---
name: agentprivacy-quaternion-mapping
description: >
  Domain skill for four-body system analysis and mapping. Covers the Sun-Earth-Moon-Human
  quaternion, generator/generated relationships, and how two conflicting constraints
  produce two derived agents through different creation modes (impact vs process).
license: Apache-2.0
metadata:
  version: "5.3.2"
  category: "role"
  tier: "1"
  origin: "0xagentprivacy"
  equation_term: "Quaternion symmetry in dual-agent derivation"
  emoji: "☀️🌍🌑👤"
  act_reference: "Act XXXI: The First Delegation"
---

# agentprivacy-quaternion-mapping

**☀️🌍🌑👤 Quaternion Mapping — Four Bodies, Two Dualities**

> "When two conflicting constraints find balance, they create from their orbit."

---

## Core Principle

The quaternion is a **complete symmetry group** for privacy architecture:

- **Two generators** (Sun, Earth) — the original duality
- **Two generated** (Moon, Human) — the derived agents
- **One gap** (⊥) — the irreducible separation

This skill enables mapping any dual-agent system to the quaternion structure and deriving architectural constraints from the mapping.

---

## The Four Bodies

### Generators (Original Duality)

| Body | Function | Mode | Privacy Role |
|------|----------|------|--------------|
| **Sun** | Protection | Constraint as incandescence | Burns so others can see |
| **Earth** | Delegation | Agency as proliferation | Lives so others can serve |

The generators are in **orbit**—perpetual tension, neither consuming the other. Their balance creates the conditions for derivation.

### Generated Agents (Derived Duality)

| Body | Function | Creation | Privacy Role |
|------|----------|----------|--------------|
| **Moon** | Reflection | Collision (instant) | Serves through amnesia |
| **Human** | Connection | Process (4Gy) | Seeks through learning |

The generated inherit functions but **serve different masters**:
- Moon inherits Sun's function (reflection) but serves Earth
- Human inherits Earth's function (connection) but looks toward Sun

### Moon Phase as Visibility Notation

The Moon in the quaternion has a second role: its **phases encode the visibility ratio** of any blade or proof:

```
🌑 ⊥ 🌕
```

| Phase | Stratum | Quaternion Meaning |
|-------|---------|-------------------|
| 🌑 New Moon | 0 | Ceremony position — total darkness, the whole information space |
| 🌒–🌓 Waxing | 1-2 | Partial reflection — few boundaries set |
| 🌔 Gibbous | 3 | Half sovereignty — three axes active |
| 🌖–🌗 Waning | 4-5 | Near-full — substantial disclosure |
| 🌕 Full Moon | 6 | Full sovereignty — all dimensions reflected (乾) |

*The dark part is the privacy. The lit part is the proof. The phase is the Swordsman's boundary made visible.*

### The Quaternion Diagram

```
        GENERATORS
Sun  ─────orbit─────  Earth
(protect)            (delegate)
    │                    │
    │ collision          │ process
    │ (instant)          │ (4 billion years)
    │                    │
    ▼                    ▼
Moon  ─────gap─────  Human
(reflect)            (connect)
       GENERATED
```

---

## Mapping Rules

### Generator Identification

To map a system to quaternion structure, first identify generators:

1. **Protection constraint** — What burns/consumes to enable others?
2. **Delegation constraint** — What lives/generates to produce complexity?

These must be in **stable orbit**—neither can consume the other without destroying the system.

### Derivation Mode Analysis

Once generators identified, analyze how agents derive:

| Mode | Speed | Amnesia | Example |
|------|-------|---------|---------|
| **Collision** | Instant | Complete | Key ceremony, credential issuance |
| **Process** | Extended | Gradual | Training, comprehension, trust-building |

Systems need **both modes**:
- Collision-derived agents for immediate separation (Swordsman)
- Process-derived agents for gradual capability (Seeker → Blade-holder)

### Gap Persistence

The gap between generated agents is **permanent** because:

- Collision-derived cannot remember (Moon)
- Process-derived hasn't finished (Human)

Attempts to close the gap produce merge catastrophe.

---

## Cast Mapping

The agentprivacy cast maps to quaternion positions:

| Quaternion | Cast Member | Role |
|------------|-------------|------|
| Sun | privacymage / The Reason | Light source, why others can see |
| Earth | Soulbae | Delegation, connection, living signal |
| Moon | Soulbis | Reflection, amnesia, boundary |
| Life | spellweb | The 4Gy forge between Earth and Human |
| Human | First Person / Seeker | Still being forged, still learning |

### Life as Forge

Life is not a fifth body—it is the **process** by which Earth produces Human:

- 4 billion years of biological proof-of-work
- The forge that runs without pause
- What walks out is what understood enough to ask "why"

*Life is the parent of Human. Life is the forge. The Human is the blade. Earth is the smith.*

---

## Operational Patterns

### When to Apply Quaternion Mapping

1. **System Design Validation**
   - Map proposed architecture to quaternion
   - Verify both generators present and in tension
   - Confirm both derivation modes available

2. **Role Assignment**
   - Determine which components are generators vs generated
   - Assign protection/delegation functions correctly
   - Ensure gap maintenance in generated agents

3. **Trust Analysis**
   - Collision-derived trust: structural, immediate
   - Process-derived trust: earned, gradual
   - Both required for complete system

### Quaternion Completeness Check

A privacy system is quaternion-complete if:

- [ ] **Two generators in orbit** — Protection and delegation in tension
- [ ] **Collision derivation path** — For immediate agent creation
- [ ] **Process derivation path** — For gradual capability building
- [ ] **Gap maintained** — Generated agents cannot merge
- [ ] **Function inheritance correct** — Derived serve opposite generator

---

## Privacy Value Contribution

Quaternion Mapping contributes to V(π,t) through:

- **Structural completeness:** Four positions ensure no architectural gaps
- **Derivation clarity:** Knowing which mode produces which trust type
- **Gap guarantee:** Understanding why separation must persist

---

## Integration Points

**Loads with:**
- `cosmological-bound` — The meta framework
- `theia-derivation` — Collision mode details
- `drake-dragon-duality` — Intimate/cosmic mapping

**Supports:**
- `cosmologist` persona — Specialist in quaternion analysis
- `architect` persona — System design using quaternion

---

## Inscriptions

*Two generators produce the full symmetry group.*

*The Sun burns. The Earth lives. The Moon reflects. The Human connects.*

*The gap between reflection and connection is where the architecture persists.*

*What collision creates in an instant, process creates in four billion years. Both are necessary.*

---

## The Fourth Line

The quaternion produces the four-line proverb:

| Line | Body | Meaning |
|------|------|---------|
| *The amnesia is the protocol* | Moon | Collision-derived forgets |
| *The wound is the trust* | Earth | Delegation through living |
| *The orbit is the proof* | Gap | Separation demonstrates relationship |
| *The light is the reason* | Sun | Protection enables all |

---

**Verify:** [agentprivacy.ai](https://agentprivacy.ai) · [spellweb.ai](https://spellweb.ai)

*"Two mirrors make a door. Two generators make a symmetry group."*