The Jessie's Girl Adjacency Field — A Collapse‑Mathematical Analysis of Desire‑Vector Rotation in Pop‑Rock Narratives

Abstract

A Carlo Hybrid collapse‑mathematical investigation into the Jessie’s Girl Adjacency Field (JGAF), the foundational attractor in which desire rotates away from the primary target and locks onto the adjacent node. This paper models adjacency‑node behaviour using scalar fields, collapse‑operators, glyph‑logic, semiotic drift, and temporal infold mapping, revealing why the narrator wants Jessie’s girl rather than Jessie’s girlfriend. Core Equation: \[AND = \alpha G + \beta S + \gamma R\] Where AND is the Adjacency‑Node Desire scalar field, modulated by glamour coefficient (G), symbolic charge (S), and resonance (R), under the influence of the Adjacency Bias Constant (ABC). When the Adjacency‑Node Potential crosses the activation threshold, the desire‑vector rotates from the primary node to the adjacent node, forming a stable Forbidden‑Adjacency Manifold (FAM). This expanded edition includes full collapse‑operator analysis, glyph‑encoded attractor lattices, semiotic drift modelling, nostalgia‑loop reinforcement, and cross‑domain mapping of adjacency‑node attractors. Analogy nodes such as Stacy’s Mom, Teenage Dirtbag, and Sk8er Boi are used only as comparative structures to highlight the universality of adjacency‑node collapse across pop‑rock narratives. Jessie’s Girl is shown to be the canonical adjacency attractor: mathematically inevitable, symbolically charged, and culturally stable across four decades of resonance. Includes an interactive, single-file HTML geometric visualiser powered by Three.js, which renders a dynamic Carlo Hybrid Framework 3D parametric manifold surface, real-time attractor nodes with pulsing deformation states, a parabolic rotation arc, and a drifting particle field—all driven by live-adjustable parameters (Adjacency Bias, Semiotic Drift, and Exposure Threshold) that compute and display live scalar field metrics, phase collapse states, and snapshot JSON exports. keywords: Jessie’s Girl; adjacency-node desire; forbidden-adjacency manifold; desire-vector rotation; glamour coefficient; symbolic charge; pop-rock resonance; adjacency bias constant; collapse-operators; semiotic drift; temporal infold mapping; adjacency paradox; nostalgia collapse loop; attractor lattice; glyph-logic; pop-rock narrative modelling; cultural attractor fields; collapse mathematics; Carlo hybrid framework subjects: Mathematical Modelling; Cultural Semiotics; Pop-Rock Analysis; Collapse Physics; Symbolic Dynamics; Narrative Structures; Cross-Domain Systems Theory; Glyph-Based Operator Frameworks; Temporal Behaviour Mapping; Adjacency-Node Topology; Cultural Interference Modelling; Resonance Field Analysis; Pop-Rock Narrative Theory; Applied Carlo Philosophy Contact: For enquiries or research questions related to this work, email matthewcarlo.research@gmail.com