[GoGoKo699]

Scope and consistency

Complete the pre-release audit under the established reader-facing and learning conventions. Preserve the core scientific results, per-contact/free-internal-control model, reference-inclusive accuracy definition, exact helper marginal versus approximate joint return distinction, and the limitations of the finite-strength compiler.

Align older descriptions in the canonical bandwidth document with results already proved elsewhere: the all-helper-count approximate guarantee, synchronized exact contact lists, and the existing mixed-helper theorem. Preserve the learner-independent 30-milestone map (14 background, 16 narrative), Watrous as the sole educational anchor, the purpose/contact paragraph, and the original MIT license. No manuscript, release tag, or additional scientific model is introduced.

Actual hosting defects and fixes

Actual GitHub inspection exposed Markdown-sensitive mathematical notation and a rejected upright-operator macro. Protect inline math and use fenced display math, supported commands, and explicitly braced starred subscripts.

A screenshot review then found a separate silent failure: numbered equations stacked vertically even though the original hosted checker reported that all math was ready. Legacy \\tag{n} produced mlabeledtr rows in native MathML. Replace all 62 equation labels in five scientific pages by ordinary \\qquad\\text{(n)} content. Every number is preserved. Reversing this substitution reproduces the preceding files byte for byte, so this step changes no mathematics.

Strengthen the hosted checker to reject unsupported native MathML rows and invalid table-cell parents, record equation geometry, and retain exact inspected public source files with SHA-256 hashes alongside screenshots. Running the stronger checker on the unfixed pages correctly failed on the five affected documents; the corrected pages pass. Source checks also reject the unsafe numbering form. Twelve regression tests include ready-but-invalid native MathML and deliberately malformed source/results.

Completed verification on d886745

• All ten scientific suites were rerun locally and passed. The eleven scientific check sources, numerical results, verifier, and dependency versions are unchanged. The checks and results Git subtree hashes match the pre-audit baseline.
• Repository navigation, license, bibliography, source/result provenance, reading-page structure, milestone dependencies, and twelve structural regression tests pass in CI. Scientific verification also passes in CI: run 38911041713.
• Actual public GitHub Chromium inspection passes for all thirteen README/learning/science pages at 1180px and 390px. All 525 mathematical expressions render at each width, with no detected math errors, unfinished expressions, unprocessed delimiters, unsupported native rows, inconsistent table columns, or page-level overflow: run 38911041521.
• The downloaded hosted artifact digest matches GitHub's recorded SHA-256. All thirteen inspected public source hashes match the corrected files. Representative actual-host screenshots were visually reviewed for the README, anchor guide, worked bridges, mixed-helper theorem (desktop/mobile), entropy inequalities, and finite-certificate page. Long mobile formulas can scroll inside their own containers.
• Local native-MathML reproduction and compilation corroborate the label fix; local previews are not substituted for the actual hosted result.

The audited final tree is 1092e86232f947c03166548d3f1e385dfcb64344. The scientific-check subtree remains aa82a2dd69e914d54bf6f82bc94f95cc08b8a81b and the recorded-results subtree remains 33a4e53748f0f757143f624c4329ad9e3d7894af.

These are internal consistency, reproducibility, and hosting checks, not independent theorem review, exhaustive priority verification, or hardware validation. This PR prepares the repository for release; it does not publish a GitHub release or tag.