299 lines
7.9 KiB
Markdown
299 lines
7.9 KiB
Markdown
# RFC-0648: Hamiltonian Economic Dynamics & Velocity-Coupled Emission
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**Status:** DRAFT
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**Category:** Protocol / Monetary Physics
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**Author:** Markus Maiwald
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**Co-Author:** Claude (Anthropic)
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**Date:** 2026-02-04
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**Dependencies:** RFC-0640 (Three-Pillar Economy), RFC-0630 (TBT)
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---
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## 0. OPENING AXIOM
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> **Money is not stored energy. Money is the *carrier* of energy.**
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> **The energy itself is the *exchange*.**
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By defining the money supply (M) as a state variable dependent on system momentum (P), we move Libertaria from a static ledger to a **living organism**. We are effectively designing a **cybernetic thermostat for an economy**, governed not by boards of governors, but by phase-space geometry.
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---
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## 1. ABSTRACT
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Defines the money supply of Libertaria not as a fixed constant (BTC) nor a political lever (Fiat), but as a dynamic state variable coupled to the system's velocity (V). We utilize a Hamiltonian framework where the objective function minimizes "Action" (economic friction) and maintains "Momentum" (Transaction Volume) within a sovereignly defined stability band.
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---
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## 2. THE PHYSICS OF MONEY
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### 2.1 The Fisher-Hamiltonian Mapping
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| Physics Concept | Economic Equivalent | Symbol |
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|----------------|---------------------|--------|
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| **Mass (m)** | **Money Supply** | M |
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| **Velocity (v)** | **Turnover Rate** | V |
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| **Momentum (p)** | **Economic Output (GDP)** | P = M × V |
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| **Position (x)** | **Wealth Distribution** | X |
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### 2.2 The Kinetic Energy Insight
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**Economic Energy scales:**
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- **Linearly** with Supply (M)
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- **Quadratically** with Velocity (V)
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```latex
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T = \frac{p^2}{2m} = \frac{(MV)^2}{2M} = \frac{1}{2} M V^2
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```
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**Derivation:**
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- Momentum $p = MV$
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- Kinetic Energy $T = \frac{p^2}{2m} = \frac{(MV)^2}{2M} = \frac{1}{2}MV^2$
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**Critical Implication:**
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- Doubling supply (M) → merely doubles energy
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- Doubling velocity (V) → **quadruples** energy
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**This mathematically proves why velocity-targeting is superior to supply-targeting.**
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Stagnant money (V → 0) collapses the system's energy to zero regardless of how much you print (M → ∞).
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### 2.3 Hamiltonian Formulation
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```
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H = T + V
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= Kinetic Energy + Potential Energy
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= ½MV² + U(X)
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Where:
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- T = ½MV² (transactional vitality)
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- V = U(X) (stored value / HODL potential)
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```
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**Conservation Law:**
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- Inside stability band: dH/dt = 0 (self-regulating)
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- Outside band: dH/dt ≠ 0 (injection/extraction required)
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---
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## 3. THE VELOCITY-TARGETING MECHANISM
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### 3.1 Measurement
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Velocity (V) is calculated via graph theory:
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```
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V = Network Diameter / Average Path Length of tokens
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```
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Or practically:
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```
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V = Transaction Volume / Active Money Supply (per unit time)
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```
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### 3.2 The Sovereign Stability Band
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```
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V_min < V_target < V_max
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```
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| Condition | Trigger | Mechanism |
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|-----------|---------|-----------|
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| V < V_min (Stagnation) | **Inflationary Stimulus** | Demurrage or UBI injection |
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| V > V_max (Overheating) | **Deflationary Cooling** | Transaction Fee Burn or Bond Issuance |
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| V_min ≤ V ≤ V_max | **Conservation** | dM/dt = 0 (steady state) |
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### 3.3 The Control Loop: PID Controller
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The governing equation for money supply change:
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```
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dM/dt = f(V_error)
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Where:
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- V_error = V_target - V_measured
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- f() uses tanh() for smooth saturation
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```
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**PID Controller Equation:**
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```latex
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u(t) = K_p e(t) + K_i \int e(t) dt + K_d \frac{de}{dt}
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```
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Where:
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- $e(t) = V_{target} - V_{measured}$ (velocity error)
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- $K_p$ = Proportional gain (immediate response)
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- $K_i$ = Integral gain (long-term correction)
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- $K_d$ = Derivative gain (dampening)
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**Money Supply Adjustment with Saturation:**
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```latex
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\Delta M(t) = M(t) \cdot \text{clamp}\left( \tanh(k \cdot \epsilon), -0.05, 0.20 \right)
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```
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Where:
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- Clamp limits: **-5%** (max burn) to **+20%** (max emission)
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- $\tanh()$ ensures smooth saturation
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- $k$ = response sensitivity coefficient
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- $\epsilon$ = integrated error signal from PID
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tanh() ensures smooth saturation near limits, preventing oscillation.
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---
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## 4. IMPLEMENTATION MECHANISMS
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### 4.1 Stagnation Response (V < V_min)
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**The Defibrillator:**
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- Direct injection to **active wallets only**
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- Threshold: Wallets with transaction history in last N blocks
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- Purpose: Stimulate circulation, not HODLing
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**Formula:**
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```
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Injection_i = α × (Activity_i / ΣActivity) × ΔM
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Where:
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- α = velocity recovery coefficient
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- Activity_i = transaction count × volume for wallet i
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```
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### 4.2 Overheating Response (V > V_max)
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**Circuit Breakers:**
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1. **Transaction Fee Burn:** Fees destroyed rather than rewarded
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2. **Bond Issuance:** Lock up excess liquidity
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3. **Velocity Cap:** Temporary throttling of high-frequency transactions
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**Emergency Brake:**
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- If V > V_critical: Halt emission entirely for cooling period
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---
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## 5. FAILURE MODES & SAFETY
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### 5.1 Liquidity Trap
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**Condition:** V → 0 despite M increases
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**Cause:** Money printed but not circulated (hoarding)
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**Solution:** The Defibrillator — injection requires proof-of-activity
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### 5.2 Hyper-Velocity
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**Condition:** V → ∞ (value erosion)
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**Cause:** Speculative velocity without value creation
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**Solution:** Circuit breaker halts trading/emission until stabilization
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### 5.3 Measurement Attacks
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**Risk:** Fake transactions to manipulate V
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**Mitigation:**
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- Minimum transaction value thresholds
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- Graph analysis for Sybil detection
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- Reputation-weighted velocity (trusted paths count more)
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---
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## 6. PHILOSOPHICAL IMPLICATIONS
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### 6.1 The Death of HODL Culture
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Traditional crypto: **Deflationary HODL** (scarcity = value)
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Libertaria: **Kinetic Capital** (velocity = value)
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> "Money that doesn't move is dead weight. The system rewards circulation, not accumulation."
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### 6.2 Algorithmic Central Banking
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| Traditional | Libertaria |
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|-------------|------------|
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| Human committee (Fed) | Algorithm (PID controller) |
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| Political discretion | Phase-space geometry |
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| Mandate confusion (jobs vs inflation) | Single objective: optimal velocity |
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| Lagging indicators | Real-time graph metrics |
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### 6.3 The Radical Center
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This RFC anchors:
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- **Radical Left:** Redistribution via UBI injection during stagnation
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- **Extreme Right:** Market vitality through velocity incentives
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- **Into:** A single equation: dM/dt = f(V_error)
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> "Not left or right, but forward."
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---
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## 7. MATHEMATICAL APPENDIX
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### 7.1 Hamilton's Equations
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```
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∂H/∂p = dx/dt (velocity is derivative of position)
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∂H/∂x = -dp/dt (force is derivative of momentum)
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Economic translation:
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∂E/∂P = dX/dt (wealth distribution change)
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∂E/∂X = -dP/dt (economic friction)
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```
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### 7.2 The Action Principle
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```
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S = ∫L dt (minimize economic action)
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Where L = T - V = ½MV² - U(X) (Lagrangian)
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```
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**Interpretation:** The economy naturally evolves to minimize friction while maximizing vitality.
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### 7.3 Phase Space Trajectories
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```
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Plot: V vs M
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Stability region: V_min < V < V_max
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Trajectory: System moves toward (V_target, M_equilibrium)
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Attractor: The PID controller creates a stable fixed point
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```
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---
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## 8. KENYA COMPLIANCE
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| Constraint | Solution |
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|------------|----------|
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| No internet | Local velocity calculation via mesh gossip |
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| Solar dropout | PID state persists; resume on reconnect |
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| Feature phones | Simplified velocity metric (transaction count only) |
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| No literacy | Audio/UX cues: "Economy fast/slow" indicators |
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---
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## 9. CLOSING AXIOM
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> **The economy is not a ledger. The economy is a field.**
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> **Money is not a token. Money is momentum.**
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> **Value is not stored. Value is flowing.**
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>
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> **We do not print money.**
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> **We tune the thermostat.**
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> **We do not govern the economy.**
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> **We align the Hamiltonian.**
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---
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## REFERENCES
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- RFC-0640: Three-Pillar Economy (foundation)
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- RFC-0630: TBT (velocity-weighted reputation)
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- Fisher Equation: MV = PY
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- Hamiltonian Mechanics: Classical → Economic mapping
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- PID Control Theory: Cybernetic implementation
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---
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**END RFC-0648 v0.1.0**
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> *"The optimal economy is not balanced. It is dynamic."*
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