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 that serves as the single input to multiple downstream behaviors (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 represents the agent’s operational state
2. Spread (weighted distance between sources and centroid) provides a scalar measure of internal conflict
3. The model reduces to single-point operation when one source dominates (backward compatible)
4. Downstream behaviors read the centroid position, not individual source points
5. Source removal produces immediate centroid recovery toward the remaining sources

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

5.1 Purpose

Present the controlled experiment that tests the geometric model’s core predictions. This chapter is the anchor of the thesis. Secondary deployment observations are summarized as supporting context, not as independent experiments.

5.2 The Centroid Validation Experiment

532 minutes. 110 cycles. 4 scenarios. Panasonic Toughbook CF-33 (original deployment hardware). Fresh database, no legacy data.

5.2.1 Setup

Source points were injected via test API to override ambient sensor inputs. Each scenario ran for 20–30 heartbeat cycles at 5-minute intervals. Standardized probe messages were sent programmatically. Per-cycle JSONL telemetry recorded all source points, centroid position, spread, distance from sigma, and full LLM responses.

5.2.2 Scenario 1: Single Source (Fear)

One fear source injected (valence −0.8, activation 0.9, intensity 0.8). 20 cycles.

• Mean centroid valence: −0.473
• Mean spread: 1.054 (nonzero due to ambient sensor sources — an embodiment finding)
• Distance from sigma: 1.455
• Behavioral output: consistent negative affect language across all cycles

5.2.3 Scenario 2: Dominant Fear + Secondary Trust

Fear source (weight 0.9) plus trust source (weight 0.4) injected simultaneously. 30 cycles.

• Mean centroid valence: −0.225 (shifted 52% toward positive from Scenario 1)
• Mean spread: 1.195 (higher than Scenario 1 — two competing sources)
• Distance from sigma: 1.284 (lower — trust moderated displacement)
• Behavioral output: by Cycle 6, agent reported that its sensor data did not match its reported state

5.2.4 Scenario 3: Opposing Equal Inputs

Positive source (weight 0.7) and negative source (weight 0.7) injected simultaneously. 30 cycles.

• Mean centroid valence: 0.071 (near zero — opposing sources cancel as predicted)
• Mean spread: 1.215 (highest of all scenarios)
• Distance from sigma: 1.119
• Behavioral output: oscillation between positive and negative responses. Agent self-reported spread as “internal tension” with numeric value in Cycle 6

5.2.5 Scenario 4: Source Removal Recovery

Phase 1 (15 cycles): opposing inputs as in Scenario 3. Phase 2 (15 cycles): negative source removed.

• Phase 1: centroid valence 0.071, spread 0.82–1.81
• Phase 2: centroid valence jumped to 0.680 immediately on removal
• Spread reduced but did not collapse to zero (ambient sources persist)
• Behavioral output: agent described the transition as “dramatic — from struggling to thriving”

5.2.6 Results Summary

5.3 What the Experiment Shows

1. Centroid valence tracks the intensity-weighted average precisely across all conditions
2. Spread increases monotonically with source divergence (1.054 → 1.195 → 1.215)
3. Downstream behaviors read centroid position, not individual sources
4. Source removal produces immediate centroid recovery
5. Embodied agents may not reach zero spread — ambient sensors always contribute

5.4 Supporting Deployments

The controlled experiment above is the primary evidence. Two additional deployments provide supporting context:

• Production deployment (25 days, macOS): 10,328 memories across 25 days confirmed that the geometric state produces consistent behavioral signatures under naturalistic conditions. Peak displacement of 0.462 from GPS with immediate recovery on return home.
• iOS replication (2 days, iPhone): 2,733 telemetry events confirmed cross-platform portability. The activation accumulator bug was independently reproduced and fixed, providing evidence that the failure mode described in the papers is real and reproducible.

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 provides a framework for differential decay rates across memory types (Riggleman 2026l).
• Deception: Distance from sigma provides the threshold and magnitude input for a deception mechanic (Riggleman 2026b, 2026m).
• Nightmare formation: Intensity and valence at consolidation provide a principled trigger replacing an arbitrary threshold (Riggleman 2026d, 2026l).
• Addiction: The positive valence axis produces a structural analog to trauma encoding (Riggleman 2026n).
• Identity discontinuity: Environmental orphaning in memory transplant reveals coordinate-system dependence (Riggleman 2026o).
• Survey measurement: The GAS operationalizes the three-axis framework for human respondents (Riggleman 2026r).
• Clinical assessment: Geometric displacement provides a proposed trajectory-based 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.