The Wave–Geometry–Snapshot (WGS) Model: A Three-Layer Ontology of Socio-Technical Systems ー Formalizing Generative Fields, Institutional Geometry, and Projected Sampled Snapshots

This preprint introduces the Wave–Geometry–Snapshot (WGS) model, a three-layer ontology for socio-technical systems. The framework distinguishes (i) the Wave layer Φ as a relational generative field where meaning, trust, participation, and creativity emerge; (ii) the Geometry layer G as institutional constraint structures that coarse-grain and stabilize interaction; and (iii) the Snapshot layer S as sampled indicators (KPIs, rankings, audits, compliance metrics) obtained through Geometry-dependent projection. The paper formalizes the irreversible mapping Φ → G → S and articulates the sampling paradox: optimizing sampled snapshots cannot, in general, reconstruct or preserve the generative field. As an ethical and governance implication, the preprint reframes “the good” as generativity preservation—maintaining the meaning-production attractor Γ and its basin of attraction—thereby motivating a shift from snapshot manipulation toward Geometry design. Highlights · Proposes the Wave–Geometry–Snapshot (WGS) model as a three-layer ontology of socio-technical reality. · Formalizes irreversible coarse-graining and projection: Φ → Ĉ → G → P̂_G → S and S = P̂_G(Φ). · Introduces the sampling paradox: improvements in sampled indicators S do not reconstruct the Wave field Φ. · Explains the KPI trap as basin shrink of the generativity attractor Γ under snapshot fixation. · Reframes governance as Geometry design: interventions u reshape Basin(Γ) rather than maximizing metrics.