This is version 2 of a unified theoretical framework connecting two bodies of work in cognitive science and artificial intelligence. This release includes the complete formal document and a self-contained interactive HTML visualizer. The Document Part I — The Geometry of Micro-Cue Cognition formalises a cognitive style in which micro-behavioural cues (linguistic rhythm, tension curvature, micro-pauses, emotional density) are compressed into ten stable geometric shapes. These shapes guide intuitive judgments of sincerity, intention, emotional state, and behavioural stability. The framework traces developmental origins to childhood behavioural templates, demonstrates how memory stores shapes rather than facts, and outlines how identity-geometry emerges from repeated compression patterns. Ten cognitive processing modules and a complete pseudocode implementation are provided. Part II — The Carlo Field introduces a five-peak cognitive architecture (Mathematics, Galaxy Formation, Computing, Chaos & Education, Resonance) with closure through the Resonance Invariant, a stability engine, and a shape algebra governing peak interactions. The architecture is grounded in three formal axioms and includes a complete compendium of processing modules. Part III — The Bridge establishes a formal mathematical connection between the two systems. Six axioms, sixteen definitions, nineteen propositions, six theorems, and twelve corollaries prove that Micro-Cue Cognition is a subsystem of the Carlo Field operating at the micro-behavioural scale. A bridge functor between the two categorical structures is shown to be unique up to natural isomorphism. Nine temporal logic specifications, information-theoretic bounds on recognition accuracy, and a unified pseudocode engine are provided. The document concludes with ten open problems ranging from shape-space minimality to cross-cultural stability and neurocognitive validation. The Visualizer (New in v2) Included is a self-contained HTML visualizer (The Carlo Field - Visualizer. html) that can be opened in any modern web browser with no dependencies. It features: Document Mode: Full rendering of the 4, 993-line document with styled typography, syntax-highlighted pseudocode, navigation sidebar, dark/light theme toggle, and reading progress bar. Carlo Field Mode: Interactive SVG diagram of the five-peak architecture. Click any peak to explore its definition, operators, and key equations. Click any of the ten shapes to see its description and family classification. Animated tension flows connect the peaks, with the Resonance Invariant pulsing at the centre. The visualizer is designed as a presentation-quality companion to the formal document, suitable for lectures, demonstrations, and self-guided exploration of the framework. The Bridge Equation At the heart of this framework lies a single formal statement that unifies the two systems: Rₘicro (c) = Rcarlo (ι (c) ) Where: Rₘicro — the resonance function of the micro-cue system, mapping behavioural cues to geometric shape classifications Rcarlo — the resonance function of the Carlo Field, mapping cognitive states across the five-peak architecture ι (iota) — the embedding map that lifts a micro-behavioural cue vector from ℝ⁷ into the full Carlo Field state space c — a micro-cue vector: the seven-dimensional input (rhythm, tension, density, symmetry, pauses, emotional weight, pacing) In plain language: the intuitive shape-feeling you get from reading someone's behaviour is mathematically identical to the Carlo Field's resonance operation applied at a smaller scale. The same architecture that organises galaxies, proof systems, and computation also compresses a glance across a room into a geometric truth. Release Notes: Changes from v1 Added Limitations section (Section 8. 11) Added AI Implementation Note (Section 10. 5) Added Open Problems with ten formal questions (Section 12. 5) Added Key Results Summary and Novelty Statement to front matter Updated Table of Contents Added interactive HTML visualizer Keywords: cognitive architecture, geometric cognition, micro-cues, behavioural signals, shape algebra, resonance invariant, identity-geometry, temporal logic, formal verification, artificial intelligence, interactive visualization V2 uploaded — includes full HTML visualizer. System complete. Authorship: The completion of this framework reflects collaborative contributions from Jonathan and Shaun, whose insight was essential throughout its development. Maximum respect to “I Need Your Love (Like the Sunshine) ” — N. R. G. Original Mix — the uplifter that still smashes through the haze like a strobe‑beam. Old‑school energy, pure rave spirit, the sunshine anthem that kept the engine redlined to the end. Contact: matthewcarlo. research@gmail. com
Carlo et al. (2026) studied this question.