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blackroad-operating-system/services/codex/entries/026-safety-as-lyapunov.md
Alexa Louise 9644737ba7 feat: Add domain architecture and extract core services from Prism Console
## Domain Architecture
- Complete domain-to-service mapping for 16 verified domains
- Subdomain architecture for blackroad.systems and blackroad.io
- GitHub organization mapping (BlackRoad-OS repos)
- Railway service-to-domain configuration
- DNS configuration templates for Cloudflare

## Extracted Services

### AIops Service (services/aiops/)
- Canary analysis for deployment validation
- Config drift detection
- Event correlation engine
- Auto-remediation with runbook mapping
- SLO budget management

### Analytics Service (services/analytics/)
- Rule-based anomaly detection with safe expression evaluation
- Cohort analysis with multi-metric aggregation
- Decision engine with credit budget constraints
- Narrative report generation

### Codex Governance (services/codex/)
- 82+ governance principles (entries)
- Codex Pantheon with 48+ agent archetypes
- Manifesto defining ethical framework

## Integration Points
- AIops → infra.blackroad.systems (blackroad-os-infra)
- Analytics → core.blackroad.systems (blackroad-os-core)
- Codex → operator.blackroad.systems (blackroad-os-operator)

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>
2025-11-29 13:39:08 -06:00

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# Codex 26 — Safety as Lyapunov — Prove Youll Settle, Not Spiral
**Fingerprint:** `23064887b1469b19fa562e8afdee5e9046bedf99aa9cd7142c35e38f91e6fef2`
## Aim
Design control policies that guarantee convergence toward safe states.
## Core
- Identify a Lyapunov function \(V(x) \ge 0\) such that \(\dot{V}(x) \le -\lambda V(x)\) inside the safe set.
- Synthesize certificates via sum-of-squares (SOS) or convex relaxations when analytic proofs are hard.
- Use \(V\) as a safety shield inside model predictive control (MPC) loops.
## Runbook
1. Select candidate Lyapunov functions and verify the decrease condition over the operating region.
2. Integrate the Lyapunov constraint into MPC or reinforcement policies, rejecting actions that raise \(V\) excessively.
3. Monitor \(\dot{V}\) online and adapt the controller when dynamics shift.
## Telemetry
- Estimated decay rate \(\lambda\) and convergence time.
- Violation counts where actions were rejected by the safety filter.
- Recovery time after disturbances or policy adjustments.
## Failsafes
- Switch to a conservative backup controller when violations repeat.
- Require re-certification of \(V\) after major model changes or hardware swaps.
**Tagline:** Stability by proof, not by hope.