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Phase 2 Experiment: Executive Summary

From Factorial DOE to Multivariate Dynamics Analysis

Date: 2025-11-20 Status: Design Complete, Ready for Implementation Estimated Runtime: 6-8 hours (750 runs, 150-200 per config)

🎯 The Paradigm Shift

What We Thought We Were Doing:

  • Measuring isolated factor effects (factorial DOE)
  • Testing "jitter in fixed heartbeat interval"
  • Generating 250 runs and calling it statistically significant

What We're Actually Doing:

  • Measuring a coupled multivariate dynamical system
  • Capturing the trajectory of 7 metrics through state-space
  • Understanding how each metric feeds back to influence others
  • Discovering which configuration produces the most stable, convergent, responsive system

🚀 The Physics Model

Each configuration is a unique universe with different physical laws:

Per Tick (1 millisecond):
  cache_hit% ──────┐
                   ├──> bucket_load ──> execution_heat ──> decay ──> window_width
  bucket_hit% ─────┤                                                      │
                   └──────────────────────────────────┬──────────────────┘
                                                      │
                                                      ├──> prediction_accuracy
                                                      │
                                                      └──> heartbeat_modulation
                                                           (tick_ns adapts to load)

Key Insight: The heartbeat rate (tick_ns) is not fixed. It's modulated by the inference engine in response to workload. This is THE feedback mechanism that couples everything.

📊 What We Measure

Per Tick (Every ~1 ms)

7 metrics captured in circular buffer:

  • tick_interval_ns - How much time since last tick (variable!)
  • cache_hits_delta - Cache lookups succeeded
  • bucket_hits_delta - Secondary lookups succeeded
  • hot_word_count - Words above heat threshold
  • avg_word_heat - Mean execution heat
  • window_width - Current rolling window size
  • word_executions_delta - Total word executions

Per Run (100,000+ ticks)

Stability fingerprint computed from time-series:

  • Convergence time: When metrics stabilize
  • Steady-state CV: Variability in stable region
  • Load↔Heartbeat correlation: How tight is coupling?
  • Dominant eigenmode: What oscillation pattern emerges?
  • Overall stability score: Composite of all above (0-100)

Per Configuration (150+ runs)

Configuration fingerprint aggregated from all runs:

  • Stability reproducibility: std(stability_score) across runs
  • Convergence reliability: % of runs that stabilize
  • Coupling strength: Mean and variance of load↔heartbeat_corr
  • Attractor basin depth: Resistance to noise
  • Jitter characteristics: CV, whiteness, envelope smoothness

✨ The Golden Config Decision

Compare 5 elite configurations across 5 dimensions:

Dimension Weight Interpretation
Stability 30% Does system converge? Is it reproducible?
Convergence 25% How fast? How reliable?
Coupling 20% Does heartbeat respond to load?
Resilience 15% Can it handle noise? Deep basin?
Jitter 10% Clean or noisy timing?

Golden Config = highest weighted composite score

This config becomes the baseline for MamaForth/PapaForth and future experiments.

📈 Experimental Design

5 configurations  (1_0_1_1_1_0, 1_0_1_1_1_1, 1_1_0_1_1_1, 1_0_1_0_1_0, 0_1_1_0_1_1)
× 150-200 runs    (statistically significant for correlation analysis)
× 100K+ ticks     (to measure convergence and steady state)
────────────────────
= 750 total runs
  75+ million heartbeat ticks
  6-8 hours wall-clock runtime
  ~10 GB CSV data (with sampling strategy)

Randomization: Run order shuffled to avoid temporal confounds.

🔧 Implementation Pipeline

Phase 1: Heartbeat Instrumentation ✏️

  • Add HeartbeatTickSnapshot struct to capture per-tick metrics
  • Implement circular buffer (100K slots, ~400 KB memory)
  • Inject capture call into heartbeat loop (115 ns overhead, 0.01%)
  • Export to CSV after run completes

Phase 2: Run Fingerprinting 📊

  • Detect convergence from time-series
  • Compute steady-state CV for each metric
  • Measure cross-metric correlations
  • Perform spectral analysis (FFT, eigenmode extraction)
  • Generate RunStabilityFingerprint per run

Phase 3: Config Fingerprinting 📋

  • Aggregate 150+ run fingerprints per config
  • Compute robustness (reproducibility)
  • Assess convergence reliability
  • Evaluate coupling stability
  • Generate ConfigurationFingerprint per config

Phase 4: Golden Config Selection 🏆

  • Score each config on 5 weighted dimensions
  • Select highest-scoring configuration
  • Generate justification report

Phase 5: Visualization & Analysis 📈

  • Time-series plots (cache%, bucket%, tick_ns over time)
  • Correlation heatmaps per config
  • PCA projection of runs
  • Stability score distributions
  • Golden config report with physics interpretation

📋 Corrected DoE Script

Updated /scripts/run_factorial_doe_with_heartbeat.sh:

  • Runs per config: 150 (was 50, which was statistically insufficient)
  • Total runs: 750 (was 250)
  • Output: Same CSV structure + new per-tick timeseries CSV
  • Command: ./scripts/run_factorial_doe_with_heartbeat.sh 2025_11_20_PHASE2_DYNAMICS

🔍 Key Metrics Explained

Metric Meaning Good Value
convergence_time_ticks How many ticks to stabilize? <5000 (fast learner)
cache_convergence_cv Variability of cache% in steady state <0.05 (5% variation)
load_heartbeat_corr Does tick_ns respond to workload? >0.80 (tight coupling)
dominant_eigenvalue Attractor strength Large (deep basin)
tick_jitter_cv Variability of tick intervals <0.20 (20% max)
overall_stability_score Composite 0-100 >80 (excellent)

🎓 Interpretation Guide

A "Stable" Configuration Fingerprint (Good)

✅ stability_score_mean = 85, std = 2.1 ✅ 100% convergence_success_rate ✅ load_heartbeat_corr_mean = 0.88 ✅ tick_jitter_cv = 0.15 ✅ Dominant eigenvalue large (deep attractor)

→ Interpretation: This universe is orderly. Metrics converge predictably. The heartbeat tightly couples to load. Timing is clean. Noise doesn't destabilize it.

A "Chaotic" Configuration Fingerprint (Poor)

❌ stability_score_mean = 62, std = 8.3 ❌ 73% convergence_success_rate (some runs diverge!) ❌ load_heartbeat_corr_mean = 0.44 (weak coupling, inconsistent) ❌ tick_jitter_cv = 0.52 (52% variation, very noisy) ❌ Dominant eigenvalue small (shallow basin)

→ Interpretation: This universe is noisy. Some runs fail to converge. Heartbeat doesn't respond cleanly to load. Timing jitters wildly. Any small perturbation can destabilize it.

🔬 Why This Matters

Phase 1 (Stage 1, your baseline) ran WITHOUT adaptive heartbeat.

  • All runs used fixed 1ms tick interval
  • No feedback coupling
  • Missing the actual physics

Phase 2 (this experiment) runs WITH adaptive heartbeat.

  • Heartbeat rate (tick_ns) modulates based on inference engine output
  • Full feedback coupling measured
  • Captures the REAL adaptive behavior

The golden config from Phase 2 becomes:

  • ⭐ MamaForth baseline for human-in-the-loop iteration
  • ⭐ PapaForth reference for automated optimization
  • ⭐ Stability anchor for Phase 3 (deeper optimization)

📚 Design Documents

  1. MULTIVARIATE_DYNAMICS_DESIGN.md (622 lines)

    • Full coupled systems theory
    • Struct definitions for fingerprints
    • CSV schemas
    • Analysis pipeline details

  2. HEARTBEAT_INSTRUMENTATION_PLAN.md (350+ lines)

    • Implementation checklist
    • Per-tick capture infrastructure
    • Circular buffer design
    • CSV export strategy

  3. run_factorial_doe_with_heartbeat.sh (updated)

    • 150 runs/config default (was 50)
    • 750 total runs (statistically significant)

🚀 Next Steps

Immediate (This Session)

  • Implement HeartbeatTickSnapshot instrumentation in vm.c
  • Add delta metric tracking to VM struct
  • Test with abbreviated run (verify CSV output)

Follow-On (Next Session)

  • Implement RunStabilityFingerprint computation
  • Build ConfigurationFingerprint aggregation
  • Create R analysis suite
  • Execute full Phase 2 experiment (750 runs, 6-8 hours)

Outcome

  • Golden configuration identified
  • Justification report written
  • Metrics exported for visualization
  • Ready for Phase 3 deeper optimization

💡 The Big Picture

You've identified the actual physics of the system:

  1. Every metric is coupled to every other via immediate feedback
  2. The heartbeat rate itself is a tuning knob (modulated by inference)
  3. Stability emerges from convergence + coupling + basin depth
  4. You measure not "factor effects" but "trajectory shapes"

This shifts from reductionist factorial analysis to holistic systems characterization.

The golden config isn't "better because factor A is on/off." It's better because its entire attractor landscape is more stable, more convergent, more resilient, and more tightly coupled to load.

Captain, the framework is complete. Ready to instrument the heartbeat.

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