# Reproducing the Research Report

**Release:** 18 October 2026. The archive contains the English publication, exact-arithmetic code, preserved historical material, and records of checks actually executed. Verification of files, verification of finite examples, and proof of a theorem are different tasks. This guide keeps them separate.

## 1. Start with the portable publication checker

Extract the complete archive. Open a terminal in its top-level folder and run:

```bash
python3 -B code/verify_publication.py
```

Python 3.10 or newer is sufficient; this checker uses only the standard library. The publication run used Python 3.12.14. Do not use `-O` or `-OO`, which can disable assertions in historical code. The portable checker rejects an optimized interpreter.

The default command checks the exact moment normalization, interval moments, all five rational Chebyshev trial values plotted in the article, positive rational sufficient-degree parameters, sampling-grid arithmetic, Fejér coefficients and norms, the two explicit Riesz examples, and the publication dates. It does not claim to solve a continuous minimum by drawing a dense curve.

If `MANIFEST_SHA256.json` or `MANIFEST.json` exists in the package root, the checker verifies the SHA-256 digest of every listed file. Without a manifest it reports `not_present`; that status is not a successful integrity check. A manifest detects changes to the listed bytes. It does not establish the truth or novelty of a mathematical claim.

The script prints JSON and never overwrites publication files. To keep a new receipt without changing the preserved release, write it **outside** the extracted package:

```bash
python3 -B code/verify_publication.py > ../publication-check.json
```

Overwriting a manifest-listed receipt before verifying its hash would correctly produce a mismatch.

## 2. Rerun the selected round 6 suites

Run:

```bash
python3 -B code/verify_publication.py --run-selected > ../publication-selected-check.json
```

This makes a disposable copy of `evidence/history/round6/`, runs six original checkers there, compares their regenerated result objects to the archived JSON, and removes the temporary copy. The source evidence remains unchanged. The six scripts are:

| Script | Principal scope |
|---|---|
| `branches_78_83_checks.py` | Integer moments, operator identities, finite-box coefficients, and Chebyshev degree certificates |
| `audit_83_quantum_checks.py` | Separate rational degree certificates and exact Chebyshev trial values |
| `branches_71_90_checks.py` | Normalization, grid formulas, and twisted-ring examples |
| `audit_90_spectral_checks.py` | Independent integer matrix and closed-walk comparisons |
| `quantum_72_77_checks.py` | Exact finite checks behind the quantum-state comparisons |
| `wavephysics_84_89_checks.py` | Wave-model identities, Fermi–Dirac constants, weighted amplitudes, and the finite Riesz search |

The last script enumerates all 262,143 nonempty subsets of `{1,...,18}` and compares 4,095 cases by a second autocorrelation method. The result `7/20` is the smallest normalized **Riesz trial quotient on that finite universe**, not a global minimum for unrestricted frequencies or a statement about the true `K`.

All six suites were rerun during publication preparation. They exited successfully, and all six regenerated JSON objects exactly matched the preserved results. The execution took approximately 16 seconds on the preparation machine; this is an execution record, not a promised runtime on another system. The default timeout is 180 seconds per script and can be adjusted, for example with `--timeout 600`.

See `evidence/current_verification.json` for the actual commands, interpreter, timestamps, outputs, result hashes, and status. Its initial run predates the final root manifest and explicitly records that the manifest was not yet present. Final package integrity can be checked with the default command after extraction.

## 3. Earlier suites and the historical evidence

Approaches 51–70 are under `evidence/history/round5/`. To repeat them manually, first copy that complete directory to a writable working folder, then run these commands in the **copy**:

```bash
python3 -B functions_51_56_checks.py
python3 -B branches_57_62_checks.py
python3 -B functions_63_68_checks.py
python3 -B root_69_70_checks.py
python3 -B audit_62_independent_checks.py
python3 -B audit_geometry_62_checks.py
```

These are the original available suite commands. This publication does not claim that this entire list was freshly rerun. The exact interval identities and selected hierarchy calculations were checked separately during the editorial review; that narrower scope is described in the mathematical audit.

The earlier unnumbered finite-search groundwork has its own independently recorded publication rerun. It covers all 4,194,303 nonempty subsets of `{1,...,22}`, with two comparison implementations and continuous certificates for the winning example. Consult `evidence/groundwork_reproduction.md` and its receipts for the exact scope and strict bounds. To repeat that work, copy `evidence/history/previous_sources/`, provide NumPy (the recorded version is 2.3.5), and run `python3 run_verification.py` inside the copy. SciPy is not required by that runner. This guide does not repeat or enlarge that result.

Other historical exploratory programs can have different dependencies or assumptions. Their original notes remain with them; they are not silently modernized into a single uniformly tested software package. Approaches 41–50 were reconstructed from surviving descriptions. The missing approach-42 collection of 1,980 certificates has not been recreated. Neither a passing current checker nor an intact archive restores missing evidence.

## 4. Reading the evidence correctly

The mathematical appendix gives the proofs of unrestricted statements. A finite script checks the arithmetic of fixtures and identities; it does not prove every asserted theorem by enumeration. A valid sampled value is a lower bound on negative depth, while exclusion of a deeper continuous minimum requires an upper certificate. Exact rational trial quotients are not automatically the optimized hierarchy values.

The article attributes the moment hierarchy to Lasserre and the polynomial-concentration architecture to prior work including Slot and Laurent. The novelty of the particular frequency-independent degree estimate is unverified. These internal mathematical and computational checks are not external peer review or formal proof-assistant verification. No claim is made that Chowla’s conjecture has been resolved or that the research establishes a Bass Plus audio-performance improvement.

## 5. Rebuild the figures and reading editions

The canonical article sources are the Markdown files under `web/` and the mathematical appendix under `appendices/`. The publication preparation used Python 3.12.14, python-docx 1.2.0, NumPy 2.3.5, SciPy 1.17.0, Matplotlib 3.10.8, Pandoc 3.1.3, and LibreOfficeDev 26.8.0.0.alpha0. Exact historical checks have their own dependencies as stated above.

With the figure dependencies available, run `python3 code/generate_figures.py` to regenerate the supplied SVG, PNG, and JSON assets. With python-docx and Pandoc available, run `python3 code/build_documents.py` to rebuild both Word editions. These programs write generated publication outputs and create intermediate working files; use a working copy if you want the released manifest to remain unchanged.

The Word files contain native Office Math objects. The builder normalizes delimiter-property order, keeps displayed equations with their labels, and prints table entries as labeled records to avoid an observed table-import defect in the PDF converter. The canonical web sources retain their comparison tables. To export PDFs locally, run LibreOffice in headless conversion mode, for example:

```bash
soffice --headless --convert-to pdf --outdir documents documents/BassPlus_Mathematics_of_Sound_Article.docx
soffice --headless --convert-to pdf --outdir documents documents/BassPlus_Mathematics_of_Sound_Research_Edition.docx
```

Rendering is a separate check from mathematical verification. Inspect the exported pages for complete formulas, correct interval endpoints, visible ceilings and norms, readable tables, intact figure captions, and stable pagination. Different converter versions or fonts may change layout. The released PDFs were inspected visually; the corresponding handoff receipts identify the reviewed files by SHA-256.