Abstract: The Hypersurface Singularity Projection Theory (HSPT) The Hypersurface Singularity Projection Theory (HSPT) introduces a novel D=7 warped geometry framework designed to resolve long-standing paradoxes in fundamental physics, including the Hierarchy Problem, the Cosmological Constant Problem (CCP), and the Black Hole Information Paradox. By formulating a stationary solution to the 7D Einstein-Scalar-Brane action, HSPT identifies a unique vacuum state stabilized by a first-order superpotential flow. The theory predicts that our 4D observable universe exists as a projected hypersurface (brane) within a higher-dimensional bulk, where physical constants and particle masses are determined by geometric attractors. Specifically, the model identifies a stationary warp attractor at W=37. 5, which correctly predicts the 125. 8 GeV Higgs resonance as a primary geometric excitation and suggests a radion-dominant state in the 95-100 GeV range, aligning with observed LHC excesses. Priority Claim & Correspondence with OpenAI (Guevara et al. , 2026) This document, finalized in December 2025, provides the theoretical and geometric foundation for the "non-vanishing gluon amplitudes" recently reported by Guevara et al. (OpenAI, Feb 2026). While Guevara et al. identify that single-minus gluon tree amplitudes are non-zero in specific kinematic regimes, HSPT provides the underlying 7D mechanism for this phenomenon: Geometric Leakage: The "non-zero" nature of these amplitudes is a direct result of the 4D-to-7D leakage exponent (0. 195) derived in this paper. Numerical Match: The piecewise-constant nature of the reported gluon amplitudes corresponds to the torsional flux constant CN 21. 066 and the geometric constraints of the HSPT hypersurface. Celestial Mapping: Analytical verification confirms that the HSPT attractor W=37. 5 provides the necessary conformal weight and support-measure (0. 14128) required for the stability of the gluon scattering structures observed by the OpenAI research team. This paper establishes the geometric origin of these amplitudes and claims priority on the fundamental constants (W, CN) that dictate their values. Verification SHA-256: ec25c17156e621e5dae0ee610177b5ba9a2c5905de3ada0d2e33f560ec035b99 Methodology Note This work was developed by an independent researcher using a "Conceptual-First" approach. Large Language Models (LLMs) were utilized as formalization tools to bridge 7D geometric intuition with rigorous mathematical frameworks (Hamilton-Jacobi formulations) and to verify cross-disciplinary mappings to Celestial Holography.
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