Open Null Transport and Closed Compact Support in a Helicoidal Spectral Geometry: A spectral gap theorem for radiation–matter separation in Helical Universe Theory

This submission contains a main theorem paper and a companion validation appendix. The main paper develops a helicoidal open/closed spectral framework within Helical Universe Theory (HUT). It proves that noncompact open helicoidal transport has null/massless dispersion, while closed compact helicoidal support is governed by an elliptic operator with compact resolvent and a positive first non-gauge eigenvalue. The result is formulated as a radiation–matter separation theorem internal to the stated HUT operator framework. The paper explicitly does not claim to solve the Clay Yang–Mills mass gap problem. The companion validation appendix checks the operator-level assumptions and limiting cases used in the theorem, including trace structure, compact-support positivity, null open-sector behavior, and the separation between mathematical spectral claims and physical HUT interpretation. Together, the two documents provide a stand-alone formulation and audit of the HUT open/closed helicoidal spectral gap theorem. 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.