Paper IX: Arithmetic Packets, Dyadic Towers, and Local Polynomial Deformation · Guided reading
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How can residue packets and precision towers organize arithmetic sequences and local lifting?
The paper develops exact coefficient reconstruction, coordinate transport, valuation estimates, and lifting constructions. Its later arithmetic results retain their individual field, ring, and precision hypotheses.
These suggested paths use this edition’s available material. Finite residue reconstruction is over a declared commutative ring. Broader extensions and the ordinary Euler-tail simplicity endpoint remain open; formal evidence covers selected developments.
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.
- Reconstruct from residues
The example is ordinary integer CRT. Paper IX develops arithmetic packets and local deformation beyond this calculation.
- Round a binary number
Paper IX supplies dyadic arithmetic background. The rounding implementation and its contracts belong to Polyphase Float.
- Euler packets, polynomials, and residuals
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.
- What this final edition establishes
Continue through the opening chapters in the edition’s order.
- Scope and conventions
Continue through the opening chapters in the edition’s order.
- Arithmetic packets and coefficient transport
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. Accepted reading release preserves scoped arithmetic, dyadic and lifting formal work. Broader extensions and the Euler reciprocal endpoint remain open.
Lean: Selected results recorded · Evidence basis: Recorded formal evidence
Remaining work. Reconcile the current claim map with the narrowed threshold-free theorem and retain the refuted stronger statement as history.
- Residue selectors
Read the selected setup or definition before using the result.
- Residue reconstruction
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.
- Current guide: source locations, correspondence, and replay limits
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.