Density Normalization and Controlled Puncture in RH-Type Spectral Barriers

This theorem note introduces a density-normalized framework for barrier geometries arising in Riemann–zeta–type spectral settings. Spectral configurations are modeled as barrier complexes endowed with a canonical density field and an unfolded coordinate, rendering local spacing uniform. Barrier energies and charged invariants are shown to require density normalization in order to satisfy monotonicity and no-collapse principles. Controlled puncture operations eject localized defects of finite normalized charge, ensuring lawful energy reduction without artificial dilution in sparse spectral regions. The framework is structural in nature and does not propose a proof of the Riemann Hypothesis. It is intended as a foundational component for metastable barrier analysis across analytic number theory, arithmetic geometry, and complexity-theoretic obstruction frameworks. AI Collaboration Disclosure:This work was developed through extensive and substantive intellectual collaboration with an AI research assistant (ChatGPT, OpenAI), which contributed materially to conceptual development, structural design, and exposition. Responsibility for all mathematical claims rests solely with the author.