Explanations

These pages describe the mathematical representations and execution semantics of the public library.

• Layouts, Storage, and Tensor Contracts defines basis order, compact coefficients, storage declarations, and axes.
• Products, Grades, and Blade Geometry states product and involution conventions and the domain of blade operations.
• Signatures and Algebraic Behavior distinguishes signed forms from coefficient-space quantities and explains their gradients and conditioning.
• Planned Execution and Resources separates fixed contracts, feasibility budgets, and executor selection.
• Structural Work and Policy Calibration explains how executor algorithms become planner-visible work profiles and how the default route policy is calibrated without turning benchmark timings into runtime cost predictions.
• Tensor Composition and PyTorch Ownership covers broadcasting, autograd, modules, placement, and compilation.

Geometric Representations and Parameters compares vectors, blades, mixed-grade values, bivectors, and rotors. Optimization and Geometric Updates starts from ordinary coefficient updates and explains the assumptions of specialized helpers.

Bivector Exponentials and Actions develops one specialized operation in depth, including finite closures, numerical evaluation, and induced actions. It builds on the same layouts and planning contracts as the other operations.