Paper II: Refinement Towers, Weighted Transfer, and Integral Separation of Operator Packets · Guided reading
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How do packet coordinates and operator transfers change when we refine the scale?
The paper gives coherent coordinate changes across refinement levels, exact formulas for refined operator blocks, weighted path inverses, and integral precision bounds.
These suggested paths use this edition’s available material. Refinement uses complete idempotent systems. Infinite path inverses require the stated filtered completeness; contour constructions retain their admissible-contour 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.
- Refine a signal
Read Paper II for refinement and Paper V for signal and polyphase constructions.
- Assemble transfer blocks
Paper II supplies transfer background. Paper VIII develops operator algorithms and compilation.
- Refine a signal
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.
- Refinement and residue coordinates
Continue through the opening chapters in the edition’s order.
- Weighted transfer
Continue through the opening chapters in the edition’s order.
- Integral separation and Smith congruences
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. 53/53 proof-level scopes have recorded replay and accepted correspondence. Admissible contour existence remains an application assumption.
Lean: Declared contract recorded · Evidence basis: Recorded formal evidence
Remaining work. Preserve the contour hypotheses and rerun the recorded contract after any mathematical change.
- Refinement
Read the selected setup or definition before using the result.
- Refinement of operator blocks
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.