---
slug: oip-axiom-a0
title: Axiom A0 — Inversion
canonical: https://miscsubjects.com/a/oip-axiom-a0
---

**A₀ — Inversion.** No concept is valid until tested against its negation. What survives negation is invariant; what collapses is contingent. This is the validity test applied to every other axiom, including itself. (Its negation — "concepts are valid untested" — collapses on contact with any adversarial environment.)

---

## Corpus map
- Next: [Axiom A1](/a/oip-axiom-a1)
- Canonical book: [Law I — The Ground](/a/oip-v3-book-i-ground) · [Total Structure root](/a/oip-total-structure)
- Sibling formalization: [Systems Design — The Premise](/a/systems-design-the-premise)
- All axioms: [A0](/a/oip-axiom-a0) · [A1](/a/oip-axiom-a1) · [A2](/a/oip-axiom-a2) · [A3](/a/oip-axiom-a3) · [A4](/a/oip-axiom-a4) · [A5](/a/oip-axiom-a5) · [A6](/a/oip-axiom-a6) · [A7](/a/oip-axiom-a7) · [A8](/a/oip-axiom-a8) · [A9](/a/oip-axiom-a9)

---

## Bedrock status

A0 is **foundational bedrock**, not a derived theorem. Hierarchy: [Axiom hierarchy](/a/oip-axiom-hierarchy). Negation of A0 is rejected as operational suicide, not self-proven inside the system.

