---
name: "applied-engineering-disciplines"
description: |
  USE FOR: Engineering disciplines relevant to formal mathematical systems — control theory, systems engineering, reliability engineering, software verification, signal processing, and testing methodology. Use for bridging mathematical foundations to engineering practice, and for formalizing engineering requirements in Lean 4.
  DO NOT USE FOR: formal verification in Lean (use @lean-ai-formalization); security-specific engineering (use @applied-data-information-security); strategy analysis (use @applied-strategy-analysis).
  TRIGGERS: control theory, systems engineering, reliability engineering, software verification, engineering discipline.
tier: "warm"
runtime_targets: [copilot-cli, claude-code]
dispatch_targets: []
handoffs:
  predecessors: ['agent:gateway', 'skill:lean-research']
  successors: ['skill:lean-ai-formalization', 'skill:lean-security-formalization', 'skill:math-nonlinear-dynamics']
metadata:
  version: "0.2.0"
  source_spec: "skills/applied-engineering-disciplines/SKILL.md (this file)"
  last_reviewed: "2026-05-27"
---


# Engineering Disciplines for Formal Mathematical Systems

Engineering methods and frameworks that connect formal mathematics to practical system design, verification, testing, and deployment.

---

## Routing

- **USE FOR:** Engineering disciplines relevant to formal mathematical systems — control theory, systems engineering, reliability engineering, software verification, signal processing, and testing methodology. Use for bridging mathematical foundations to engineering practice, and for formalizing engineering requirements in Lean 4.
- **DO NOT USE FOR:** formal verification in Lean (use @lean-ai-formalization); security-specific engineering (use @applied-data-information-security); strategy analysis (use @applied-strategy-analysis).
- **TRIGGERS:** control theory, systems engineering, reliability engineering, software verification, engineering discipline.

## Workflow

1. Identify the discipline match: control theory, systems engineering, reliability engineering, or software verification.
2. Pick the relevant section of the body; trace the chosen methodology end-to-end.
3. Produce the engineering artifact (control law, FMEA, reliability budget) in the form the caller needs.
4. Hand off: to `@lean-ai-formalization` for formal proofs of correctness, to `@math-nonlinear-dynamics` if control-theoretic dynamics dominate, to `@lean-zettelkasten`.

## Recovery & STOP

- STOP if the question is about the formal-verification proof itself — delegate to `@lean-ai-formalization`.
- STOP if the discipline match is unclear — surface a clarifying question rather than guessing.
- STOP if the answer needs domain-specific data not in the body — escalate to `@research-council`.

## Handoffs

- **Predecessors:** `agent:gateway`, `skill:lean-research`.
- **Successors:** `skill:lean-ai-formalization`, `skill:lean-security-formalization`, `skill:math-nonlinear-dynamics`.

---

## Detailed reference

Full content for `applied-engineering-disciplines` lives in
[`references/applied-engineering-disciplines-handbook.md`](../../references/applied-engineering-disciplines-handbook.md).
Load that file when the skill is convened; the SKILL.md only carries
the dispatch contract and the parts index.

| Section | Topic |
|---|---|
| Part 1 | Control Theory |
| Part 2 | Systems Engineering |
| Part 3 | Reliability Engineering |
| Part 4 | Software Verification & Testing |
| Part 5 | Signal Processing & Estimation |
| Part 6 | Engineering Process for Lean Projects |
| Part 7 | Configuration Management |
| Part 8 | Cross-References |

---

## See also

- [`../../references/applied-engineering-disciplines-handbook.md`](../../references/applied-engineering-disciplines-handbook.md) — Full handbook (extracted from this skill)
- [`../lean-ai-formalization/SKILL.md`](../lean-ai-formalization/SKILL.md) — Successor
- [`../lean-security-formalization/SKILL.md`](../lean-security-formalization/SKILL.md) — Successor
- [`../math-nonlinear-dynamics/SKILL.md`](../math-nonlinear-dynamics/SKILL.md) — Successor