Triadic Metaperception in Local Sociometric Networks: The M3-AΩ Framework for Analyzing Expansiveness, Accuracy, Projection, and Consensus

M3-AΩ Scientific Preprint (Version 1.0.2, October 2026) · NEXORD / VISORD Ecosystem. Research on social network cognition has historically been constrained by two major bottlenecks: the combinatorial burden of full Cognitive Social Structures (CSS, requiring O(N²) queries), which leads to participant fatigue, and the psychological reactivity induced by direct inquiries regarding interpersonal rejection. This paper introduces the M3-AΩ Framework, a methodological approach that reduces the elicitation of third-party network cognition to a focused battery of micro-probes targeted at boundary positions (extremes of proximity and relational distancing, alongside their adjacent boundaries) under the Clélie Protocol of non-maleficence by design (substituting explicit rejection with relational abstention or distancing and banning queries regarding third-party rejections). The framework rigorously disentangles three levels of social cognition: Self-centrality perception: where an individual places themselves within the team hierarchy (k_self). Dyadic reflexive metaperception: inward expectations of affinity (pE) and relational distancing (pR). Triadic metaperception of alterity: third-party cognitive conjectures regarding whom boundary peers will preferentially choose. Leveraging a Complete Disjunctive Table, data are analytically decomposed into attributed expansiveness (x), volume error (G), factual accuracy (P, Rec, F₁, J), projection (Pr), and inter-observer consensus, while formalizing the additive decomposition of relational differentials (D = Δe + ΔG). Furthermore, we outline a strategic Correspondence Analysis (CA) where realized interactions establish the active metric space and metaperceptive attributions are projected as supplementary illustrative points, visually tracing individual cognitive distortion vectors. To incorporate higher-order factorial contributions into an exploratory planar synthesis without dimensional truncation, an Exometric 6D → 2D Projection is formulated, incorporating factors 3 to 6 through specific angular displacements (+30°, +60°, -30°, -60°) weighted by singular values, with explicit reporting of its metric distortion (r = 0.4558, Kruskal Stress-1 = 0.3915). The framework is demonstrated on a controlled synthetic dataset (N = 7), establishing algebraic consistency and reproducibility. Open Science Supplement: Includes complete input ORBIT matrices, attribution sets, contingency tables, 6D factorial coordinates, and full bilingual editions (English and Spanish). Platform & Interactive Visualizers: https://josemancor.github.io/nex-ord-web/