Paper II: Refinement Towers, Weighted Transfer, and Integral Separation of Operator Packets
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.
Assumptions and limits. Refinement uses complete idempotent systems. Infinite path inverses require the stated filtered completeness; contour constructions retain their admissible-contour assumptions.
Completion: Scoped release · Lean: Declared contract recorded · Confidence: Recorded formal evidence
Before you start
Suggested background: 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.
Recorded results and limits: 53/53 proof-level scopes have recorded replay and accepted correspondence. Admissible contour existence remains an application assumption.
Remaining work: Preserve the contour hypotheses and rerun the recorded contract after any mathematical change.
The background advice is an editorial starting point. The work itself states its prerequisites and hypotheses.
Reading routes · Glossary · Claim links · Download this work
Worked examples for this work
These introductory calculations lead into this work’s subject. The source and evidence links below retain the work’s recorded scope.
- 4. Assemble transfer blocks · Terms and source routes
- 5. Refine a signal · Terms and source routes
- 11. Build spectral projectors · Terms and source routes
Complete demonstration with runnable code: Refine a signal.
Read
Back to work navigation · Worked examples
Written proofs
Read the written arguments in the PDF. The manuscript source remains available below.
Find the statement number or section in the reading files, then read its assumptions and argument. A claim map may cover only part of the written result.
Find this work among other written proofs
Back to work navigation · Worked examples
Lean
Start with the edition guide and the build instructions below. Check the correspondence records to see which written claims the Lean declarations cover. Source links lead to .lean files. PDF guides explain the formalization.
Find this work among other Lean projects
Back to work navigation · Worked examples
Code
These links include code, examples, checks, or build tools. Read the edition guide for setup instructions and what each command does. All software is beta and work in progress.
Find this work among other code projects
Back to work navigation · Worked examples
Evidence
- Completion, Lean coverage, confidence, and cited evidence
- Source-file receipt (identity and availability)
- All files in this source edition
The evidence records describe the reviews and runs completed for this edition.
Back to work navigation · Worked examples