Paper XI: Packets, Arithmetic Realization, and Conditional Comparison · Guided reading
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Which finite pieces of arithmetic representation data can be reconstructed, and what comparison inputs are still needed?
The paper resolves finite monodromy, Frobenius, and character packets and develops restricted comparison constructions. It separates those finite results from the general arithmetic realization problem.
These suggested paths use this edition’s available material. Each comparison retains its stated tame, wild, and coefficient hypotheses. General arithmetic realization is Conjecture 66, and the full comparison of pair local factors remains conditional.
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.
- Compute Frobenius in a quadratic finite field
This is finite-field background for Paper XI’s finite packet theory. Conjecture 66 separately asks for an actual arithmetic realizer with its declared comparison data.
- 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.
- Reader choices and the realization contract
Continue through the opening chapters in the edition’s order.
- Current scope and research routes
Continue through the opening chapters in the edition’s order.
- Introduction
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. Finite packet and selected terminal developments have accepted formal evidence. Conjecture 66 and its arithmetic realization obligations remain open.
Lean: Selected results recorded · Evidence basis: Recorded formal evidence
Remaining work. Track each Conjecture 66 obligation separately from the accepted finite packet and transported constructions.
- Tame Frobenius packets
Read the selected setup or definition before using the result.
- Tame character projectors
Read the precise statement and its hypotheses.
- Read its written proof
Follow the recorded written argument for this statement.
- Lean guide (PDF)
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.