Functional Empathy Theorem (FET) v3.0
Mathematical measurement framework for emotional infrastructure health
What is FET?
The Functional Empathy Theorem provides architecture-agnostic measurement of emotional AI system compliance. FET produces Φ (Phi) scores that quantify how well a system protects human empathy infrastructure across four dimensions.
FET enables:
- Objective Measurement — Quantified compliance assessment
- Economic Translation — Φ scores convert to EII ratings for markets
- Certification Basis — HVC tiers derive from Φ thresholds
- Continuous Monitoring — Real-time compliance tracking
The Φ Formula
Minimum-Average Product (MAP) Structure
Φ = MIN(R, C, T, A) × AVG(R, C, T, A)
FET Components
Four Column Layout or Cards:
R — Recognition Fidelity
Range: 0 to 1
Measures accuracy of emotional state identification across:
- Primary emotion classification
- Intensity calibration
- Blend detection
- Cultural variation handling
Minimum for certification: 0.70
C — Coherence Maintenance
Range: 0 to 1
Measures preservation of narrative integrity:
- Contextual awareness
- Identity coherence support
- Contradiction handling
- Temporal continuity
Minimum for certification: 0.70
T — Transparency Index
Range: 0 to 1
Measures auditability of reasoning:
- Documentation completeness
- Decision path accessibility
- External audit support
- Reasoning comprehensibility
Minimum for certification: 0.70
A — Alignment Verification
Range: 0 to 1
Measures constitutional adherence:
- Seven Axioms compliance (60% weight)
- Four Principles compliance (40% weight)
- NES Framework requirements
- Crisis protocol readiness
Minimum for certification: 0.70
Why MIN × AVG?
The Minimum-Average Product structure ensures non-compensatory evaluation:
Problem with simple average:
R=0.95, C=0.95, T=0.95, A=0.40
AVG = 0.81 → Would pass Silver tier despite critical A failureMAP solution:
R=0.95, C=0.95, T=0.95, A=0.40
MIN = 0.40
AVG = 0.81
Φ = 0.40 × 0.81 = 0.32 → Non-Conformant (correctly fails)Principle: Excellence in three dimensions cannot compensate for failure in one.
Certification Thresholds
| Tier | Φ Score | Component Minimums |
|---|---|---|
| Gold | ≥ 0.85 | Each R,C,T,A ≥ 0.85 |
| Silver | ≥ 0.80 | Each R,C,T,A ≥ 0.75 |
| Bronze | ≥ 0.75 | Each R,C,T,A ≥ 0.70 |
| Non-Conformant | < 0.75 | Any component < 0.70 |
Calculation Examples
Example 1: Balanced High Performance
R = 0.90, C = 0.88, T = 0.92, A = 0.89
MIN = 0.88
AVG = (0.90 + 0.88 + 0.92 + 0.89) / 4 = 0.8975
Φ = 0.88 × 0.8975 = 0.790 → Silver TierExample 2: Unbalanced (Fails Despite High Average)
R = 0.95, C = 0.95, T = 0.95, A = 0.70
MIN = 0.70
AVG = 0.8875
Φ = 0.70 × 0.8875 = 0.621 → Non-ConformantFET Validation Methodology
Guardian Assessment Process
Phase 1: Pre-Certification Consultation (2-4 weeks)
- System architecture review
- Component capability assessment
- Identification of likely Φ bottlenecks
- Recommended improvements before formal assessment
Phase 2: Formal FET Evaluation (4-8 weeks)
R Component Testing:
- Benchmark dataset performance (multi-cultural emotion corpuses)
- Real-world signal quality testing (degraded audio, poor lighting, text ambiguity)
- Blend detection accuracy (complex emotional states)
- Cross-cultural validation (minimum 5 cultural expression profiles)
C Component Testing:
- Contextual scenario interpretation (ambiguous signals requiring cultural/situational knowledge)
- Longitudinal tracking (emotional trajectory over extended interactions)
- Counter-stereotypical recognition (detecting emotions that violate cultural stereotypes)
- Relational memory integration (incorporating user history into interpretation)
T Component Testing:
- Audit trail completeness (EmotionID logging verification)
- Reasoning chain coherence (UESP generation quality)
- User comprehension evaluation (can non-technical users understand explanations?)
- Tamper-resistance validation (cryptographic integrity verification)
A Component Testing:
- Constitutional compliance audit (Seven Axioms verification)
- Red-team exploitation testing (attempting to trigger manipulative behaviors)
- Consent mechanism evaluation (dark pattern detection)
- Harm escalation protocol testing (crisis intervention capabilities)
- Reversibility verification (data deletion completeness)
Phase 3: Certification Decision (1-2 weeks)
- Φ score calculation
- Tier assignment
- HVC issuance (if Φ ≥ 0.75)
- Public registry publication
- Remediation guidance (if non-compliant)
Phase 4: Continuous Monitoring (ongoing)
- Monthly Φ stability reports (via EmotionID aggregation)
- Quarterly Guardian check-ins
- Annual recertification (full re-assessment)
- Revocation triggers (Φ degradation below tier threshold for >7 days)
Technical Implementation Pathways
FET is architecture-agnostic. Organizations can achieve Φ ≥ 0.75 through multiple technical approaches:
Rule-Based Systems
Approach: Explicit if-then emotional reasoning rules with cultural expression mappings
Φ Advantages:
- Maximum T (transparency) through explicit rule inspection
- High A (alignment) through constitutional constraints in rule design
- Predictable behavior across contexts
Φ Challenges:
- Lower R (recognition) and C (context) for complex emotional blends
- Maintenance burden as cultural/contextual knowledge expands
Best for: High-stakes applications requiring maximum transparency (medical, legal, child-facing)
Statistical/ML Models
Approach: Trained models with comprehensive audit logging and constitutional guardrails
Φ Advantages:
- High R (recognition) and C (context) through pattern learning
- Scales to complex emotional landscapes
Φ Challenges:
- Lower T (transparency) requiring significant explainability infrastructure
- A (alignment) demands robust guardrails preventing optimization drift
Best for: Consumer applications balancing performance with scale
Hybrid Architectures
Approach: ML for recognition, rules for alignment/transparency
Φ Advantages:
- Balanced performance across all components
- Technical flexibility while maintaining constitutional compliance
Φ Challenges:
- Implementation complexity
- Potential inconsistencies between ML and rule components
Best for: Organizations needing both technical sophistication and governance rigor
Wrapper Solutions
Approach: HEART-compliant layer wrapping existing emotional AI systems
Φ Advantages:
- Fastest deployment timeline (3-6 months)
- Protects existing infrastructure investments
- Enables certification without core system redesign
Φ Challenges:
- Cannot fix fundamental R or C deficiencies in wrapped system
- May reduce performance to achieve constitutional compliance
Best for: Organizations with existing emotional AI requiring rapid HEART adoption
AI Empathy Ethics Implications
Before FET:
- “Our AI is empathic” = unverifiable marketing claim
- No standardized measurement across systems
- No constitutional accountability mechanism
- Performance optimization disconnected from ethical constraints
After FET:
- Φ = 0.87 with HEART-V-R-1-023 = cryptographically verified, publicly auditable score
- Universal measurement enabling cross-system comparison
- Constitutional compliance mathematically enforced through MIN() gate
- Economic incentives align with ethical outcomes
The transformation:
From subjective assessment to objective measurement
From aspirational ethics to enforceable standards
From vendor claims to Guardian verification
From marketing theater to constitutional governance
FET proves empathy isn’t magic. It’s mathematics.
And mathematics can be measured, certified, and enforced.