Accelerating Hypothesis Generation in Comparative Archaeology and Cultural Diffusion via Semantic Knowledge Hypergraphs and Multimodal Cosine Similarity

Author: Luigi Usai Affiliation: Independent Researcher, PSCA Computational Framework (Paradigma Sardo-Corso-Atlantideo) Repository & Namespace: [https://www.luigiusai.it/ontology/](https://www.luigiusai.it/ontology/) Date: November 11, 2026 Keywords: Computational Archaeology, Knowledge Hypergraphs, Linked Open Data (LOD), CIDOC-CRM, Multimodal Vector Embeddings, Cosine Similarity, Archaeometallurgy, Lead Isotope Analysis (LIA), Cultural Diffusion Abstract Comparative archaeology and historical archaeometallurgy frequently suffer from disciplinary and regional compartmentalization, wherein artifact datasets remain isolated across linguistic, geographic, and chronological boundaries. This paper introduces a formal computational methodology that integrates Linked Open Data (LOD), RDF/NDJSON-LD semantic knowledge hypergraphs, and multimodal vector embeddings to automate cross-cultural anomaly detection and hypothesis generation. By encoding multi-domain diagnostic markers—spanning geometric invariants, iconographic topologies, trace-element geochemistry, Lead Isotope Analysis (LIA: $^{206}\text{Pb}/^{204}\text{Pb}$, $^{207}\text{Pb}/^{204}\text{Pb}$, $^{208}\text{Pb}/^{204}\text{Pb}$), and calibrated radiocarbon determinations ($^{14}\text{C}$)—into an ontology aligned with ISO 21127 (CIDOC-CRM), heterogeneous artifact records are projected into shared high-dimensional embedding spaces. Utilizing cosine similarity across visual-semantic vectors coupled with Mahalanobis distance in archaeometric space and Bayesian hypothesis testing, the framework systematically identifies non-trivial structural homologies across distant Eurasian and Mediterranean contexts (e.g., Nuragic Sardinia, Gandhara, and the Dian culture of Yunnan). Rather than replacing empirical excavation, this methodology shifts comparative research from manual, fragmented literature review to scalable, falsifiable heuristic discovery over federated open datasets. 1. Introduction and Problem Statement In conventional historiography and comparative archaeology, cross-regional artifact similarities are predominantly evaluated within localized disciplinary silos. When complex morphological or technological traits—such as double-volute ornamental grammars, horned warrior iconographies, or specific bronze alloy recipes—appear in geographically distant regions (e.g., the Western Mediterranean Basin and the Yunnan/Indochina metallurgical corridors), the prevailing interpretive consensus typically defaults to the null hypothesis ($H_0$) of independent evolutionary convergence (Elementargedanke or functional determinism). While independent convergence accounts for many simple structural parallels, defaulting to $H_0$ without quantitative testing is frequently driven by a data interoperability barrier: specialists in Southeast Asian or Steppe Bronze Age metallurgy rarely cross-query raw archaeometric and morphological repositories from Mediterranean Nuragic or Levantine contexts. Furthermore, traditional visual comparisons rely heavily on qualitative connoisseurship, which is rightly criticized as subjective and prone to confirmation bias. To overcome both qualitative subjectivity and database fragmentation, this paper formalizes a hybrid computational architecture—the Hypergraph-Assisted Multimodal Comparative Archaeology (HAMCA) pipeline, developed within the PSCA research framework. The methodology combines $n$-ary semantic hypergraph modeling, Linked Open Data federation, high-dimensional vector similarity metrics, and empirical archaeometric cross-validation to systematically test whether multi-trait artifact overlaps exceed the statistical threshold of random convergence. 2. Mathematical and Architectural Framework The proposed methodology operates through a four-stage computational pipeline: [1. Raw Archaeological, Iconographic & Archaeometric Data] │ ▼ [2. N-ary Semantic Hypergraph Modeling (RDF / NDJSON-LD / CIDOC-CRM)] │ ▼ [3. Multimodal Feature Extraction (Vision/Graph Embeddings) & Cosine Alignment] │ ▼ [4. Bayesian Probabilistic Filtering & Archaeometric Falsification (LIA / 14C)] 2.1. Stage 1: Formal Knowledge Hypergraph Representation Standard RDF graphs are restricted to binary relations $(s, p, o)$, which struggle to represent complex archaeological contexts where an artifact, its stratigraphic provenance, multiple iconographic motifs, alloy ratios, and isotopic measurements form an indivisible $n$-ary event. We define a directed, labeled, and typed Knowledge Hypergraph as a 6-tuple: $$H = (V, E, \mathcal{T}_V, \mathcal{T}_E, \phi, \psi)$$ where $V$ is a finite set of vertices (artifacts, motifs, geographic sites, chemical signatures, chronological intervals) and $E \subseteq \mathcal{P}(V) \setminus \{\emptyset\}$ is a family of $n$-ary hyperedges ($\vert{}e_k\vert{} \ge 2$) representing complex archaeological or comparative assertions. Each entity and hyperedge is dereferenceable via bijective URI mappings $\phi, \psi$ under the canonical namespace [https://www.luigiusai.it/ontology/](https://www.luigiusai.it/ontology/). Within the ontology, each physical artifact node $v_a \in V$ (instantiating crm:E22_Human-Made_Object) is linked to three orthogonal feature domains: Morpho-Topological Invariants ($\mathcal{F}_{\text{morph}}$): Geometric ratios, symmetry groups, ornamental motifs (e.g., double volutes, meanders, annular bosses), and manufacturing techniques (e.g., lost-wax casting cire perdue, granulation). Archaeometric & Geochemical Signatures ($\mathcal{F}_{\text{chem}}$): Bulk alloy compositions ($\text{Cu-Sn-Pb}$ ratios), trace element profiles ($\text{Ag, As, Sb, Ni, Bi}$), and Lead Isotope Analysis (LIA) ratios. Spatiotemporal Context ($\mathcal{F}_{\text{ctx}}$): Geodesic coordinates, stratigraphic horizon, and calibrated $^{14}\text{C}$ probability density functions. 2.2. Stage 2: Federated Linked Open Data (LOD) Serialization To ensure machine-readability and scalability across distributed repositories, the hypergraph is serialized in both hierarchical JSON-LD and streaming-ready NDJSON-LD (Newline-Delimited JSON-LD), aligned with W3C standards, CIDOC-CRM (ISO 21127), Dublin Core (dcterms), and SKOS/OWL equivalences (owl:sameAs, skos:exactMatch) pointing to Wikidata and DBpedia entities. Exposing these schemas allows automated harvesting by federated SPARQL endpoints, academic data portals (e.g., Zenodo, OpenAIRE, ARIADNEplus), and neural indexing pipelines. 2.3. Stage 3: Multimodal Vector Embeddings and Cosine Similarity To eliminate subjective visual impressionism, high-resolution artifact imagery and structured hypergraph neighborhoods are projected into a unified $d$-dimensional vector space $\mathbb{R}^d$ using pre-trained multimodal vision-language encoders (e.g., CLIP, DINOv2) concatenated with Knowledge Graph Embeddings (e.g., RotatE, CompGCN). Given two artifact feature vectors $\mathbf{u}, \mathbf{v} \in \mathbb{R}^d$ originating from distinct cultural spheres $A$ and $B$, structural and morphological affinity is quantified via the cosine similarity metric: $$S_C(\mathbf{u}, \mathbf{v}) = \cos(\theta) = \frac{\mathbf{u} \cdot \mathbf{v}}{\Vert{}\mathbf{u}\Vert{}_2 \Vert{}\mathbf{v}\Vert{}_2} = \frac{\sum_{i=1}^{d} u_i v_i}{\sqrt{\sum_{i=1}^{d} u_i^2} \sqrt{\sum_{i=1}^{d} v_i^2}}$$ When $S_C(\mathbf{u}, \mathbf{v}) \ge \tau$ (where $\tau \in [0.85, 1.0)$ is an empirically calibrated threshold derived from intra-assemblage variance), the pair $(A, B)$ is flagged as a candidate structural anomaly warranting archaeometric and probabilistic verification. 2.4. Stage 4: Probabilistic Hypothesis Testing and Archaeometric Distance Because isolated morphological similarities can arise through functional convergence, the framework evaluates candidate pairs against a null hypothesis of random independent invention ($H_0$) versus a hypothesis of historical connectivity, trade, or shared technological tradition ($H_1$). For a complex artifact sharing a set of $K$ conditionally independent diagnostic sub-traits $\{M_1, M_2, \dots, M_K\}$ (controlling for functional covariance), the joint probability of random co-occurrence under $H_0$ is bounded by: $$P(M_1, \dots, M_K \mid H_0) = \prod_{k=1}^{K} P(M_k \mid M_{1 \dots k-1}, H_0)$$ We evaluate the strength of evidence via the Bayes Factor ($BF_{10}$): $$BF_{10} = \frac{P(M_1, \dots, M_K \mid H_1)}{P(M_1, \dots, M_K \mid H_0)}$$ To prevent false positives across large database comparisons, $p$-values are adjusted using the Benjamini-Hochberg False Discovery Rate (FDR) procedure. Crucially, whenever archaeometric data are available, morphological similarity is cross-checked against geochemical compatibility. For two metallic artifacts with Lead Isotope vectors $\mathbf{x}, \mathbf{y} \in \mathbb{R}^3$ representing $\left(\frac{^{206}\text{Pb}}{^{204}\text{Pb}}, \frac{^{207}\text{Pb}}{^{204}\text{Pb}}, \frac{^{208}\text{Pb}}{^{204}\text{Pb}}\right)$ and ore-field covariance matrix $\mathbf{\Sigma}$, the framework computes the Mahalanobis distance: $$D_M(\mathbf{x}, \mathbf{y}) = \sqrt{(\mathbf{x} - \mathbf{y})^\top \mathbf{\Sigma}^{-1} (\mathbf{x} - \mathbf{y})}$$ If $S_C(\mathbf{u}, \mathbf{v}) \to 1$ (high morphological/topological identity) and $D_M(\mathbf{x}, \mathbf{y})$ falls within the analytical error margin of a known ore deposit or overlapping chronological window ($^{14}\text{C}$), the hyperedge is promoted to a high-priority empirical research target. 3. Exploratory Case Studies and Applications The pipeline has been deployed to formalize and test three trans-regional comparative clusters: Sardinian Nuragic Bronzes and Dian Culture Metallurgy (Yunnan): Multimodal vector alignment identified high topological c