IMR — Quantum Core: Reflective Coherence, Deviation Geometry, and Logistic Emergence in Quantum Regimes

This work presents the Quantum Core of the IMR (Reflective Multidimensional Intelligence) framework. The document introduces a mathematically consistent formulation of reflective coherence in quantum regimes, based on density operators, whitening transformations, and a deviation functional defined in trace-class operator spaces. The framework establishes: – A quantum deviation functional DQ – A normalized deviation variable z – A bounded reflective coherence functional RQ – A logistic emergence law derived from Quantum Scale Consistency (Q-RSC) – Stability under CPTP quantum channels The formulation ensures: – Unitary invariance – Trace-norm continuity – Classical-limit correspondence – Spectral / Fourier interpretability The derivation of the logistic profile is obtained without reliance on specific ontological interpretations, emerging instead from semigroup consistency constraints on the deviation variable. This module represents a core theoretical component of the IMR framework, linking quantum information geometry, deviation measures, and bounded coherence mappings.