Paper I: Typed Operator Systems, Seed Rank, and Exact Packet Coordinates
How many starting vectors do we need to generate a space under a fixed family of operators?
For a fixed operator action, seed rank counts the generators needed. The finite-dimensional single-operator count uses classical polynomial-module structure. Complete packet coordinates reconstruct vectors and operators from their components, connecting generation, relations, and transfer blocks.
Assumptions and limits. The single-operator count assumes finite dimension over the declared field. Infinite reconstruction retains the stated topology and convergence assumptions.
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- 1. Split and reconstruct a vector · Terms and source routes
- 2. Generate a space from one seed · Terms and source routes
- 3. Change coordinates · Terms and source routes
- 6. Use redundant coordinates · Terms and source routes
- 10. Find a kernel and its fibers · Terms and source routes
- 11. Build spectral projectors · Terms and source routes
- 15. Compose typed operations · Terms and source routes
Complete demonstration with runnable code: Reconstruct an operator.
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