0. Plain Statement

Stability requires repeated perturbation tolerance.

Plain-language version:

Stability requires repeated perturbation tolerance.

1. Formal Definition

Stability Proof Law is currently defined by the source registry excerpt below. This scaffold awaits editorial expansion into the full law spec sheet format.

2. Canonical Form

TBD

Related variables:

TBD

3. Core Mechanism

TBD. Expand from the source excerpt and related UTS modules during editorial review.

4. When This Law Applies

TBD. Define applicability conditions during editorial review.

5. When This Law Does Not Apply

TBD. Define boundary conditions and false-positive cases during editorial review.

6. Diagnostic Signature

TBD. Map diagnostics only when supported by source material or later canon updates.

7. Failure Pattern

TBD. Map failure patterns only when supported by source material or later canon updates.

8. Restoration Implications

TBD. Map restoration arcs only when supported by source material or later canon updates.

9. Design Rule

TBD. Add design rules during editorial review.

10. Cross-Scale Expressions

TBD. Add U-layer expressions during editorial review.

11. Examples

TBD. Add examples during editorial review.

12. Relationship to Nearby Laws

TBD. Add related laws and deduplication notes during editorial review.

13. Operator Mapping

TBD. Add operator mappings during editorial review.

14. Machine-Readable Summary

id: "LAW-052"
name: "Stability Proof Law"
type: "law"
status: "draft"
family:
  - "Cybernetics"
summary: "Stability requires repeated perturbation tolerance."
canonical_statement: "Stability requires repeated perturbation tolerance"
canonical_form: "TBD"
source: "content/archive/laws/technical.md"

15. Compact Card Version

LAW-052 — Stability Proof Law

Stability requires repeated perturbation tolerance.

Plain meaning: Stability requires repeated perturbation tolerance.

Canonical form:

TBD

16. Source Status

This scaffold was generated from the current laws technical registry. Sections marked TBD should be expanded only from source material, related canon pages, or later editorial review.

17. Source Excerpt

Stability requires repeated perturbation tolerance.

A system is stable only if:

H(t+Δt) ≤ H(t)
𝓓 > 0
εₙ₊₁ ≤ εₙ
recurrence↓
symmetric recovery

Visible calm is not enough.