The Spiral Coordinate System (SCS): A Unified Structural Model of Phase, Scalar, and Emergent Time

This paper introduces the Spiral Coordinate System (SCS) as a unifying structural framework integrating six prior stages of research on inquiry, cognition, time, and human–AI collaboration. Earlier work established: the Λ-State as a liminal transition structure in inquiry, the underlying geometric distinction between metric identification and recursive meaning, later unified here as WHAT–WHY (with its structural basis developed across Stages II and VI), the Rhythm–Information Time Principle defining time as observer-dependent rhythmic grouping, Human–AI Collaborative Research (HAICR) as a dialogical methodology, a graded Information–Consciousness boundary, and a systems-theoretic distinction between phase-dominant and scalar-dominant temporal organization.

SCS formalizes these components within a single coordinate space, representing scalar accumulation as a radial dimension (r), phase relationship as an angular dimension (θ), and experienced time as an emergent interval (h) arising from phase rotation under constraint rather than as a primitive axis. Λ-States are treated as transition operators within this space, enabling consistent mapping of convergence, compression, and observer-dependent temporal experience.

The framework is presented as a conservative structural synthesis. It does not propose new physical mechanisms, attribute consciousness to artificial systems, or replace empirical investigation. Instead, it provides a diagrammable coordinate model supporting planned empirical validation, including micro-convergence analysis and constraint-driven organization studies, while enabling disciplined translation into applied domains without metaphysical overreach.

Keywords: spiral coordinates, phase-scalar dynamics, emergent time, consciousness geometry, observer-dependent temporal experience, rhythmic grouping, human-AI collaborative research, structural synthesis, coordinate framework, HAICR methodology, temporal phenomenology, systems theory, multi-scale time, coordinate geometry