SINAP: Systems-based Interpersonal and Narrative Algorithmic Prediction

A heuristic computational model for dynamic assessment of emotional dysregulation in clinical and forensic psychology contexts.

Keywords / Palabras Clave: Borderline Personality Disorder (BPD), Trastorno Límite de la Personalidad (TLP), Reactive Abuse, Abuso Reactivo, Intermittent Reinforcement, Refuerzo Intermitente, DARVO, Narcissistic Abuse, Abuso Narcisista, Trauma Bonding, Systems Theory, Emotion Regulation, Regulación Emocional, Dinámicas Vinculares, Psicología Clínica, Computational Psychology.

Author: Juan Andres Ubeda
Affiliation: Juan Andres Ubeda - Psicología - Universidad Maimónides (Argentina)
Year: 2026
License: MIT

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📐 The Equation

Core Tension Oscillator

$$T_d = \text{clamp}\left( T_{d-1} \cdot \lambda + V + E - R_1 + \gamma \cdot R_2^2,\ 0,\ 10 \right)$$

Delta (Rate of Change)

$$\Delta T_d = T_d - T_{d-1}$$

Critical Risk Index

$$R_c = \frac{T_d}{10} \cdot \left(1 + \Delta T_d + \frac{E}{10} + A\right)$$

where $\text{clamp}(x, 0, 10)$ bounds the output to the $[0, 10]$ interval.

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🔠 Variable Glossary

Symbol	Name	Range	Description
$T_{d-1}$	Prior Tension	0–10	Emotional tension level at the previous time step
$\lambda$	Persistence	0.5–0.95	Rate at which prior tension carries over to the next state
$V$	Vulnerability	0–10	Activation level of maladaptive schemas (CBT framework)
$E$	External Stressors	0–10	Intensity of environmental stressors at time $d$
$R_1$	Effective Regulation	0–10	Functional coping and emotional regulation resources
$R_2$	Intrusion / Over-regulation	0–10	Ineffective, intrusive, or coercive regulation attempts
$\gamma$	Intrusion Sensitivity	0.1–1.0	Individual sensitivity coefficient to over-regulation
$A$	Systemic Asymmetry	0–10	Power imbalance, invalidation, or social/relational pressure

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🏛️ The Five Pillars: S-I-N-A-P

S — Systems Theory

Emotional dysregulation is modeled as a dynamic system, not a static trait. The model captures the temporal evolution of tension through recursive calculation ($T_d$ depends on $T_{d-1}$), drawing from General Systems Theory and cybernetic feedback loops.

I — Interpersonal Dynamics

The variables $A$ (Systemic Asymmetry) and $R_2$ (Intrusion/Over-regulation) encode the relational context of the subject. Dysregulation is not purely intrapsychic — it is co-constructed within interpersonal fields, including coercive control, triangulation, and power differentials.

N — Narrative & Cognitive Schema Activation

The variable $V$ (Vulnerability) operationalizes the activation of cognitive schemas (Young, 2003) and trauma-based narrative distortions. A subject's internal working models and narrative frameworks directly amplify or attenuate the tension state.

A — Algorithmic & Predictive

The model generates concrete, time-windowed behavioral predictions (0–24h, 24–48h, 48–72h), classifying probable behavioral phases: Stonewalling, Baiting, Escalation, Discharge, or Re-engagement. This operationalizes clinical intuition into testable hypotheses.

P — Psychometric & Quantitative Foundation

All variables are scored on a normalized $[0, 10]$ scale, enabling cross-case comparison, longitudinal tracking, and sensitivity analysis. The $\text{clamp}$ function ensures numerical stability. The model is compatible with standard psychometric frameworks (e.g., PTSD Checklist, Difficulties in Emotion Regulation Scale — DERS).

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🎓 Academic Research & Thesis Methodology (APA / SCED Standard)

Note for Academic Thesis Directors & Peer Reviewers: SINAP is designed as a hybrid computational framework combining Natural Language Processing (NLP) feature extraction with a deterministic dynamic systems equation. To ensure methodological rigor, eliminate investigator bias, and prevent AI hallucination, SINAP research adheres to the following protocols:

1. Deterministic Math Engine vs. NLP Extraction

To refute "AI hallucination" or prompt-alignment bias:

• LLM Function: The LLM acts strictly as a standardized NLP text parser to score qualitative conversational segments into normalized metrics $[0, 10]$ based on a closed clinical coding taxonomy.
• Deterministic Engine: The dynamic tension equation ($T_d = \text{clamp}(T_{d-1}\cdot\lambda + V + E - R_1 + \gamma\cdot R_2^2,\ 0,\ 10)$) is 100% deterministic. It is executed via Python script (sinap_calculator.py), completely independent of LLM generative generation.

2. Single-Case Experimental Design (SCED) Protocol

When applying SINAP to qualitative clinical transcripts or longitudinal case studies ($N=1$ exploratory pilot):

1. De-identification & Anonymization: Datasets are strictly stripped of all PII and contextual markers.
2. Inter-Rater Reliability ($\kappa > 0.80$): Independent clinical judges (blind to the SINAP equation) code the transcript for DARVO, Splitting, and Escalation markers using standardized CBT/DBT scales.
3. Statistical Concordance: The deterministic output of $T_d$ and $R_c$ is correlated against the blind human inter-rater scores to calculate construct validity ($R^2$ and Fleiss' Kappa $\kappa$).

3. Grounding in State-of-the-Art Dynamical Systems

SINAP extends established literature in computational psychiatry and mathematical psychopathology:

• Gottman & Murray (2002): Non-linear differential equations for dyadic relational stability.
• Zeeman (1976) & Tschacher (2015): Catastrophe theory applied to Borderline Personality Disorder affective flips.
• Linehan (1993): Biosocial model of emotional lability and invalidating environments.

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🩺 Clinical Applications & Diagnostic Framework

This section is intended for clinical psychologists working within CBT (Cognitive-Behavioral Therapy) and Systemic frameworks. Each SINAP variable is directly mapped to observable clinical phenomena, enabling the clinician to parameterize the model from session notes, behavioral observation, and standardized assessment instruments.

1. Personality Disorders — DSM-5 Alignment

The SINAP model demonstrates particular efficacy in the functional analysis of Borderline Personality Disorder (BPD / TLP), as defined in the DSM-5 (APA, 2013). The model's variables directly operationalize three core diagnostic criteria:

DSM-5 BPD Criterion	SINAP Variable(s)	Clinical Observation
Criterion 1 — Frantic efforts to avoid real or imagined abandonment	$E$ (External Stressors) + $A$ (Asymmetry)	Separation cues or perceived rejection spikes $E$; perceived power imbalance elevates $A$, accelerating $T_d$
Criterion 2 — Unstable and intense interpersonal relationships	$R_2$ (Intrusion) + $\gamma$ (Sensitivity)	The subject oscillates between idealization and devaluation; intrusive relational attempts ($R_2$) are amplified quadratically by $\gamma$, generating rapid $T_d$ escalation
Criterion 6 — Affective instability due to a marked reactivity of mood	$\lambda$ (Persistence) + $\Delta T_d$	A high $\lambda$ value (e.g., 0.90) reflects the persistence of dysregulated mood states across days; a large $\Delta T_d$ captures sudden affective shifts — a direct correlate of emotional lability

Clinical Note (CBT/DBT perspective): In BPD cases, the clinician should pay special attention to the $\gamma \cdot R_2^2$ term. Because $R_2$ is squared, even moderate intrusive regulation attempts (e.g., repeated phone calls, guilt-inducing messages, triangulation via third parties) produce a disproportionate increase in $T_d$. This non-linearity models the BPD subject's extreme sensitivity to perceived control or abandonment threats. This aligns directly with Linehan's (1993) biosocial theory of BPD, in which emotional sensitivity + invalidating environment = dysregulation spiral.

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2. Attachment Dynamics

The SINAP model provides a formal framework for analyzing attachment system collapse. The variables $\gamma$ and $R_2$ are the primary operationalizers of attachment dysregulation:

🔴 Disorganized Attachment (Main & Hesse, 1990)

Characterized by the simultaneous activation of approach and avoidance behavioral systems. In SINAP terms:

• $\gamma$ (Intrusion Sensitivity) is maximally elevated (close to 1.0): any proximity attempt by the attachment figure simultaneously activates the fear system.
• $R_2$ (Intrusion) is high because the subject or the attachment figure uses paradoxical, coercive, or frightening strategies that function as regulation attempts but produce the opposite effect.
• Systemic result: The $\gamma \cdot R_2^2$ term becomes the dominant driver of $T_d$, collapsing the secure base and making stable $T_d$ values ($< 3$) functionally impossible without external containment.

🟡 Anxious-Ambivalent Attachment (Ainsworth, 1978)

Characterized by hyperactivation of the attachment system and fear of abandonment:

• $\lambda$ (Persistence) is elevated: relational anxiety from previous interactions persists into the current state.
• $A$ (Asymmetry) is consistently high: the subject perceives a chronic power differential with the attachment figure, generating a self-reinforcing loop where $T_d$ rarely returns to baseline.
• $R_1$ (Effective Regulation) is chronically low: the subject struggles to self-soothe in the absence of external reassurance from the attachment figure.

Clinical Note (Systemic framework): For clinicians using structural or strategic family therapy models, $A$ (Systemic Asymmetry) maps directly to coalitional patterns and boundary violations. A persistently high $A$ indicates that the therapeutic focus must address the relational system before individual regulation is achievable.

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3. Cluster B Dysregulation Spectrum

Beyond BPD, the SINAP model is applicable across the Cluster B personality spectrum where interpersonal conflict maintenance is a central feature:

Narcissistic Personality Disorder (NPD) — Devaluation Phase

During the devaluation phase (following idealization collapse), the NPD subject generates a relational context in which the other person's SINAP variables are severely impacted:

• The NPD subject's behaviors function as a constant $E$ (External Stressor) source for their interlocutor.
• $A$ (Systemic Asymmetry) is architecturally maintained by the NPD subject through mechanisms of contempt, gaslighting, and social invalidation — keeping the other party's $A$ chronically elevated.
• Intervention implication: Lowering $A$ is the primary clinical lever. This is achieved not through confronting the NPD subject directly, but by rebuilding the interlocutor's identity resources ($R_1$), reducing their schema activation ($V$), and creating external boundary structures that reduce $E$.

Histrionic & Antisocial Spectra

• Histrionic: High $E$ generation (dramatic, stimulus-seeking behaviors) combined with low $R_1$ produces rapid $T_d$ oscillation. The model can track the subject's own regulation trajectory across sessions.
• Antisocial: $\gamma$ is characteristically low in the subject itself (reduced emotional sensitivity), but the subject functions as a high-$E$ and high-$A$ agent in the relational system of others.

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🧭 Clinical Usage Guide

For CBT Clinicians

Map the following CBT constructs directly to SINAP variables during case formulation:

CBT Construct	SINAP Variable	Assessment Source
Schema Activation (Young, 2003)	$V$	YSQ-S3 (Young Schema Questionnaire)
Life Events / Stressors	$E$	LES (Life Experiences Survey) or session observation
Coping Skills / Regulation Repertoire	$R_1$	DERS (Difficulties in Emotion Regulation Scale) — inverted score
Reassurance-Seeking / Intrusive Behaviors	$R_2$	Direct behavioral observation or collateral report
Emotional Sensitivity (baseline)	$\gamma$	Clinical estimate; cross-validate with DERS Subscale 1
Relational Power Differential	$A$	IIP-32 (Inventory of Interpersonal Problems)
Baseline Affect / Mood Inertia	$\lambda$	PANAS across multiple sessions; or MSSD (Mean Square Successive Difference)

For Systemic Clinicians

• Use $A$ (Systemic Asymmetry) as the entry point for circular questioning: "What would happen to the tension in the system if the power differential were reduced?"
• Map $R_2$ to communication patterns: intrusive or paradoxical communication acts as over-regulation, amplified by the other party's $\gamma$.
• Use $\Delta T_d$ to evaluate homeostatic vs. morphogenetic system trajectories across sessions: a positive $\Delta T_d$ trend over multiple sessions indicates a morphogenetic spiral (escalation); a negative trend suggests homeostatic stabilization.
• The recursive structure of the model ($T_d$ depends on $T_{d-1}$) aligns with circular causality principles in systemic epistemology.

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🚦 System State Classification

$T_d$ Range	Status	Interpretation
$T_d < 3$	🟢 Stable	System in equilibrium
$3 \leq T_d \leq 6$	🟡 Unstable	Escalation risk, monitoring required
$6 < T_d \leq 8$	🟠 Storm Forming	Active baiting or provocation phase
$T_d > 8$	🔴 Critical Event	Imminent discharge or decompensation

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⚙️ Sensitivity Analysis Protocol

To assess model robustness, the following perturbations are evaluated for each case:

• What happens if $R_2$ increases by $+2$? (More intrusive regulation — models escalation of contact attempts)
• What happens if $R_1$ increases by $+2$? (Better coping resources — models therapeutic progress)
• What happens if $E$ decreases by $-2$? (Stressor reduction — models environmental containment)

Each perturbation recalculates $T_d$ and $R_c$ to show directional sensitivity, enabling the clinician to identify the highest-leverage intervention point for a given case.

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🤖 How to Test SINAP with AI: The Clinical Vignette Method

You don't need to be an expert in algebra or computational modeling to use SINAP. You can use any modern LLM (like ChatGPT, Claude, or Gemini) to simulate the equation for your clinical cases using conversational data (like WhatsApp exports).

[NEW] Extended Clinical Vignette: For a full, multi-page transcript demonstrating a complete cycle of dysregulation, gaslighting, and DARVO, check out our new VIGNETTES.md file. It contains the raw chat log and the exact prompt to test the AI's diagnostic capabilities.

Instructions:

1. Open your preferred AI chatbot.
2. Copy and paste the prompt below, which includes a real (anonymized) clinical vignette of a couple in high conflict.
3. Watch the AI extract the variables from the text, run the SINAP equation, and provide a systemic risk assessment.

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🔬 Intended Use

• Clinical Supervision: Structured case formulation and risk assessment.
• Academic Research: Computational modeling of affect regulation dynamics.
• Forensic Psychology: Threat assessment in high-conflict interpersonal contexts.
• Teaching: Operationalizing abstract DSM-5 criteria into quantifiable, trackable variables for psychology training programs.

⚠️ Disclaimer: SINAP is a heuristic model. It organizes clinical variables and generates operational prognoses. It does not replace formal diagnosis or clinical judgment by a licensed professional.

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📚 References

• American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). APA Publishing.
• Ainsworth, M. D. S., Blehar, M. C., Waters, E., & Wall, S. (1978). Patterns of attachment. Erlbaum.
• Beck, A. T. (1979). Cognitive therapy and the emotional disorders. International Universities Press.
• Bertalanffy, L. von (1968). General System Theory. Braziller.
• Gottman, J. M., & Murray, J. D. (2002). The mathematics of marriage: Dynamic nonlinear models. MIT Press.
• Gratz, K. L., & Roemer, L. (2004). Multidimensional assessment of emotion regulation and dysregulation. Journal of Psychopathology and Behavioral Assessment, 26(1), 41–54.
• Linehan, M. M. (1993). Cognitive-behavioral treatment of borderline personality disorder. Guilford Press.
• Main, M., & Hesse, E. (1990). Parents' unresolved traumatic experiences are related to infant disorganized attachment status. In M. T. Greenberg, D. Cicchetti, & E. M. Cummings (Eds.), Attachment in the preschool years (pp. 161–182). University of Chicago Press.
• Tschacher, W. (2015). Nonlinear dynamical systems in psychiatry and clinical psychology. Frontiers in Psychiatry, 6, 124.
• Young, J. E., Klosko, J. S., & Weishaar, M. E. (2003). Schema therapy: A practitioner's guide. Guilford Press.
• Zeeman, E. C. (1976). Catastrophe theory. Scientific American, 234(4), 65-83.

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📄 Citation

See CONTRIBUTING.md for citation instructions.