Structural Consistency and Channel Exclusion via LMC

This work introduces the Leue Modulation Coefficients (LMC) as a lossless, purely algebraic framework for testing the structural realizability of discrete data. LMC enforces a single global consistency condition across all modulation channels and induces a canonical geometric structure whenever such consistency is possible.Unlike reconstruction or optimization-based methods, LMC does not approximate, smooth, or fit data. It operates as a binary decision framework: either a globally consistent realization exists, or an exact algebraic obstruction is detected. Structural failure is therefore not treated as noise or numerical instability, but as meaningful diagnostic information. A central result is the channel exclusion principle: a modulation channel cannot be partially active. If a channel contains both strictly positive and exactly zero coefficients, no globally consistent LMC geometry exists. This exclusion is exact, scale-invariant, and independent of dimension or representation. The paper develops explicit consistency tests, adversarial examples, and no-go results demonstrating that:- pairwise consistency does not imply global realizability,- exact zeros induce intentional topological discontinuities,- extreme dynamic ranges do not compromise consistency,- forward and inverse LMC reconstruction is idempotent. LMC is positioned as a structural preconditioner that operates prior to geometry, optimization, or statistical inference. It separates questions of realizability from interpretation and modeling, and applies uniformly to algebraic data, discretized analytic constructions, probability distributions, and derived geometric configurations. The framework is exact, lossless, and domain-independent, providing a structural consistency filter for mathematical and applied data analysis.