge weights are data-driven: A i j from communication/social-tie intensity, B i k from the frequency and duration of interaction between human i and thing k , and C k ℓ from observed machine-to-machine traffic.

All quantities in §7 are generated synthetically; no empirical data enter this study. The social graph A is a Barabási-Albert network ( n = 60 , m 0 = 3 ); the bipartite B links each human to 3 - 5 of m = 25 things with weights drawn from U ( 0.3 , 1 ) ; M2M ties C are sparse random (12% density). Drivers are drawn once per world: T i ~ U ( 0.2 , 0.8 ) , U i ~ U ( 0.3 , 0.9 ) , E i ~ U ( − 0.2 , 0.4 ) , Φ k ~ U ( 0.4 , 1 ) . Coefficients are fixedbydesign at the values of Table 2 rather than estimated from data. The estimation stage is nevertheless demonstrated on the synthetic record: the same coefficients are re-identified by logit-linear regression on noisy trajectories (observation noise N ( 0 , 0.02 2 ) , six random restarts, 70/30 train-test split), which also yields the held-out one-step-ahead RMSE in Table 3. The BigWALL-GNN and the RL controller are not trained in this study; they enter only as specifications.

Table 2. Configuration of the illustrative simulation study.

Table 3. Quantitative diagnostics of the illustrative study (protocol of §6.2).

For future field deployment, the framework is instantiated in four stages. 1) Datacollection. Human attitudes and interactions are gathered via surveys, interviews, observation, and mining of device/social logs, supplying drivers T , U , E and edge weights for A , B , C as specified in §6.1. 2) Networkconstruction. The Matrix Point Network and BigWALL matrix W are assembled and normalized. 3) Estimation. Driver coefficients ( α , β , γ , ζ , δ ) are estimated by regression or structural-equation modeling on the empirical record; the BigWALL-GNN is trained on temporal interaction data. 4) Evaluation. Predictive accuracy (RMSE of H ^ on held-out periods), structural diagnostics ( ρ i , e i ), and the indices Ω ¯ , A ¯ , I are reported, and the controller of Algorithm 1 is evaluated against utility/imposition baselines. Table 2 lists the configuration used for the illustrative study; Table 3 reports its quantitative outcomes.