---
slug: oip-axiom-hierarchy
title: Axiom Hierarchy — Bedrock vs Derived
canonical: https://miscsubjects.com/a/oip-axiom-hierarchy
---

# Axiom Hierarchy — Bedrock vs Derived

## §SELF — oip-axiom-hierarchy

**What this page is:** the dependency ordering the twelve axioms were missing.
**What it explains:** A0 cannot fully self-justify without circularity; bedrock is admitted; derived axioms are prosecuted by bedrock.
**Why read it:** reflexive incompleteness (Gödel-adjacent; you published the no-go shape) demands a named un-prosecutable floor.

### Bedrock (asserted — load-bearing — cannot self-justify without circularity)

| ID | Name | Role |
|---|---|---|
| **A0** | Inversion | Validity test: concepts face negation. **Bedrock of method.** |
| **A11** | Receipt is the proof | Validity test for *claims about systems*: checkable record. **Bedrock of evidence.** (If A11 is not numbered in a given edition, the same role is held by the receipt principle in OIP + [what-is-receipt-is-proof](/a/what-is-receipt-is-proof).) |

We **admit**: A0 cannot be proven by A0 without circularity. Its negation ("untested claims are fine in adversarial environments") is rejected as **operational suicide**, not as a theorem inside the system. That is the price of a floor.

### Derived / prosecuted by bedrock

| ID | Prosecuted by | How |
|---|---|---|
| A1–A3 | A0 | Survive negation tests in ground book |
| **A4** | A0 + **declared choice** | Meta-ethical atom is **chosen**; rivals named on [A4](/a/oip-axiom-a4) |
| A5 | A0 + A4 | Prejudice contamination |
| A6–A7 | A0 | Structural/recurrence |
| **A8** | A0 + A5 | Must compose: [A8×A5](/a/oip-axiom-a8-times-a5) |
| A9+ | A0 + A11 | Downstream operational |

### What we refuse

All twelve floating at the same level as if each were self-proving. That is the trap.

### Links

- [A0](/a/oip-axiom-a0) · [A4](/a/oip-axiom-a4) · [A5](/a/oip-axiom-a5) · [A8](/a/oip-axiom-a8)
- [Twelve axioms](/a/oip-the-12-axioms)
- [No-go theorems](/a/oip-no-go-theorems)

