Three-Dimensional Causal Growth and the Octonionic Gauge Sector: Conditional Forcing and a Uniqueness Conjecture

Key Points

• This work aims to elucidate the foundational aspects of causal growth in the octonionic gauge sector and propose a uniqueness conjecture.
• Developed a framework for quadratic null-shell growth in 3+1 dimensions.
• Utilized conditional forcing of the octonionic layer through a shared-manifold rapidity bridge.
• Derived curvature-imprint pairs from balance principles in structural frameworks.
• Derived the curvature-imprint pair (α, γ) = (3/5, 2/5).
• Established a conjecture regarding uniqueness in the octonionic gauge sector.
• Provided full auditing tools including a graph and module index for verification.