Whitepaper

The Problem

Current observability solutions split along two failing axes:

• Open-source stacks (Prometheus + Grafana + Loki) demand 5+ services, 8 GB+ RAM, and weeks of integration. They answer "What is broken?" via static thresholds — never "When will it break?"
• Enterprise SaaS (Datadog, Dynatrace) provide black-box AI at prohibitive cost with opaque decision logic.

Neither predicts. Neither explains.

The Ruptura Approach

Ruptura treats infrastructure as a living organism — measuring vital signs, behaviours, stress responses, and social dynamics through 8 auditable composite signals, an adaptive ensemble of 5 prediction models, and a dual-scale acceleration detector.

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Rupture Index™ — the core prediction metric

R(t) = |α_burst(t)| / max(|α_stable(t)|, ε)

Two ILR windows run in parallel per metric:

Window	Size	Captures
ILR_stable	60 min	Long-term baseline — what is normal?
ILR_burst	5 min	Short-term acceleration — is something diverging?

When R > 3, a metric accelerates 3× faster than its own baseline — Ruptura raises a warning before the metric reaches 80% saturation.

Why ILR over LSTM?

Model	MAE	RAM	Inference	Efficiency
LSTM	2.0%	200+ MB	500 ms	< 0.0001
ARIMA	4.1%	85 MB	210 ms	0.0001
ILR (Ruptura)	6.2%	0.5 MB	0.8 ms	1,550×

ILR trades +2.1% MAE for 170× less RAM and 262× faster inference. 1,550× more efficient than ARIMA — validated on a Raspberry Pi 4 over 40,320 samples.

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8 Composite Signals

All inputs are normalised to [0, 1]. Formulas are versioned release artifacts — every coefficient is auditable.

1. Stress

stress(t) = 0.3·CPU(t) + 0.2·RAM(t) + 0.2·Latency(t) + 0.2·Errors(t) + 0.1·Timeouts(t)

Value	State
< 0.3	Calm
0.3–0.6	Nervous
0.6–0.8	Stressed
≥ 0.8	Panic

2. Fatigue (dissipative)

F(t) = max(0,  F(t−1) + (stress(t) − R_threshold) − λ)

  R_threshold = 0.3   (rest threshold)
  λ           = 0.05  (healing rate per interval)

The λ dissipation term prevents false alarms from planned load spikes (nightly backups, batch jobs). The system "heals" during low-stress periods, eliminating ~90% of false-positive fatigue alerts observed in v5.0 field deployments.

Value	State	Action
< 0.3	Rested	Normal
0.3–0.6	Tired	Increase observation
0.6–0.8	Exhausted	Plan maintenance
≥ 0.8	Burnout imminent	Preventive restart

3. Pressure

pressure(t) = d(stress̄)/dt + ∫₀ᵗ errors̄(τ) dτ

Measures the rate of systemic load increase plus accumulated error burden. Sustained positive pressure (> 0.1 for 10+ min) predicts a "storm" ~2 hours ahead.

4. Contagion

contagion(t) = Σ_{i,j} E_{ij}(t) × D_{ij}

E_ij = error rate from service i to j, D_ij = dependency weight (0–1). Measures how fast failures propagate across the service graph.

Value	State	Action
< 0.3	Isolated	Normal
0.3–0.6	Spreading	Monitor
0.6–0.8	Epidemic	Isolate affected
≥ 0.8	Pandemic	Global response

5. Resilience

resilience(t) = 1 − P_failure(t)

P_failure(t) = σ( α·R(t) + β·fatigue(t) + γ·contagion(t) )

  α = 0.5, β = 0.3, γ = 0.2  (default weights)
  σ = sigmoid function

Resilience is the complement of estimated failure probability, combining the Rupture Index, fatigue, and contagion into a single 0–1 score. A resilience score below 0.4 means the system is more likely to fail than not.

Value	State
> 0.8	Robust
0.6–0.8	Adequate
0.4–0.6	Fragile
< 0.4	Failure likely

6. Entropy

entropy(t) = −Σ_i p_i(t) · log₂(p_i(t))

  p_i = normalised frequency of metric i crossing its baseline threshold

Measures behavioural unpredictability — how many metrics are deviating from their baseline simultaneously. High entropy indicates configuration drift, deployment side effects, or cascading anomalies. Normalised to [0, 1] via entropy / log₂(N) where N is the number of tracked metrics.

Value	State
< 0.2	Predictable
0.2–0.5	Some drift
0.5–0.8	High drift
> 0.8	Chaotic

7. Sentiment

sentiment(t) = (Uptime(t) × Throughput(t)) / (Errors(t) × Timeouts(t) × Restarts(t) + ε)

A high sentiment means the service is performant and stable. Near zero indicates degraded user experience. Normalised logarithmically to [0, 1].

Value	State
> 0.8	Happy
0.6–0.8	Content
0.4–0.6	Neutral
0.2–0.4	Sad
< 0.2	Depressed

8. Health Score

healthscore(t) = (1 − stress) × (1 − fatigue) × (1 − pressure) × (1 − contagion) × 100

A single 0–100 operational score combining the four primary signals. Below 60: needs attention. Below 40: action required.

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Adaptive Ensemble (v6.1)

Five models weighted by online MAE over a 1-hour sliding window:

Model	Strengths
CA-ILR	O(1), detects acceleration, edge-native
ARIMA	Strong on stationary trending series
Holt-Winters	Excellent on periodic/seasonal patterns
MAD	Robust to outliers
EWMA	Reacts to recent data, smooth

Weights update every 60 s: weight_i = (1/MAE_i) / Σ(1/MAE_j). No manual tuning. No profile configuration.

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Production Benchmarks

Criterion	Prom/Grafana/Loki	Datadog	Ruptura v6.1
RAM idle	~450 MB	~180 MB	22 MB
Setup time	~30 min	~5 min	< 1 min
Prediction	❌ None	✅ Black-box	✅ Transparent, 6.2% MAE
False positives (backup spikes)	❌ Yes	⚠️ Sometimes	✅ No (λ dissipation)
Exponential crash detection	❌ No	✅ Black-box	✅ R > 3 (auditable)
Air-gapped ready	⚠️ Complex	❌ Impossible	✅ Native
Efficiency score	1×	~0.0001×	1,550×

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Design Principles

Three principles non-negotiable since v4.0:

1. Transparent AI — every prediction traceable to a published formula. No black boxes.
2. Sovereign deployment — single static binary, no external database, runs on a Raspberry Pi 4.
3. Auditable by design — KPI formulas are versioned release artifacts. CISOs, auditors, and SREs can challenge any decision.

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Full Technical Reference

The v5.0 whitepaper contains the complete mathematical formalization and canonical METRICS.md standard:

Read OHE v5.0 Whitepaper (GitHub) →

"Stop staring at dashboards hoping for the best. Sleep. Ruptura watches."

— Selim Benfradj, Architect & Founder