COS Method · Guided reading
Start here
Quadratic-form probability calculations, tail accuracy, and numerical evidence.
These suggested paths use this edition’s available material. Exact finite algebra and conditional error bounds remain separate from analytic and numerical backend obligations.
Visual introduction
Useful background: multivariate Gaussian distributions, quadratic forms, eigenvalues, and numerical integration.
- How to read this book
Choose the probability, operator, or numerical route that matches your background.
- Visual studies
Follow the Gaussian form, spectral packets, and probability enclosure through the visual examples.
- A worked probability enclosure
Follow the directed-enclosure calculation and its stated input and error requirements.
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.
- Gaussian quadratic forms
Enter this part of the retained reading sequence.
- Structured operators and spectral recovery
Enter this part of the retained reading sequence.
- The K-COS method
Enter this part of the retained reading sequence.
- Certified numerical computation
Enter this part of the retained reading sequence.
- 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. Closing 138-page publication with a finite Gram/enclosure Lean companion. Full numerical correctness is outside the official companion.
Lean: Selected results recorded · Evidence basis: Recorded formal evidence
Remaining work. Keep the official monograph stable and route end-to-end numerical proof work to the separate continuation.
- Find a statement and written proof
Use the work’s statement directory to locate an argument.
- Formalization and theorem correspondence
Compare the written results with the finite formal companion and its assumptions.
- Computation and reproducibility
Inspect the retained commands, replay results, and their tested scope.
- 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.