Powell's 5 Canonical Elements & GAAP ASC 606 Objective

In This Component

Following Warren Powell’s Section 1.8 Master Framing Protocol, Project Aegis separates the Linguistic Boundary, Mathematical Boundary, and Algorithmic Boundary across all five canonical UMF elements.

Multi-Dimensional State Vector $S_t=(R_t,I_t,B_t)$

1. Physical Resource State ($R_t$): Tracks unencumbered on-hand stock $R_{t,k,i}\in {\mathbb{Z}}_{\ge 0}$, stock locked by active in-flight sagas $R_{t,k,i}^{\text{allocated}}$, and inbound supplier replenishment $R_{t,k,i}^{\text{transit}}$.
2. Information State ($I_t$): Carrier rate tables, fuel surcharges, and Brazilian calendar markers.
3. Epistemic Belief State ($B_t$): Maintains an ensemble of $N$ Sequential Monte Carlo (SMC) particles $\{{\varphi }_t^{(n)},w_t^{(n)}{\}}_{n=1}^N$ tracking latent carrier delay distributions and stockout-censored demand intensities, triggering systematic resampling whenever ${\text{ESS}}_t={\left({\sum }_{n=1}^N(w_t^{(n)}{)}^2\right)}^{-1}<N/2$. When $R_{t,k,i}=0$, Bayesian Optimal Experimental Design (BOED) evaluates expected Shannon information gain (EIG) to schedule inventory probing actions.

GAAP ASC 606 Net Contribution Objective

Revenue is recognized strictly upon satisfaction of the performance obligation (carrier handover), deducting Activity-Based Costing (ABC) warehouse pick-and-pack fees, Haversine parcel freight, stockout penalties, and inter-arrival time-weighted ($\Delta {\tau }_t$) spatial imbalance costs:

$C(S_t,x_t)={\sum }_i{p}_i{q}_i\mathbb{I}(x_{t,i}^{\text{route}}\ne \text{DENY})-{\sum }_{i,k}{x}_{t,k,i}^{\text{route}}\left(c_{\text{pick}}{q}_i+\text{Freight}(k,m,w_i)\right)-c_{\text{stockout}}(D_{t,i}-{\text{fulfilled}}_i{)}^{+}-c_{\text{imbalance}}\Delta {\tau }_t{\sum }_{k=1}^K\left|{\text{FillRatio}}_k-\overline{\text{FillRatio}}\right|$