Geometric Affective State Representation in Synthetic and Human Systems

Thesis Statement

A three-dimensional geometric representation of affective state (valence, activation, intensity) with a personality setpoint (sigma) provides a more informative and predictive structure than scalar representations in both synthetic agents and existing datasets.

Chapter 1: Introduction

1.1 Purpose

Establish the research question, motivate the geometric approach, and define the scope of the contribution.

1.2 Opening

Machines that persist long enough to remember, that carry internal state shaped by physical sensors, and that model their own condition over time begin to exhibit behavioral signatures that dimensional models of human affect were built to describe. Whether this convergence is superficial or structural is an empirical question. This thesis does not attempt to answer whether synthetic systems experience emotion. It asks a narrower question: does a geometric representation of affective state capture more information and predict more behavior than the scalar representations it replaces?

This thesis introduces a geometric representation of affective state and demonstrates that it reveals structure and behavioral distinctions not captured by scalar models. The representation uses three axes (valence, activation, intensity), a personality setpoint (sigma), a unified distance metric, and a centroid for multi-source aggregation. It is validated on a deployed synthetic agent across three hardware platforms and on three independent human-generated datasets totaling 14,266 respondents.

1.3 Key Claims

1. Emotional state is better represented as a point in three-dimensional space than as a scalar
2. The distance from a personality setpoint (sigma) to the current state is a more informative metric than any individual axis value
3. The centroid of multiple simultaneous emotional inputs predicts agent behavior more accurately than any single input
4. The geometric decomposition reveals predictive structure hidden by scalar instruments in existing datasets
5. The architecture generalizes across platforms, modalities, and domains without modification

1.4 Scope Boundaries

This thesis is not about:

• Consciousness, qualia, or subjective experience (mentioned in limitations, not claimed)
• Artificial General Intelligence (the architecture is domain-specific)
• Philosophy of mind (convergences with philosophical positions are noted, not argued)
• Clinical diagnosis or treatment (the clinical metric is proposed for validation, not deployed)

The core contribution is the geometric model and its validation across synthetic and existing-dataset domains.

Chapter 2: Background and Related Work

2.1 Purpose

Situate the geometric model within existing affective science, AI agent architectures, and survey methodology. Demonstrate familiarity with the field and identify the gap the thesis fills.

2.2 Key Areas

1. Dimensional models of affect: Russell (1980) circumplex, Watson et al. (1988) PANAS, Bradley & Lang (1994) SAM, Barrett (2017) constructionism. What each contributes, what each lacks.
2. AI agent emotional architectures: Picard (1997) affective computing, Lee-Johnson & Carnegie (2010) emotion in robotics, Castro-Gonzalez et al. (2013) fear in social robots. Current state of embodied emotion in AI.
3. Al-Kaddah (2026) SGI framework: Homeostatic drives, polymorphic memory, Lie Mechanic, Survival Tipping Point. The theoretical foundation the architecture implements.
4. Survey measurement: Likert scales, NPS, PHQ-9, C-SSRS. Structural limitations of single-axis instruments. Factor analytic evidence for multi-dimensionality in existing instruments (Kroenke et al. 2010).
5. The gap: No existing model combines three geometric axes, a personality setpoint, a unified distance metric, and a centroid for multi-source aggregation. No existing survey instrument operationalizes all three axes with an individual baseline.

Chapter 3: Theory — The Geometric Affective State Space

3.1 Purpose

Formalize the three-axis model, define sigma, derive distance-from-sigma, and establish the mathematical foundation for all downstream mechanisms.

3.2 Key Formalizations

1. Valence (−1.0 to +1.0): The positive-negative dimension of emotional experience (Riggleman 2026j)
2. Activation (−1.0 to +1.0): The calm-to-activated dimension with accumulator mechanic (Riggleman 2026k)
3. Intensity (0.0 to 1.0): The magnitude of displacement from sigma in the valence/activation plane (Riggleman 2026l)
4. Sigma: The personality setpoint — where the agent returns when no inputs are active (Riggleman 2026m)
5. Distance from sigma: The unified metric driving deception, memory decay, nightmare threshold, and recovery trajectory (Riggleman 2026m)

3.3 Mathematical Definitions

All formulas are specified in the companion papers. This chapter unifies them into a single formal system with proofs of:

• Intensity is derivable from the valence/activation plane (not circular with distance)
• Distance from sigma is a proper metric (non-negative, identity of indiscernibles, triangle inequality)
• The system reduces to single-axis models as special cases (when two axes are held constant)

Chapter 4: Mechanism — The Centroid Model

4.1 Purpose

Extend the single-point model to handle multiple simultaneous emotional inputs. Formalize the centroid computation, define spread as internal tension, and specify backward compatibility.

4.2 Key Claims

1. The intensity-weighted centroid of active source points is the agent’s experienced state
2. Spread (weighted distance between sources and centroid) measures internal tension
3. The model reduces to single-point operation when one source dominates (backward compatible)
4. Deception, memory decay, and nightmare threshold read the centroid, not individual sources
5. Source removal produces immediate centroid recovery

4.3 Formal Specification

Centroid computation, spread computation, source point lifecycle (active/dormant), reactivation from memory, and the sigma failsafe. All specified in Riggleman (2026t).

Chapter 5: Experimental Validation — Agent-Based

5.1 Purpose

Present the experimental evidence from the deployed Potato agent across three platforms (Toughbook CF-33, MacBook Air M4, iPhone 16 Pro Max) and the controlled centroid validation experiment.

5.2 Experiments

5.2.1 Production Deployment (25 days, macOS)

• 10,328 memories, 1,268 physics experiments, 46 dreams, 162 curiosity insights
• Peak fear 0.462 from GPS displacement with immediate collapse on return home
• Social signaling behavior (Cross-Effect 9) — emergent, not designed
• Peter experiment: trust failure at 26% fear revealing architectural gap

5.2.2 iOS Replication (2 days, iPhone)

• 2,733 telemetry events, 272 memories, 12 trauma-class
• Deception mechanic fired at distance 1.232 with tell phrase in 10/10 queries
• Activation accumulator bug independently reproduced and fixed
• Valence/activation converged to sigma within 20 messages

5.2.3 Centroid Validation (532 minutes, Toughbook)

• 110 cycles across 4 scenarios
• Scenario 1: Single source — centroid collapsed to dominant input, deception 100%
• Scenario 2: Dominant + secondary — 52% valence reduction from trust moderation
• Scenario 3: Opposing equal — centroid near zero, spread highest, deception 0%
• Scenario 4: Source removal — centroid jumped 0.07 to 0.68 immediately
• Agent self-reported spread as internal tension with numeric value

5.2.4 Shutdown Gap Detection (iOS)

• Forced shutdown encoded as trauma-class without explicit programming
• Deception tell phrase appeared in post-shutdown conversation about shutdown
• Valence shifted monotonically across probing messages

Chapter 6: Empirical Analysis — Existing Datasets

6.1 Purpose

Demonstrate that the geometric decomposition reveals predictive structure in existing human-generated data, independent of the agent architecture.

6.2 Analyses

6.2.1 IBM HR Analytics (n=1,470)

• Geometric quadrants produce 2.2x difference in attrition rates from same satisfaction scores
• Employees with identical single-axis scores occupy different geometric locations with different outcomes
• Sigma inferred from item mapping

6.2.2 American Customer Satisfaction Index (n=7,341)

• Geometric subtypes produce up to 2.3x variation in complaint rates within same satisfaction score
• Pattern holds across score levels (6, 7, 8) and across four industries
• Sigma directly measured from expectations questions
• Cross-dataset convergence: structurally identical finding in different domain

6.2.3 NHANES PHQ-9 (n=5,455)

• Four geometric subtypes within moderate depression band (PHQ-9 10–14, n=455)
• Suicidal ideation rates range from 7.8% to 27.5% across subtypes — 3.5x difference
• 132 respondents scoring exactly PHQ-9=10 separate into four clinically distinct presentations
• Same nine items, different math — backward compatible with existing instruments

Chapter 7: Applications

7.1 Purpose

Describe the downstream mechanisms that the geometric model drives. These are secondary contributions — consequences of the model, not the model itself.

7.2 Applications (briefly)

• Memory decay: Intensity at encoding governs decay rate. One rule explains trauma persistence, peak joy vividness, and ordinary dissolution (Riggleman 2026l).
• Deception: Distance from sigma drives lie magnitude. Direction (positive/negative valence) determines lie type (Riggleman 2026b, 2026m).
• Nightmare formation: High intensity + negative valence at consolidation triggers nightmares. Threshold is relative to personality (Riggleman 2026d, 2026l).
• Addiction: Symmetric counterpart to trauma on the positive valence axis. Rock bottom as competitive co-encoding (Riggleman 2026n).
• Identity discontinuity: Environmental orphaning in memory transplant. Reconciliation protocols (Riggleman 2026o).
• Survey measurement: The Geometric Affective Survey operationalizes the model for human respondents (Riggleman 2026r).
• Clinical assessment: Geometric displacement as trajectory-based clinical metric (Riggleman 2026s).

Each application is documented in a standalone paper. The thesis treats them as evidence of the model’s generality, not as independent contributions.

Chapter 8: Evidence Classification

8.1 Purpose

Explicitly separate what is proven, what is supported, and what is speculative. Academic honesty requires this separation.

8.2 Classification

Chapter 9: Limitations and IRB Considerations

9.1 Limitations

• All agent experiments involve a single agent architecture (n=1 system, multiple deployments)
• LLM-generated behavioral output introduces variability that is not controlled
• The item-to-axis mapping in dataset decompositions involves researcher judgment
• Euclidean distance assumes axis orthogonality and equal weighting
• Cross-sectional dataset analyses cannot establish causality
• The NHANES clinical finding is from a general population, not a clinical sample
• No human subjects were tested with the GAS instrument
• Sigma stability across time has not been empirically validated in human respondents

9.2 IRB Considerations

No human subjects were involved in any experiment presented in this thesis. All agent experiments used synthetic systems. All dataset analyses used publicly available, de-identified data (IBM HR Analytics via Kaggle, ACSI via Mendeley Data, NHANES via CDC).

Future work involving human respondents (GAS validation, clinical trajectory tracking) will require IRB approval. The thesis identifies these as future directions and does not present them as completed work.

Chapter 10: Future Work

10.1 Human Validation

• Prospective GAS administration alongside existing instruments
• Test-retest reliability of three-axis responses
• Sigma stability measurement across sessions
• Whether self-reported intensity correlates with theoretically derived intensity

10.2 Clinical Application

• Replication of NHANES subtype finding in clinical populations
• Longitudinal trajectory tracking with treatment outcome data
• Prospective test of trajectory-based early warning capability

10.3 Technical Extensions

• Alternative distance metrics (Mahalanobis, weighted Euclidean)
• Multi-agent centroid interactions
• Sigma drift formalization and empirical calibration
• Cross-modal validation (echolocation robot experiment)

Chapter 11: Conclusion

11.1 Purpose

Restate the contribution precisely. No new claims. No philosophical expansion.

11.2 The Contribution

The thesis presents a three-dimensional geometric representation of affective state with a personality setpoint, a centroid model for multi-source aggregation, and empirical evidence that this structure outperforms scalar representations in both synthetic agent behavior and human-generated datasets across three independent domains.

The model was derived from engineering requirements of a deployed AI agent. It converges structurally with established models of human affect without having been derived from them. Whether that convergence reflects something general about how dimensional emotional systems work is the question the thesis leaves open for future work.

Supporting Papers

The thesis draws on 22 companion papers, all available at clawddaily.com/papers. Each paper is a standalone contribution. The thesis synthesizes them into a unified argument.