Emergence-Convergence Framework I: Correlation Spectrum — Fundamental Principles of the Emergence-Convergence Framework

We propose a minimal set of fundamental principles—the correlation spectrum framework—with "existence is correlation" as its sole ontological postulate. The framework contains only three undefined terms: correlation, constraint dimension, and strength dimension. Self-consistency is a constitutive condition of constraint itself. From this basis, the individuality of existents is derived as a theorem: an existent is a structural position in the correlation network. A single parameter λ∈[0,1] characterizes global correlation strength. We prove a boundary inaccessibility theorem, confining existence strictly to λ∈(0,1). Two independent unfoldings arise: inferential unfolding (logical space, foundation of mathematics) and metric unfolding (physical state space, foundation of physics). Self-dual symmetry λ↔1-λ is established, and the system converges inevitably to λ=1/2 as the unique globally asymptotically stable fixed point. At this self-dual fixed point, constraint-strength equivalence provides an ontological answer to Wigner's "unreasonable effectiveness of mathematics." We further prove the IMAT theorem: in the continuum limit at λ=1/2, the inferential-face backbone category L and the metric-face backbone category P are categorically equivalent, forced by the simultaneous optimality of logical richness and information capacity. The argument is organized into four theoretical tiers (A–D), distinguishing presuppositions from derivations, constructive choices, and conjectures. Five companion papers supply full technical constructions and philosophical implications. Changes in V2.0:- Reduced undefined terms from 4 to 3 (removed "existent" as primitive)- Individuality of existents now Theorem 1, derived from pure correlation- Self-consistency absorbed as constitutive condition of constraint (Axiom P1)- All companion papers updated with valid Zenodo DOIs- See the full V1-to-V2 changelog for details.