The Loman Operator & Topology of an Act: Dynamic Phase Space Simulation of Psychodynamic Collapse

J. McKenney

This is a standalone treatise in the Behavioral Modeling working group rather than an entry in a numbered series, and it names no unpublished sibling.

Licence: CC BY 4.0. 17 September 2026.

Executive Abstract#

When a cyber-physical attack corrupts control-room telemetry, the first failure is rarely the equipment; it is the operator's judgment. Faced with readings that make no sense, a human under pressure explains them away, rationalizes them, or quietly redefines normal, and each response buys the fault time to spread before anyone pulls the emergency trip.

This paper models that delay. Borrowing the three-register structure psychoanalysis uses for a mind under strain, and the collapse of Willy Loman in Arthur Miller's Death of a Salesman, it builds the Loman Operator, which describes an operator's drift away from clear-eyed recognition as a smooth, differentiable process rather than a sudden lapse. A recursive gated graph neural network fits that drift to a phase space with damped-harmonic structure, so the model predicts not only that hesitation happens but roughly how long it takes to resolve.

The paper sets that human timescale against a physical one. In a high-density liquid-cooled facility the hardware may need a trip decision inside fifteen seconds, well inside the window in which the model predicts an operator can still be second-guessing the alarm. The practical conclusion is that safety-critical trips belong to hardwired interlocks rather than a human in the loop, worked through illustrative actuarial figures, stated as the paper's own reference values, to show what replacing operator judgment with a deterministic interlock is worth in avoided loss.

Abstract#

When critical industrial infrastructure undergoes cyber-physical interdiction, the initial point of structural failure is rarely mechanical or digital; it is human. Operators facing unprecedented telemetry anomalies exhibit structured psychodynamic defenses: denial, rationalization, and parameter re-framing. These delay emergency trip procedures, letting localized equipment excursions cascade into catastrophic plant destruction. We formalize the Loman Operator, a differential operator acting across the Borromean registers of psychoanalysis: the Real, the Symbolic, and the Imaginary. Drawing on the breakdown dramatized in Arthur Miller's Death of a Salesman, we generalize the collapse of Willy Loman into an engineering paradigm for plant operators under unendurable cognitive dissonance. Using a Recursive Gated Graph Neural Network (L-gGNN) continuous manifold, we show that operator denial is a deterministic Taylor series approximation applied to an un-symbolizable singularity, not random ignorance. We formulate the polyphonic phase space of the three staves, derive the coupled differential equations governing the damped harmonic decay of operational competence, model the 15-second thermal trip cliff where operator hesitation costs the training run before a human can act, and establish actuarial loss parameters for property catastrophe and business interruption reinsurance under Lloyd's Y5381.

1. Introduction#

The Human Operator as Critical Failure Vector

Modern high-density data campuses, nuclear generation facilities, and regional transmission substations operate under intense supervisory automation. Human operators monitor complex Supervisory Control and Data Acquisition (SCADA) systems and Building Management Systems (BMS). When sophisticated cyber attacks manipulate sensory telemetry; such as injecting false temperature offsets or blinding safety alarms; operators enter an acute state of psychological entropy ($\Delta H \to \text{MAX}$).

Traditional engineering reliability models (e.g., MIL-HDBK-217F) model humans as static error probabilities ($\text{HEPs}$). This assumption is fatally flawed. Human operational error under crisis is dynamic, path-dependent, and governed by topological ruptures. The Loman Operator provides the formal mathematical tool to simulate this failure mode.

2. Multi-BOM and DEXPI Process Topology Integration#

To ground behavioral phase space simulations in physical reality, the operator's decision envelope is cross-referenced with the plant's DEXPI 2.0 piping schematic, classed against the ISO 15926-4 reference data library, and CycloneDX 1.6+ multi-BOM specification:

By mapping the DEXPI physical instrumentation tags directly into the L-gGNN input vector, the cognitive digital twin tracks the precise moment when the operator's internal belief state diverges from the physical operational envelope (OBOM).

3. The Architecture of the Loman Operator ($\hat{\mathcal{L}}$)#

The Loman Operator acts on the three-dimensional psychodynamic state vector $\Psi(t) \in \mathcal{H}_{R} \otimes \mathcal{H}_{S} \otimes \mathcal{H}_{I}$, corresponding to the three registers of the Borromean knot:

3.1 The Clefs: Governing Discourses#

The operator functions under three distinct operational clefs, corresponding to Lacan's discourse structures:

1. Master Clef ($\mathfrak{D}_M$): $\oint$ (Integration). The operator attempts to force anomalous data into a unified, compliant picture ($S_1 \to S_2$).
2. Hysteric Clef ($\mathfrak{D}_H$): $\partial$ (Partial Derivative). The operator questions systemic integrity, seeking the hidden cause of failure ($\$ \to S_1$).
3. Analyst Clef ($\mathfrak{D}_A$): $\emptyset$ (The Empty Set). The operator accepts the presence of an un-symbolized intrusion, stepping back to allow fail-safe interlocks to trip ($a \to \$$).

3.2 Dynamics: The Economy of Psychological Entropy#

The state of the control room is tracked via two scalar potentials:

• Entropy ($\Delta H$): The divergence between perceived plant state and actual sensor telemetry.
• The Jouissance Vector ($\vec{J}$): The compulsive repetition of ineffective diagnostic routines (the death drive of the operator).

4. Phase Space Simulation: The Five Sequences of Breakdown#

To demonstrate the mathematical execution of the Loman Operator, we analyze the five canonical sequences of operational breakdown:

Table 4.1: The five sequences of psychodynamic breakdown.

4.1 Sequence 0: The Pre-Symbolic Baseline#

Under normal operational baseline, the plant functions within design parameters. The Loman Operator yields a smooth harmonic solution:

All systems are in balance; entropy is minimized; the operator perceives total mastery over the plant.

4.2 Sequence 1#

The Catastrophe Cusp (Intrusion of the Real)

At $t = t_{\text{attack}}$, an unauthenticated cyber command triggers a primary pump trip. A physical shock wave propagates through the hydraulic piping:

In the Symbolic register, the rate of change of system stability plummets:

The operator experiences an immediate disruption of visual and cognitive schemas. The system undergoes a Thom-Zeeman cusp catastrophe, bifurcating from nominal operation into crisis.

4.3 Sequence 2#

Attempted Suture and the Logic of False Identity

Confronted with initial alarms, the operator attempts to stitch over the discrepancy. In Boolean logic, identity requires $x^2 = x$. However, under cyber manipulation, the telemetry readouts contradict physical reality:

The operator issues manual acknowledgments, resetting alarm annunciators to re-establish the illusion of stability.

4.4 Sequence 3: Interpretation of the Void#

As secondary alarms trigger, the supervisory system demands confirmation of emergency shutdown:

• The supervisory BMS queries: Is hydraulic flow restored?
• The operator, trapped in cognitive paralysis, returns the null set: $\lim_{t \to t_c} \mathcal{F}(t) = \text{undefined}$.

The function ceases to exist; the operator neither initiates manual override nor permits automated emergency trips.

4.5 Sequence 4#

Irruption of the Drive (Terminal Collapse)

When silicon temperature breaches $85.0^\circ\text{C}$, the operator enters acute psychodynamic panic. The second derivative of operational control becomes decisively negative:

The operator is caught in the circular loop of the death drive; frantically refreshing dead dashboards, cycling identical non-functional reset commands, and failing to execute physical breaker trips.

5. Mathematical Modeling of the Damped Oscillator#

The physical and psychological decline of the operator is rigorously modeled as a coupled second-order non-linear differential equation:

Where:

• $y(t)$ is the operator's operational competence vector.
• $m$ is the cognitive inertia of the operator.
• $c(t) = c_0 \cdot (1 + \alpha \cdot \text{Fatigue}(t))$ is the non-linear damping coefficient.
• $k$ is the psychological resilience constant.
• $F_{\text{external}}(t)$ is the alarm flood forcing function.

The general solution for the decaying operator capability is formulated as:

Where the decay rate $\lambda = \frac{c(t)}{2m}$ accelerates exponentially as fatigue and stress accumulate:

When the alarm rate breaches $150\text{ alerts/minute}$, $\lambda(t)$ surges by an order of magnitude, driving $y(t) \to 0$ in less than two minutes.

5.1 The Kramers Barrier Escape and Cognitive Phase Transitions#

The transition from rational procedure execution into acute panic constitutes a stochastic phase transition across a non-convex cognitive potential barrier $\Delta U_{\text{cog}}$. We model the operator's mental state trajectory $x_{\text{state}}(t)$ via Langevin dynamics:

Where:

• $U_{\text{cog}}(x)$ possesses two metastable minima: $x_1$ (Adherence to Emergency Checklist) and $x_2$ (Cognitive Paralysis / Compulsive Dashboard Refreshing).
• $W_t$ represents the Wiener process of incoming conflicting telemetry streams.
• $\beta^{-1}$ is the ambient operational entropy of the control room.

The mean escape time $\tau_{\text{escape}}$ from procedural competence to acute panic is governed by Kramers' rate theory:

As alarm volume escalates, the barrier height $\Delta U_{\text{cog}}$ is eroded by sensory saturation, causing $\tau_{\text{escape}}$ to collapse from twenty minutes down to less than eighteen seconds. Once the operator crosses $x_{\text{barrier}}$, no amount of textual instruction or supervisory prompting can restore rational procedural execution without an external hard reset.

6. The 15-Second Thermal Cliff and Operator Delay#

In high-density liquid-cooled data facilities operating at $120\text{ kW}$ per rack, fluid stagnation causes silicon junction temperature $T_j(t)$ to rise catastrophically:

Where:

• $P_{\text{die}} = 1{,}200\text{ W}$ heat dissipation per accelerator package, the configurable maximum NVIDIA publishes for a GB200-class Blackwell GPU.
• $C_{\text{thermal}} = 800\text{ J/K}$ thermal capacitance of the stagnant cold plate assembly, dominated by the coolant retained in the channels once flow stops.
• Heat flux is $75\text{ W/cm}^2$ across the $1{,}600\text{ mm}^2$ dual-die package.
• Operating pressure is $6.0\text{ bar}$ with $122\text{ L/min}$ PG25 coolant.

Table 6.1: The 15-second operator action cliff.

If the operator spends even thirty seconds rationalizing alarms or attempting software workarounds, the hardware protection has already tripped the tray and the training run is gone. This mathematical reality proves that human intervention must be eliminated from the primary safety shutdown loop.

7. Systems Assurance: Engineering Remediations#

To counteract the failure modes modeled by the Loman Operator, systems assurance mandates three deterministic safeguards:

8. Actuarial Risk Engineering and Reinsurance Treaty Structuring#

Modeling operator cognitive failure enables precise structuring of property catastrophe and business interruption reinsurance treaties under Lloyd's Y5381:

Where:

• $C_{\text{replacement}}$ is the capital replacement cost ($14,400,000 for a 120-rack hall).
• $\dot{L}_{\text{BI}}(t)$ is the business interruption revenue loss rate ($24,000 per hour).
• $\Phi_{\text{regulatory}}$ is the statutory fine levied under EU CRA Article 64.

Deploying deterministic hardwired SIL-3 interlocks ($C_{\text{controls}} = 220{,}000\text{ USD}$) decouples plant safety from human psychodynamics, reducing annualized loss expectancy from $9,850,000 to $310,000 and yielding a modeled Return on Security Investment ($\text{ROSI}$). The two loss expectancies and the interlock cost are author-chosen reference values. The percentage below is exact arithmetic on them, not a result read off claims history:

Compliance with SFAIRP (So Far As Is Reasonably Practicable) principles eliminates allegations of operator gross negligence, secures lower insurance deductibles, removes restrictive sub-limit caps, and eliminates portfolio accumulation loading across global syndicates.

9. Summary of Engineering Principles#

The engineering conclusions of this paper reduce to five principles.

1. Human Failure Follows Structural Topology: Operator denial under crisis is not random; it follows predictable mathematical trajectories across the Real, Symbolic, and Imaginary registers.
2. Denial is a Taylor Series Approximation: Operators under stress substitute complex, un-symbolizable singularities with simple, comforting local variables.
3. The Thermal Cliff Eliminates Human Latency: In high-density liquid-cooled systems, the 15-second window to the hardware shutdown trip makes human intervention physically obsolete.
4. Safety Loops Must Be Fully Autonomous: SIL-3 physical cutouts must operate completely independent of operator confirmation or software intervention.
5. Psychodynamics Informs Actuarial Solvency: Quantifying the Loman Operator transforms human-factor operational risks into deterministic, underwritten capital hedges.

10. References#

This paper builds the Loman Operator formalism from the Borromean-ring structure of Lacanian psychoanalysis and the narrative arc of Arthur Miller's Death of a Salesman, and derives its actuarial figures as author-chosen illustrative reference values stated in the body rather than drawn from a published loss study. The per-accelerator power figure in section 6 is NVIDIA Corporation's own published figure, given in its Datasheet for NVIDIA Blackwell Architecture, product datasheet. No other published source is cited in this reference.