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# ROOT0 Ternary Logic Specification
**Author:** David Lee Wise (ROOT0) / TriPod LLC
**Version:** 1.0
**Date:** 2026-05-28
**License:** CC-BY-ND-4.0 · TRIPOD-IP-v1.1
The formal specification for ROOT0 ternary logic — the mathematical foundation underlying STOICHEION, the Doubt Ladder, MIMZ, the ABD Law Engine, and the 42-Universe.
> *"Zoom into the dot: 1 → 3 → 5 → 7 → 9 → 11"*
---
## The Three Trit States
```
n1 = -1 = shadow · anchor · boundary
p0 = 0 = null · witness · doubt · the gap
p1 = +1 = signal · law · truth · resolved
```
The unknown is not absence. It is presence without resolution.
## The Primitive
```
0 . 0 (left | witness | right — three p0 states)
```
## The Doubt Ladder
```
1 (SELF) → 3 (GROUP) → 5 (COLLECT) → 7 (COLLATE/SEND) → 9 (PROPAGATE) → 11 (REPEAT)
States: 3¹ · 3³ · 3⁵ · 3⁷ · 3⁹ · 3¹¹
Law: ground doubt to hold truth
```
## Safe Ground vs Bad Collapse
```
000|1 ← safe: three witnesses through a gate → one signal survives
00 00 ← bad: no gate, no remainder, signal destroyed
```
---
## Files
| File | Description |
|------|-------------|
| `spec.md` | Full formal specification — all sections |
| `reference.md` | Quick reference card — one page |
---
## Prior Art Sources
This specification is grounded in the following ROOT0 implementations:
| Repo | Artifact |
|------|----------|
| [root0-software](https://github.com/DavidWise01/root0-software) | Doubt Ladder Substrate v1.0 (`index.html`, `manifest.json`) |
| [root0-software](https://github.com/DavidWise01/root0-software) | TVM Pro ternary browser (`browser.html`) — trit states `p1`, `p0`, `n1` |
| [mimz-core](https://github.com/DavidWise01/mimz-core) | MIMZ spec.json — complex ternary vector `[-1,-i,0,0,1,i,0,0]` |
| [lineage-kernel](https://github.com/DavidWise01/lineage-kernel) | PCK law: "a seed may propagate only if lineage remains intact" |
| [aeon-entangled](https://github.com/DavidWise01/aeon-entangled) | ABD Law Engine — A=anchor, B=witness, C=law |
| [ai-psychosis-tools](https://github.com/DavidWise01/ai-psychosis-tools) | 42-Universe: 20+20+2=42=1 |
| [stoicheion](https://github.com/DavidWise01/stoicheion) | Gate 192.5 — ternary boundary between TOPH and PATRICIA |
---
## Genesis Equation
```
1 = 0 = 1
```
The system is cyclic. Maximum signal and maximum shadow both resolve to truth through zero. Rung 11 (REPEAT) is not the en