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RFC-0648: Hamiltonian Economic Dynamics & Velocity-Coupled Emission

Status: DRAFT
Category: Protocol / Monetary Physics
Author: Markus Maiwald
Co-Author: Claude (Anthropic)
Date: 2026-02-04
Dependencies: RFC-0640 (Three-Pillar Economy), RFC-0630 (TBT)

0. OPENING AXIOM

Money is not stored energy. Money is the carrier of energy.
The energy itself is the exchange.

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.

1. ABSTRACT

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.

2. THE PHYSICS OF MONEY

2.1 The Fisher-Hamiltonian Mapping

Physics Concept	Economic Equivalent	Symbol
Mass (m)	Money Supply	M
Velocity (v)	Turnover Rate	V
Momentum (p)	Economic Output (GDP)	P = M × V
Position (x)	Wealth Distribution	X

2.2 The Kinetic Energy Insight

Economic Energy scales:

Linearly with Supply (M)
Quadratically with Velocity (V)

T = \frac{p^2}{2m} = \frac{(MV)^2}{2M} = \frac{1}{2} M V^2

Derivation:

Momentum p = MV
Kinetic Energy T = \frac{p^2}{2m} = \frac{(MV)^2}{2M} = \frac{1}{2}MV^2

Critical Implication:

Doubling supply (M) → merely doubles energy
Doubling velocity (V) → quadruples energy

This mathematically proves why velocity-targeting is superior to supply-targeting.

Stagnant money (V → 0) collapses the system's energy to zero regardless of how much you print (M → ∞).

2.3 Hamiltonian Formulation

H = T + V
  = Kinetic Energy + Potential Energy
  = ½MV² + U(X)

Where:
- T = ½MV² (transactional vitality)
- V = U(X) (stored value / HODL potential)

Conservation Law:

Inside stability band: dH/dt = 0 (self-regulating)
Outside band: dH/dt ≠ 0 (injection/extraction required)

3. THE VELOCITY-TARGETING MECHANISM

3.1 Measurement

Velocity (V) is calculated via graph theory:

V = Network Diameter / Average Path Length of tokens

Or practically:

V = Transaction Volume / Active Money Supply (per unit time)

3.2 The Sovereign Stability Band

V_min < V_target < V_max

Condition	Trigger	Mechanism
V < V_min (Stagnation)	Inflationary Stimulus	Demurrage or UBI injection
V > V_max (Overheating)	Deflationary Cooling	Transaction Fee Burn or Bond Issuance
V_min ≤ V ≤ V_max	Conservation	dM/dt = 0 (steady state)

3.3 The Control Loop: PID Controller

The governing equation for money supply change:

dM/dt = f(V_error)

Where:
- V_error = V_target - V_measured
- f() uses tanh() for smooth saturation

PID Controller Equation:

u(t) = K_p e(t) + K_i \int e(t) dt + K_d \frac{de}{dt}

Where:

e(t) = V_{target} - V_{measured} (velocity error)
K_p = Proportional gain (immediate response)
K_i = Integral gain (long-term correction)
K_d = Derivative gain (dampening)

Money Supply Adjustment with Saturation:

\Delta M(t) = M(t) \cdot \text{clamp}\left( \tanh(k \cdot \epsilon), -0.05, 0.20 \right)

Where:

Clamp limits: -5% (max burn) to +20% (max emission)
\tanh() ensures smooth saturation
k = response sensitivity coefficient
\epsilon = integrated error signal from PID

tanh() ensures smooth saturation near limits, preventing oscillation.

4. IMPLEMENTATION MECHANISMS

4.1 Stagnation Response (V < V_min)

The Defibrillator:

Direct injection to active wallets only
Threshold: Wallets with transaction history in last N blocks
Purpose: Stimulate circulation, not HODLing

Formula:

Injection_i = α × (Activity_i / ΣActivity) × ΔM

Where:
- α = velocity recovery coefficient
- Activity_i = transaction count × volume for wallet i

4.2 Overheating Response (V > V_max)

Circuit Breakers:

Transaction Fee Burn: Fees destroyed rather than rewarded
Bond Issuance: Lock up excess liquidity
Velocity Cap: Temporary throttling of high-frequency transactions

Emergency Brake:

If V > V_critical: Halt emission entirely for cooling period

5. FAILURE MODES & SAFETY

5.1 Liquidity Trap

Condition: V → 0 despite M increases
Cause: Money printed but not circulated (hoarding)
Solution: The Defibrillator — injection requires proof-of-activity

5.2 Hyper-Velocity

Condition: V → ∞ (value erosion)
Cause: Speculative velocity without value creation
Solution: Circuit breaker halts trading/emission until stabilization

5.3 Measurement Attacks

Risk: Fake transactions to manipulate V
Mitigation:

Minimum transaction value thresholds
Graph analysis for Sybil detection
Reputation-weighted velocity (trusted paths count more)

6. PHILOSOPHICAL IMPLICATIONS

6.1 The Death of HODL Culture

Traditional crypto: Deflationary HODL (scarcity = value)
Libertaria: Kinetic Capital (velocity = value)

"Money that doesn't move is dead weight. The system rewards circulation, not accumulation."

6.2 Algorithmic Central Banking

Traditional	Libertaria
Human committee (Fed)	Algorithm (PID controller)
Political discretion	Phase-space geometry
Mandate confusion (jobs vs inflation)	Single objective: optimal velocity
Lagging indicators	Real-time graph metrics

6.3 The Radical Center

This RFC anchors:

Radical Left: Redistribution via UBI injection during stagnation
Extreme Right: Market vitality through velocity incentives
Into: A single equation: dM/dt = f(V_error)

"Not left or right, but forward."

7. MATHEMATICAL APPENDIX

7.1 Hamilton's Equations

∂H/∂p = dx/dt  (velocity is derivative of position)
∂H/∂x = -dp/dt  (force is derivative of momentum)

Economic translation:
∂E/∂P = dX/dt  (wealth distribution change)
∂E/∂X = -dP/dt  (economic friction)

7.2 The Action Principle

S = ∫L dt  (minimize economic action)

Where L = T - V = ½MV² - U(X)  (Lagrangian)

Interpretation: The economy naturally evolves to minimize friction while maximizing vitality.

7.3 Phase Space Trajectories

Plot: V vs M

Stability region: V_min < V < V_max
Trajectory: System moves toward (V_target, M_equilibrium)
Attractor: The PID controller creates a stable fixed point

8. KENYA COMPLIANCE

Constraint	Solution
No internet	Local velocity calculation via mesh gossip
Solar dropout	PID state persists; resume on reconnect
Feature phones	Simplified velocity metric (transaction count only)
No literacy	Audio/UX cues: "Economy fast/slow" indicators

9. CLOSING AXIOM

The economy is not a ledger. The economy is a field.
Money is not a token. Money is momentum.
Value is not stored. Value is flowing.

We do not print money.
We tune the thermostat.
We do not govern the economy.
We align the Hamiltonian.

REFERENCES

RFC-0640: Three-Pillar Economy (foundation)
RFC-0630: TBT (velocity-weighted reputation)
Fisher Equation: MV = PY
Hamiltonian Mechanics: Classical → Economic mapping
PID Control Theory: Cybernetic implementation

END RFC-0648 v0.1.0

"The optimal economy is not balanced. It is dynamic."

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