Paper I: Typed Operator Systems, Seed Rank, and Exact Packet Coordinates · Guided reading
Start here
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.
These suggested paths use this edition’s available material. The single-operator count assumes finite dimension over the declared field. Infinite reconstruction retains the stated topology and convergence assumptions.
Visual introduction
Vectors, matrices, linear maps, kernels and images, and reading a statement with hypotheses. Consult the selected paper for any additional algebra or analysis it uses.
- Generate a space from one seed
Paper I develops seed generation with its stated algebra and module hypotheses.
- Split and reconstruct a vector
Exact packet coordinates provide the source setting for the elementary decomposition.
- Reconstruct an operator
Follow the worked calculation, its expected output, and its source links.
- Visual guide in HTML
Explore the drawings and their accompanying explanations.
- Question, background, and scope
Use the work overview to identify the problem and required background.
Checkpoint: Explain the question and the model in your own words before continuing.
Full study
Keep the work’s definitions and hypotheses with each result.
- Begin the HTML reading edition
Start at the opening section, then use previous and next to continue in order.
- Foundations and seed rank
Continue through the opening chapters in the edition’s order.
- Packets and transfer graphs
Continue through the opening chapters in the edition’s order.
- Transport and realization
Continue through the opening chapters in the edition’s order.
- Full contents
Choose any chapter or companion section from the complete contents.
- All reading files
Return to the edition’s full reading-file list.
Checkpoint: Choose a result or example and record its assumptions, conclusion, and source location.
Proof and evidence
Read the corresponding statement and its assumptions before inspecting an evidence record.
Recorded coverage. 69 accepted proof-level correspondences in the stated manuscript scope. 108 correspondence records are not 108 theorems.
Lean: Declared contract recorded · Evidence basis: Recorded formal evidence
Remaining work. Maintain the exact statement map and reproduce the pinned formal contract before a changed release.
- Seed rank
Read the selected setup or definition before using the result.
- Single-operator seed rank
Read the precise statement and its hypotheses.
- Read its written proof
Follow the recorded written argument for this statement.
- 108-record correspondence map (JSON)
Read the correspondence map or formal guide before interpreting formal coverage.
- Lean guide (PDF)
Read the correspondence map or formal guide before interpreting formal coverage.
- Formal replay instructions (text)
Read the correspondence map or formal guide before interpreting formal coverage.
- Inspect retained Lean sources
Compare the full types with the written statements and recorded coverage.
- Code and reproduction files
Read the input limits, expected results, and reproduction instructions.
- Evidence and recorded limits
Check the edition and evidence behind the work’s status.
Checkpoint: Distinguish the written claim, what was checked, and what remains open.