Capital Displacement Minimization
We define the Capital Displacement Ratio (CDR) as a measure of how much physical capital movement a settlement network requires relative to the gross economic obligations it resolves, and examine how corridor topology, epoch length, and domain liquidity affect it.
1. Defining Displacement
Every settlement system eventually requires some capital to physically move — liquidity must be rebalanced across domains that are structurally net exporters or importers of value. We are not interested in eliminating this movement, only in minimizing it relative to the volume of economic activity it supports.
CDR = residual capital movement ÷ gross obligation value.
2. Structural Determinants
Three factors dominate observed CDR in simulation: (a) the degree of bidirectional corridor traffic between domain pairs, (b) epoch length, which determines how much obligation volume accumulates before a compression pass, and (c) the availability of local liquidity able to satisfy obligations without cross-domain movement at all.
Longer epochs generally lower CDR by allowing more offsetting obligations to accumulate, at the cost of slower finality for any individual obligation.
3. A Simple Bound
For a domain pair with gross opposing flows F(A→B) and F(B→A), the minimum possible residual displacement is |F(A→B) − F(B→A)|, achieved when all obligations within the pair are visible to the same compression pass. CDR approaches this bound as epoch coverage and corridor density increase.
4. Discussion
CDR is a useful north-star metric precisely because it is legible: it does not require disclosing individual obligation details to be computed, only aggregate gross and residual figures per epoch. It is reported throughout this interface as a synthetic illustration of the underlying mechanism.