The Model
Defines the formal mechanism of Operation Abigail as a median-indexed constraint on household wealth, with excess accumulation recaptured at the terminal balance sheet and redistributed through a state and citizen framework. The model specifies a self-correcting, state-contingent system that aligns apex growth with median gains without requiring continuous policy calibration.
Operation Abigail: A median-indexed feedback model.
1. Agent Objective
\[ \max_{a_{i,t}} W_{i,t} \]Agents choose strategies \(a_{i,t}\) to maximize attainable household wealth \(W_{i,t}\), subject to the constraint and system dynamics below. The constraint defines the feasible set.
2. Core Constraint
\[ W_{i,t} \leq k \cdot W_{\mathrm{median},t} \]3. Enforcement: Recapture Function
\[ T_{i,t}=\max\left(0,\; W_{i,t}-\max\left(kW_{\mathrm{median},t},G_i\right)\right) \]Enforces the constraint at terminal wealth; not flow-based or revenue-maximizing. Applied at the household level independent of asset composition.
4. Aggregate Recapture and Allocation
\[ R_t=\sum_i T_{i,t} \] \[ \frac{1}{3}R_t \rightarrow \mathrm{sovereign\ wealth\ fund} \] \[ \frac{2}{3}R_t \rightarrow \mathrm{states} \]5. Sovereign Wealth Fund Dynamics
\[ F_T=\sum_{t=1}^{T} R_{\mathrm{swf},t}(1+r)^{T-t} \] \[ V_t=\frac{\omega F_t}{N_{\mathrm{adult},t}} \]6. Median as Endogenous State Variable
\[ \widetilde{W}_{\mathrm{median},t+1} = g(a_{1,t},\ldots,a_{N,t},X_t) \] \[ W_{\mathrm{median},t+1} = \widetilde{W}_{\mathrm{median},t+1}+V_t \]7. Temporal Smoothing
\[ W_{\mathrm{median},t} = \frac{1}{5} \sum_{s=t-4}^{t} W_{\mathrm{median},s}^{\mathrm{obs}} \]8. Parameter Constraints
\[ k \in [1{,}000,\;10{,}000] \]9. Jurisdictional Constraint
For households satisfying:
\[ W_{i,t} \geq 0.8 \cdot k \cdot W_{\mathrm{median},t} \]10. Notes
