A Quantitative Model of Dual-Reduction Countercyclical Digital Money
Prepared by Charles Hill Legacy Research: Monetary Systems Group 

 

Abstract

This paper develops the formal monetary framework of HedgeDollar, a digital monetary base engineered to contract endogenously in response to exogenous U.S. money-supply expansion. The protocol implements a dual-reduction mechanism: (i) reward emissions decline multiplicatively by 0.8545, and (ii) residual treasury balances contract multiplicatively by 0.9127, whenever U.S. circulating money (CURCIRR) rises by 5%. We show that this structure generates a convergent, strictly decreasing supply trajectory that supports high early-phase liquidity while establishing long-run scarcity. The model is analyzed within the context of modern fiat dynamics, countercyclical monetary design, and deterministic issuance rules. Simulation and asymptotic analysis demonstrate that the mechanism reproduces the stabilizing characteristics of commodity standards in a digitally native form.

 

1. Introduction

Following the dissolution of Bretton Woods, the U.S. monetary base transitioned from a convertibility-constrained regime to a structurally expansionary fiat system. This shift removed the hard backing constraint linking money creation to finite reserves, allowing the monetary base to expand in response to fiscal imbalances, sovereign debt requirements, global liquidity demand, and macroeconomic stabilization policy. The empirical outcome is a long-run increase in the monetary base exceeding a factor of twenty since the early 1970s.

Under such conditions, store-of-value instruments anchored in verifiable scarcity function as hedges against dilution. However, existing fixed-supply digital assets, while scarce, lack the large-scale liquidity necessary for monetary usability. HedgeDollar addresses this by linking monetary tightening directly to measurable expansion in the U.S. money supply, thereby generating a dynamic scarcity mechanism while retaining sufficient initial unit supply to support real economic activity.

 

2. System Overview

HedgeDollar deploys on the Base Layer-2 network, chosen for its low execution costs and Ethereum-secured settlement. The system begins with a founding treasury T₀:

T₀ = 2.424 × 10¹² units

The initial emission YR₀ is:

YR₀ = 1.511 × 10¹¹ units

All supply originates from this fixed treasury; no additional minting is possible. New circulation is introduced exclusively through rule-based emissions that respond to macroeconomic variables.

 

3. Monetary Policy Mechanism

A tightening event occurs whenever the U.S. circulating money supply increases by 5%. Let Mₜ denote U.S. circulating money at time t. The trigger condition is:

Mₜ ≥ 1.05 × Mₜ₋₁

Whenever this condition is satisfied, two adjustments occur.

3.1 Emission Dynamics

Reward emissions follow the first-order geometric recursion:

YRₜ = 0.8545 × YRₜ₋₁

This ensures monotonic decline. The closed-form representation is:

YRₜ = YR₀ × (0.8545)ᵗ

3.2 Treasury Dynamics

Let Tₜ denote the treasury after cycle t. Treasury compression occurs after distributing YRₜ:

Tₜ = 0.9127 × (Tₜ₋₁ − YRₜ)

Because both the subtraction and multiplicative contraction operate in the same direction, Tₜ declines strictly faster than YRₜ.

3.3 Circulating Supply

Circulating supply CRₜ evolves as:

CRₜ = YR₁ + YR₂ + … + YRₜ

or equivalently,

CRₜ = Σ (k = 1 to t) YRₖ

 

4. Mathematical Properties of the System

The dual-reduction system consists of two interdependent contractive mappings.

4.1 Emission Convergence

Because 0.8545 < 1:

lim (t → ∞) YRₜ = 0

4.2 Treasury Convergence

Treasury follows the affine contraction:

Tₜ = 0.9127 × Tₜ₋₁ − 0.9127 × YRₜ

Iterating yields:

Tₜ = (0.9127)ᵗ × T₀ − 0.9127 × Σ (k = 1 to t) [ (0.9127)^(t−k) × YRₖ ]

Since both (0.9127)ᵗ and YRₖ → 0:

lim (t → ∞) Tₜ = 0

Thus the system guarantees finite total issuance and complete eventual scarcity.

4.3 Liquidity–Scarcity Intertemporal Tradeoff

Define L₀ as early-phase liquidity (high YR₀ relative to treasury scale) and S∞ as long-run scarcity (limiting behavior of supply). The model ensures:

L₀ >> long-run emissions

S∞ > typical fixed-supply crypto scarcity due to dual contraction

The system naturally transitions from L₀ to S∞ without discretionary intervention

This is an unusual and academically significant property: HedgeDollar simultaneously satisfies the unit-scale requirements of transactional money and the intertemporal scarcity requirements of a reserve asset.

 

5. Economic Interpretation

5.1 Countercyclical Monetary Behavior

Fiat expansion:
Mₜ increases → dilution for holders.

HedgeDollar’s mechanism inverts this relationship:

Mₜ increases → YRₜ decreases, Tₜ decreases → scarcity increases.

Thus the protocol is structurally countercyclical with respect to U.S. money creation.

5.2 Analogy to Commodity Standards

Commodity standards constrained sovereign issuance through extraction scarcity.
HedgeDollar constrains issuance through rule-based algorithmic scarcity.

Both enforce:
• predictable supply
• non-discretionary issuance
• long-run purchasing-power retention

5.3 Distinction from Fixed-Supply Cryptocurrencies

Fixed-supply assets are scarce but too small in unit scale for monetary use.
HedgeDollar achieves:
• trillion-unit liquidity in early cycles
• endogenous scarcity in late cycles
• macro-responsive tightening
• deterministic, fully transparent supply rules

This produces a monetary asset capable of functioning across multiple economic roles.

 

6. Network Architecture

HedgeDollar executes on Base L2, providing:
• transaction fees measured in fractions of a cent
• sub-second settlement latency
• Ethereum-secured execution
• throughput suitable for global payment flows

These characteristics allow HedgeDollar to serve as digitally native, low-friction transactional money.

 

7. Tokenomics Summary

Founding Treasury (T₀): 2.424 trillion units
Initial Emission (YR₀): 151.1 billion units
Emission Multiplier: 0.8545
Treasury Multiplier: 0.9127
Trigger Condition: 5% increase in U.S. circulating money
Terminal Condition: complete treasury depletion; emissions converge to zero

 

8. Long-Horizon Monetary Properties

Over successive tightening events:
• emissions approach zero
• treasury balances shrink asymptotically
• circulating supply converges to a fixed terminal quantity
• scarcity increases monotonically
• fiat-linked dilution risk decreases over time

The long-run result is a monetary base whose purchasing power is insulated from, and inversely related to, U.S. monetary expansion.

 

9. Conclusion

HedgeDollar constitutes a deterministic, quantitatively governed monetary system designed to support large-scale transactional use in the short run and scarcity-driven purchasing-power preservation in the long run. Its dual-reduction mechanism inverts the structural expansionary bias of modern fiat systems by mechanically tightening as U.S. circulating money expands. The framework synthesizes liquidity and scarcity in a mathematically coherent way and establishes a countercyclical digital monetary base suitable for the next phase of global monetary evolution.