papers/zoo-data-commons/sections/03-fair-native-data-object-model.tex

\section{FAIR-Native Data Object Model}

\label{sec:data_model}

\subsection{Object Structure}

A Zoo Data Object (ZDO) is the atomic unit of the Data Commons.
Each ZDO comprises four components:

\begin{equation}
    \text{ZDO} = (\mathcal{M}, \mathcal{D}, \mathcal{P}, \mathcal{G})
\end{equation}

\noindent where $\mathcal{M}$ is the metadata envelope, $\mathcal{D}$ is the data payload, $\mathcal{P}$ is the provenance chain, and $\mathcal{G}$ is the governance specification.

\subsection{Metadata Envelope}

The metadata envelope $\mathcal{M}$ is a structured document conforming to a JSON-LD schema that extends Darwin Core with additional fields for FAIR compliance:

\begin{equation}
    \mathcal{M} = (\text{id}, \text{schema}, \text{taxon}, \text{spatial}, \text{temporal}, \text{method}, \text{quality}, \text{links})
\end{equation}

\begin{table}[H]
\centering
\caption{Metadata envelope fields and their FAIR mapping.}
\label{tab:metadata}
\begin{tabularx}{\textwidth}{@{}llcX@{}}
\toprule
\textbf{Field} & \textbf{Type} & \textbf{FAIR} & \textbf{Description} \\
\midrule
\texttt{id} & CID & F1 & Content-addressed identifier (IPFS CID) \\
\texttt{schema} & URI & I1 & Reference to the data schema definition \\
\texttt{taxon} & OntologyRef & I2 & Taxonomic classification with ontology mapping \\
\texttt{spatial} & GeoJSON & F3 & Geographic extent with coordinate reference system \\
\texttt{temporal} & ISO8601 & F3 & Temporal coverage with resolution specification \\
\texttt{method} & MethodRef & R1 & Collection methodology with controlled vocabulary \\
\texttt{quality} & QualityScore & R2 & Automated quality assessment scores \\
\texttt{links} & LinkSet & F4 & Related ZDOs, publications, and external resources \\
\bottomrule
\end{tabularx}
\end{table}

\subsection{Taxonomic Ontology Integration}

ZDC maintains a unified taxonomic knowledge graph that reconciles multiple backbone taxonomies:

\begin{equation}
    \mathcal{T}_{\text{unified}} = \text{Reconcile}(\mathcal{T}_{\text{GBIF}}, \mathcal{T}_{\text{ITIS}}, \mathcal{T}_{\text{CoL}}, \mathcal{T}_{\text{WoRMS}})
\end{equation}

The reconciliation algorithm produces a mapping $\phi: \mathcal{N}_{\text{source}} \rightarrow \mathcal{N}_{\text{unified}}$ from source taxonomy names to unified nodes, with confidence scores and conflict annotations.
Each ZDO's taxonomic field references a node in the unified graph, enabling cross-dataset queries that are invariant to naming conventions.

We use a graph embedding approach to detect synonyms and near-matches:

\begin{equation}
    \text{sim}(n_i, n_j) = \cos(\mathbf{e}_i, \mathbf{e}_j) + \lambda \cdot \text{Jaccard}(\text{features}(n_i), \text{features}(n_j))
\end{equation}

\noindent where $\mathbf{e}_i$ is the embedding of node $n_i$ from a graph neural network trained on the taxonomy structure, and $\text{features}(n_i)$ includes morphological, ecological, and geographic characteristics.

\subsection{Data Quality Assessment}

Each ZDO undergoes automated quality assessment producing a vector of scores:

\begin{equation}
    \mathbf{q} = (q_{\text{complete}}, q_{\text{consistent}}, q_{\text{spatial}}, q_{\text{temporal}}, q_{\text{taxonomic}})
\end{equation}

\begin{itemize}[leftmargin=*]
    \item $q_{\text{complete}} \in [0,1]$: Fraction of required metadata fields populated.
    \item $q_{\text{consistent}} \in [0,1]$: Internal consistency score (e.g., species range vs.\ reported coordinates).
    \item $q_{\text{spatial}} \in [0,1]$: Spatial precision and validity assessment.
    \item $q_{\text{temporal}} \in [0,1]$: Temporal precision and plausibility.
    \item $q_{\text{taxonomic}} \in [0,1]$: Confidence of taxonomic identification.
\end{itemize}

The composite quality score is:

\begin{equation}
    Q = \sum_{k} w_k \cdot q_k \cdot \mathbb{1}[q_k > q_k^{\min}]
\end{equation}

\noindent where $w_k$ are domain-specific weights and $q_k^{\min}$ are minimum thresholds; objects failing any threshold are flagged for review rather than rejected outright.

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