This guide accompanies the final traditional edition and the Lean guide. Its twenty-six worked pages preserve the mathematical models of the original visual appendix. Final references and evidence descriptions connect those models to the present edition.
| Evidence layer | What it supports |
|---|---|
| Current formal audit | All 118 production modules freshly compiled. Separate kernel replay and manuscript correspondence checks cover the 68 scoped results. Exact counts, hypotheses, and controls appear in the Lean guide. |
| Current exact checks | All 1,008 rational algebra assertions and fifteen finite transfer-derivative polynomial identities passed. Fifteen deliberate corruptions were rejected. These are bounded checks. |
| Historical certificates | The retained visual run records 147 checks, five rejected controls, and four rational zero brackets of width \(10^{-20}\). The brackets certify local existence and uniqueness. The symbolic suites were hash-validated, not rerun in this edition. |
| Numerical visualization | Sampled analytic curves, finite products, moment shares, and displacement diagnostics have the roles stated on their pages. They are not exact global zero censuses. |
| Figure provenance | The twenty-four editable TikZ figures are preserved. Earlier regeneration evidence remains historical. Twenty-three match the original release; V13 retains the reviewed label adjustment. No figures were regenerated for this audit. |
| Editorial preservation | The original worked formulas, model code, checker, and vector figure sources are preserved. Updated locators refer to the final traditional edition. |
Boundaries that remain in force
The general family has eventual positivity and simplicity of its reduced zeros, not an assertion that every reduced zero is positive and simple. The paper leaves universal simplicity, positivity of every reduced zero, full displacement expansions, and a zeta functional equation open. The exact order-two and order-four models do not settle those questions for every order. Imported standard fact 11.1 stays outside the 68-result contract. Fixed logarithms, zero-free domains, multiplicities, and the hypotheses of nearest-pole asymptotics remain explicit. No historical priority is inferred from successful computation or formal verification.
Replay the worked layer
Run python build.py in this editable guide folder to compile the PDF in an isolated temporary directory. The separate model checker is checks/verify_examples.py. The plate generator is source/generate_graphics.py. They require the listed Python dependencies. Run those mathematical tools in a temporary copy to preserve the delivered evidence.
Read this as
A proof, a finite exact test, a root enclosure, and a sampled curve answer different questions. Keeping their scopes explicit makes the pictures useful mathematical evidence.
Evidence note from the source edition
The source package preserves the formal release, proofread review, independent audit, exact certificates, and rebuild instructions. PDF assembly is a separate operation from mathematical verification.