HUT Radiation and Matter as Open and Closed Helicoidal Phases: A Spectral-Admissibility Theorem and Numerical Validation Suite

This archival deposit presents the foundational results of the Helical Universe Theory (HUT) regarding the geometric nature of mass. This work establishes a topological distinction between radiation (open helicoidal phase) and matter (closed helicoidal phase). By utilizing a first-order phase action on helicoidal support, the theorem derives the emergence of a spectral gap—and thus rest mass—directly from the holonomy of the support seam. Included Documents & Resources: Primary Manuscript: A formal field-theoretic bridge connecting helicoidal geometry to the Standard Model. Key features include: The Kernel-Holonomy Lemma, proving why mass is a mandatory topological consequence of closed phase support. The Exponent-Minus-Log (EML) Potential, identifying the Omega Constant as a non-arbitrary support-locking mechanism. The Seam-Level Dirac Lift, deriving spinorial behavior directly from geometric torsion. Validation Study: A technical supporting document that subjects the theoretical operators to rigorous numerical testing. It verifies the stationarity of the EML potential and the positivity of the stress-energy tensor. Numerical Suite (Python/JSON): Full source code and raw data outputs proving that the HUT operators maintain a precision of 10⁻¹² in identifying stable matter-like states. This ensures the reproducibility of the claims. Core Findings Topological Mass Origin: Mass is not an added field (Higgs) but a consequence of "closed" helicoidal support. Omega-Lock Stability: The geometry of the universe has a natural "fixed point" that dictates the stability of matter without requiring external "fudge factors." Admissibility Filter: A six-stage logical gate that explains why only specific geometric configurations persist as stable particles. Intellectual Property & Licensing This work is the original discovery of Ara Kavlakian, PhD. All rights are reserved. This deposit serves as the permanent date-of-record for the Helical Universe Theory (HUT) framework. For inquiries regarding peer-review, collaboration, or licensing of the HUT-VAL numerical suite, please contact the author at [ara.kavlakian@gmail.com].