excellence-gradient

Excellence Gradient

Trit: -1 (VALIDATOR - measures, constrains, reduces toward optimum)

Core Principle

Quality is not a gate—it's a gradient. Binary pass/fail obscures the path to excellence. Measure everything. Descend continuously toward the minimum of the loss function: distance from ideal.

The Airlock Principle

The airlock should not eat the air.

Validation exists to protect value, not consume it. If your quality gates:

• Take longer than the work they validate → broken
• Block more than they enable → broken
• Cost more than the bugs they catch → broken
• Kill momentum instead of channeling it → broken

Cost(validation) << Value(protected)
Time(gate) << Time(work)
Friction(process) < Momentum(team)

airlock_efficiency = value_protected / momentum_consumed
# Target: efficiency > 10x
# If < 1x: gate eats more than it saves → remove or automate

The airlock is a membrane, not a wall. It regulates flow, doesn't stop it.

Quality Lineage

Pioneer	Contribution	Key Metric
Deming	14 Points, PDCA	Variation reduction
Juran	Pareto principle, Quality Trilogy	Cost of poor quality
Ohno	Toyota Production System	Lead time, waste (muda)
Shingo	Poka-yoke, SMED	Defects approaching zero
Crosby	Zero defects, Quality is free	Price of non-conformance

Excellence Temperature (τ)

Distance from optimal. Lower is better. τ = 0 is perfection.

def excellence_temperature(metrics: dict) -> float:
    """
    τ ∈ [0, ∞) where τ → 0 as quality → perfect
    Analogous to simulated annealing: high τ = chaos, low τ = crystallized excellence
    """
    weights = {
        'coverage': 0.20,      # Test coverage
        'latency': 0.15,       # P99 response time
        'satisfaction': 0.25,  # User NPS/CSAT
        'debt_ratio': 0.20,    # Technical debt / LOC
        'defect_rate': 0.20,   # Defects per KLOC
    }
    
    # Normalize each to [0,1] where 0 = optimal
    τ = sum(weights[k] * distance_from_optimal(k, v) 
            for k, v in metrics.items())
    return τ

Measurable Excellence Criteria

1. Code Quality Metrics

Metric	Formula	Target	Critical
Coverage	tested_lines / total_lines	≥ 0.80	< 0.60
Complexity	Cyclomatic per function	≤ 10	> 20
Duplication	dup_lines / total_lines	≤ 0.03	> 0.10
Debt Ratio	remediation_time / dev_time	≤ 0.05	> 0.20
Doc Coverage	documented / public_symbols	≥ 0.90	< 0.50

2. Performance Metrics

Metric	Formula	Target	Critical
P50 Latency	50th percentile	≤ 100ms	> 500ms
P99 Latency	99th percentile	≤ 500ms	> 2000ms
Error Rate	errors / requests	≤ 0.001	> 0.01
Availability	Uptime %	≥ 99.9%	< 99.0%
Throughput	RPS at P99 SLO	≥ baseline×1.2	< baseline

3. User Satisfaction Metrics

Metric	Formula	Target	Critical
NPS	promoters - detractors	≥ 50	< 0
CSAT	satisfied / respondents	≥ 0.85	< 0.70
Task Success	completed / attempted	≥ 0.95	< 0.80
Time to Value	signup → first value	≤ 5min	> 30min
Churn	lost / total per period	≤ 0.02/mo	> 0.10/mo

4. Technical Debt Indicators

Metric	Formula	Target	Critical
TODO Count	grep -r TODO	≤ 10	> 100
Dependency Age	avg months since update	≤ 6	> 24
Security Vulns	CVE count (high/critical)	0	> 0
Dead Code	unreachable / total	≤ 0.01	> 0.05
Build Time	CI pipeline duration	≤ 10min	> 30min

Gradient Descent Protocol

def descend_toward_excellence(current_state: Metrics) -> Action:
    """
    Not binary pass/fail. Continuous improvement via gradient.
    """
    τ = excellence_temperature(current_state)
    gradient = compute_gradient(current_state)
    
    # Priority = steepest descent direction
    worst_metric = max(gradient.items(), key=lambda x: x[1])
    
    return Action(
        focus=worst_metric[0],
        expected_τ_reduction=worst_metric[1],
        effort_estimate=effort_model(worst_metric[0])
    )

def compute_gradient(state: Metrics) -> dict:
    """
    ∂τ/∂metric for each metric
    Higher gradient = faster improvement opportunity
    """
    return {
        metric: partial_derivative(excellence_temperature, metric, state)
        for metric in state.keys()
    }

Anti-Patterns Detection

Code Anti-Patterns

ANTI_PATTERNS = {
    'god_class': lambda c: c.methods > 20 or c.lines > 500,
    'feature_envy': lambda m: external_calls(m) > internal_calls(m) * 2,
    'shotgun_surgery': lambda f: len(dependents(f)) > 10,
    'primitive_obsession': lambda c: primitive_params(c) > 5,
    'speculative_generality': lambda c: unused_abstractions(c) > 0,
    'dead_code': lambda f: call_count(f) == 0 and not exported(f),
    'copy_paste': lambda b: similar_blocks(b) > 2,
}

def detect_anti_patterns(codebase) -> list[Violation]:
    violations = []
    for name, detector in ANTI_PATTERNS.items():
        for entity in codebase.entities():
            if detector(entity):
                violations.append(Violation(
                    pattern=name,
                    location=entity.location,
                    severity=PATTERN_SEVERITY[name],
                    fix_effort=PATTERN_EFFORT[name]
                ))
    return sorted(violations, key=lambda v: v.severity, reverse=True)

Process Anti-Patterns

Anti-Pattern	Detection Signal	Response
Heroics	1 person on all critical paths	Distribute knowledge
Scope Creep	Requirements grow > 20%/sprint	Freeze and ship
Gold Plating	Features beyond spec	Ship MVP, iterate
Analysis Paralysis	> 2 weeks without shipping	Timebox decisions
Bikeshedding	> 30min on trivial choices	Executive decision
NIH Syndrome	Rewriting solved problems	Adopt proven solutions

GF(3) Triads

# Excellence Gradient Bundle (VALIDATOR ⊗ COORDINATOR ⊗ GENERATOR = 0)
excellence-gradient (-1) ⊗ chromatic-walk (0) ⊗ refuse-mediocrity (+1) = 0 ✓  [Quality Pursuit]
excellence-gradient (-1) ⊗ unworld (0) ⊗ refuse-mediocrity (+1) = 0 ✓  [Standard Derivation]
excellence-gradient (-1) ⊗ kinetic-block (0) ⊗ refuse-mediocrity (+1) = 0 ✓  [Momentum Measure]
excellence-gradient (-1) ⊗ implicit-coordination (0) ⊗ refuse-mediocrity (+1) = 0 ✓  [Parallel Quality]
excellence-gradient (-1) ⊗ topos-catcolab (0) ⊗ refuse-mediocrity (+1) = 0 ✓  [Collaborative Excellence]

# With other generators
excellence-gradient (-1) ⊗ acsets (0) ⊗ gay-mcp (+1) = 0 ✓  [Metric Coloring]
excellence-gradient (-1) ⊗ open-games (0) ⊗ agent-o-rama (+1) = 0 ✓  [Quality Games]
excellence-gradient (-1) ⊗ cognitive-surrogate (0) ⊗ koopman-generator (+1) = 0 ✓  [Learning Dynamics]

Commands

# Compute current excellence temperature
just excellence-τ

# Run full quality audit
just quality-audit

# Detect anti-patterns
just anti-patterns

# Gradient descent: suggest next improvement
just descend

# Compare τ over time
just τ-history --days 30

Implementation

#!/usr/bin/env bash
# excellence-gradient.sh

compute_excellence_temperature() {
    coverage=$(just coverage-report | grep -oP '\d+\.\d+')
    latency_p99=$(just latency-p99)
    debt_ratio=$(just tech-debt-ratio)
    defect_rate=$(just defect-rate)
    
    # Weighted sum (lower = better)
    τ=$(python3 -c "
weights = [0.25, 0.20, 0.30, 0.25]
metrics = [$((100 - coverage))/100, $latency_p99/2000, $debt_ratio, $defect_rate]
print(sum(w*m for w,m in zip(weights, metrics)))
")
    echo "τ = $τ"
}

The Validator Role (-1)

This skill is MINUS because it constrains and measures:

• Measures distance from excellence
• Detects deviations (anti-patterns)
• Provides gradient direction (what to fix next)
• Validates improvements (τ decreased?)

Without measurement, "excellence" is just opinion. With measurement, it's navigation.

Deming's 14 Points (Selected)

1. Constancy of purpose → Track τ daily
2. Cease dependence on inspection → Build quality in
3. Drive out fear → Measure to improve, not punish
4. Break down barriers → Shared metrics, shared goals
5. Eliminate slogans → Replace with measurable targets

The Equation

Excellence = lim(t→∞) descent(τ₀, gradient, t)

Where:
- τ₀ = starting temperature
- gradient = ∇τ (direction of steepest improvement)
- t = iterations of PDCA

One Rule

If you can't measure it, you can't improve it. If τ isn't decreasing, you're not improving.

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Autodiff

• jax [○] via bicomodule
  • Hub for autodiff/ML

Bibliography References

• general: 734 citations in bib.duckdb

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.